Thesis DieterPauwels vFinal

8/4/2019 Thesis DieterPauwels vFinal

http://slidepdf.com/reader/full/thesis-dieterpauwels-vfinal 1/221

Nuclear structure

around Z = 28 and N = 40

investigated by the β decay

of Fe, Co and Ni isotopes

Promotoren: Proefschrift ingediend totProf. Dr. M. Huyse het behalen van de graad vanProf. Dr. P. Van Duppen doctor in de wetenschappen

door

Dieter Pauwels

Leuven 2009



c 2009 Faculteit Wetenschappen, Geel Huis, Kasteelpark Arenberg 11, 3001Heverlee (Leuven)

Alle rechten voorbehouden. Niets uit deze uitgave mag worden vermenigvuldigd

en/of openbaar gemaakt worden door middel van druk, fotokopie, microfilm,

elektronisch of op welke andere wijze ook zonder voorafgaandelijke schriftelijke

toestemming van de uitgever.

All rights reserved. No part of the publication may be reproduced in any

form by print, photoprint, microfilm, electronic or any other means without

written permission from the publisher.

ISBN 978-90-8649-232-9

D/2009/10.705/10



If you have a target in your life, a real target, doesn’t matter if you arevery poor or rich people, if you work hard and believe in God, you can

get the success, success in the life.Ayrton Senna





Dankwoord

Omdat het geleverde thesiswerk enkel tot stand kon komen met de hulpvan vele mensen, wil ik hen via deze weg mijn oprechte dank betuigen.

Eerst en vooral verdienen mijn promotoren, Mark en Piet, veel woor-den van lof en dank. Bedankt om mij een kans te geven in de boeiendewereld van kernstructuuronderzoek. Bovendien hebben jullie mij niet alleen deskundig weten te sturen met jullie verworven expertise, maar

jullie hebben mij vooral ook weten te inspireren met jullie niet-aflatendenieuwsgierigheid en gedrevenheid.

I would like to thank the members of the jury, Prof. Dr. G. Neyens,Prof. Dr. M. Van Bael, Prof. Dr. S. Lenzi, Prof. Dr. N. Jachowicz, and Prof. Dr. A. Andreyev, for their careful reading of the first manuscript and the discussion during the first defense.

The performed experiments at LISOL in Louvain-La-Neuve would not have been possible without the professional work of Johnny Gen-tens, Yuri Kudryavtsev, Paul Van den Bergh, and the CRC engineers,Guido Ryckewaert and Marc Loiselet. There are several other peoplethat deserve special attention, because of their significant contribution tothe successful runs we had over the last years at LISOL: Jean-Charles

Thomas, Marius Facina, Oleg Ivanov, Maria Sawicka, Thomas Cocolios,and Tetsu Sonoda. I would also like to thank other former and present members of the ”Kernspectroscopie” group for the nice working atmo-sphere and for all the enlightening discussions: Beyhan, Hilde, Iain,

i



ii

Irina, Ivan, Jan (Ponsaers and Diriken), Jarno, Jeroen, Nick, Nikolas,

Riccardo, and Shelly.

In the spirit of ”Mens sana in corpore sano”, we had several sportiveinitiatives at IKS. With our talented IKS football team, we have played some unforgettable matches. Jeroen, thanks for taking care of all thepractical issues there. Of course, I also enjoyed enormously the IKS runs and the ”Bike & Run” editions, as well as the intense ping-pong battles.

Sally, Martine, Isabel, Josee en Katia, ik prijs me gelukkig dat jullieer waren om mij bij te staan in de bij wijlen administratieve jungle.

Willy, Bart en Eddy, bedankt voor de mechanische ondersteuning; Luk,Bert, Joris en Pascal, bedankt voor de digitale bijstand; Nancy, bedankt voor al je kuiswerk en het goede humeur dat je altijd meebracht.

Mijn ultieme dankbetuigingen gaan uit naar de ganse familie, in het bijzonder naar de (groot)ouders. Jullie vormen de basis van de persoon die ik geworden ben. Het geeft een veilig gevoel om te weten dat ik altijd op jullie kan rekenen.

En Kel, bedankt voor je onvoorwaardelijke liefde en steun.

Bedankt allemaal!

Dieter Leuven, februari 2009



Preface

This thesis is devoted to an experimental nuclear-structure study in theZ = 28 and N = 40 region of the nuclear chart. New insights are

delivered based on experimental results obtained in a β -decay study of the 65,67,71Co, 65,67Fe and 71Ni isotopes produced at the Leuven-Isotope-Separator-On-Line (LISOL) facility of the Centre de Recherches du Cy-clotron (CRC) at Louvain-La-Neuve, Belgium. The achievements of thework performed during 2004−2008 have been concentrated in four scien-tific papers published in (or submitted to) international peer-reviewed

journals, which form the skeleton of the thesis:

1. Decay correlations in the seconds range with laser-ionized,

mass-separated beams,D. Pauwels, O. Ivanov, J. Buscher, T. E. Cocolios, J. Gentens,

M. Huyse, A. Korgul, Yu. Kudryavtsev, R. Raabe, M. Sawicka,I. Stefanescu, J. Van de Walle, P. Van den Bergh, P. Van Duppen,Nuclear Instruments and Methods in Physics Research Section B

266 (2008) 4600.

2. Shape isomerism at N = 40: Discovery of a proton in-

truder state in 67Co,D. Pauwels, O. Ivanov, N. Bree, J. Buscher, T. E. Cocolios, J. Gen-tens, M. Huyse, A. Korgul, Yu. Kudryavtsev, R. Raabe, M. Saw-icka, I. Stefanescu, J. Van de Walle, P. Van den Bergh, P. Van Dup-pen, W. B. WaltersPhysical Review C 78 (2008) 041307(R)

3. Structure of 65,67Co studied through the β decay of 65,67Fe

and a deep-inelastic reaction,D. Pauwels, O. Ivanov, N. Bree, J. Buscher, T. E. Cocolios, M.

iii



iv

Huyse, A. Korgul, Yu. Kudryavtsev, R. Raabe, M. Sawicka, I. Ste-

fanescu, J. Van de Walle, P. Van Duppen, W. B. Walters, R.Broda, M.P. Carpenter, R.V.F. Janssens, B. Fornal, A.A. Hecht,N. Hoteling, A. Wohr, W. Krolas, T. Lauritsen, T. Pawlat, D.Seweryniak, J.R. Stone, X. Wang, J. Wrzesinski, S. ZhuSubmitted to Physical Review C

4. Evidence for a 1/2− β -decaying isomer in 71Ni,I. Stefanescu, D. Pauwels, N. Bree, T. E. Cocolios, J. Diriken,S. Franchoo, M. Huyse, O. Ivanov, Yu. Kudryavtsev, N. Patronis,J. Van de Walle, P. Van Duppen, W. B. Walters,Submitted to Physical Review C

To introduce the papers and motivate the performed investigations,the region around Z = 28 and N = 40 is first discussed in detail. TheLISOL facility and the βγ detection setup are briefly described in chap-ter 3. In chapter 4 an overview is given of the obtained results. Theavailability of very pure 65,67Fe and 65,67Co ion beams allowed the devel-opment of a novel correlation technique, as described in the first paper.More details are given in appendix A. The construction of the 65,67Feand 65,67Co β -decay schemes are discussed. The correlation techniqueis applied to disentangle the 67Fe→67Co→67Ni β -decay chain and fullycharacterizes a long-lived isomeric state at 492 keV in 67Co. In addition,

results are presented from a re-investigation of

71

Co and

71

Ni β -decaydata acquired some time ago at LISOL. In chapter 5, the decay schemesand their implications for the interpretation of the nuclear structure inthe neutron-rich nickel region is discussed. Conclusions and an outlookare given in chapter 6.



Contents

Dankwoord i

Preface iii

1 Introduction 1

1.1 The strong interaction bounding nucleons . . . . . . . . . 2

1.2 The nuclear shell model . . . . . . . . . . . . . . . . . . . 2

1.3 Shell model calculations . . . . . . . . . . . . . . . . . . . 3

1.4 Evolution of shell gaps and the development of deformation 5

1.5 The Z = 28 and N = 40 (sub)shell gaps . . . . . . . . . . 7

2 Features of nuclear structure in the region around Z = 28and N = 40 11

2.1 The nickel isotopes between N = 28 and N = 50: theproperties of 68Ni . . . . . . . . . . . . . . . . . . . . . . . 11

2.1.1 56Ni at N = 28 . . . . . . . . . . . . . . . . . . . . 11

2.1.2 78Ni at N = 50 . . . . . . . . . . . . . . . . . . . . 12

2.1.3 68Ni at a stabilizing N = 40 gap . . . . . . . . . . 12

2.1.4 Systematics of 0+ states between N = 28 and N =40 . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.5 Enhanced collectivity beyond N = 40 . . . . . . . 16

2.2 68Ni-coupled structures in the adjacent nuclei . . . . . . . 17

2.2.1 67Ni . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.267

Co . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2.3 69Ni . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2.4 68Cu . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.5 69Cu . . . . . . . . . . . . . . . . . . . . . . . . . . 22

v



vi

2.2.6 70Cu . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.2.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . 252.3 The odd-mass cobalt isotopes with A ≤ 63 . . . . . . . . . 26

2.3.1 57Co . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.2 59Co . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.3 61Co . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.3.4 63Co . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.3.5 65Co . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3.6 67Co . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . 35

2.4 Onset of deformation below Z = 28 in the N = 40 region 36

2.5 The relevance of studying the 65,67Fe β decay . . . . . . . 42

3 Experimental setup 45

4 Results 49

4.1 Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2 β decay of 65,67Fe and 65,67Co . . . . . . . . . . . . . . . . 51

4.2.1 β decay of 67Fe . . . . . . . . . . . . . . . . . . . . 51

4.2.2 β decay of 65,67Fe and 65Co . . . . . . . . . . . . . 52

4.2.3 β decay of 67Co . . . . . . . . . . . . . . . . . . . . 54

4.3 β decay of 71Ni and 71Co . . . . . . . . . . . . . . . . . . 58

5 Discussion 615.1 The odd-mass cobalt isotopes with A ≤ 67 . . . . . . . . . 61

5.2 Intruder properties of 68Ni compared to 90Zr . . . . . . . 64

5.2.1 Shell gaps and intruder states at Z = 28, N = 40and Z = 40, N = 50 . . . . . . . . . . . . . . . . . 64

5.2.2 Monopole ρ2(E0) and quadrupole B(E2) transi-tion strengths . . . . . . . . . . . . . . . . . . . . . 69

5.2.3 The Z = 28 gap towards N = 50 . . . . . . . . . . 70

5.2.4 The N = 40 gap towards Z = 20 . . . . . . . . . . 71

5.3 Discovery of a collective (1/2−) state in 71Cu . . . . . . . 71

6 Conclusions and outlook 736.1 A new correlation technique . . . . . . . . . . . . . . . . . 73

6.2 Discovery of a low-energy proton intruder in 67Co and β decay of 67Co . . . . . . . . . . . . . . . . . . . . . . . . . 74



vii

6.3 Intruder properties of 68Ni . . . . . . . . . . . . . . . . . . 75

6.4 The β decay of 65,67Fe . . . . . . . . . . . . . . . . . . . . 756.5 The β decay of the 71Ni isomer . . . . . . . . . . . . . . . 766.6 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Paper I: Decay correlations in the seconds range with laser-

ionized, mass-separated beams 79

Paper II: Shape isomerism at N = 40: Discovery of a proton

intruder state in 67Co 95

Paper III: Structure of 65,67Co studied through the β decay

of 65,67Fe and a deep-inelastic reaction 109

Paper IV: Evidence for a 1/2− β -decaying isomer in 71Ni 149

A Correlations 167

A.1 Construction of correlations: technical information . . . . 167A.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 172A.3 Monte-Carlo simulations . . . . . . . . . . . . . . . . . . . 177A.4 Experimental conditions at LISOL . . . . . . . . . . . . . 181

Nederlandstalige samenvatting 189

Bibliography 199

Publication list 207





Chapter 1

Introduction

Atomic nuclei are composed of two sorts of nucleons, positively chargedprotons and neutral neutrons. The number of protons in a nucleuscharacterizes each of the elements in the Periodic Table – from hydrogenwith one proton to the superheavies up to 118 protons. The number of neutrons for each element, however, can vary. Nuclei with the samenumber of protons, but with a different number of neutrons are calledisotopes, each having a different mass.

The nucleons interact with each other in a complicated way and

can bind in nuclei in many different combinations. As a consequence,nuclei possess a rich and fascinating structural diversity, which providesa powerful probe of the fundamental forces in nature1. By studyingtheir structure, researchers hope to gain a better understanding of theforces that govern the evolution and behavior of matter. Because theelements in our Universe are made in stars by various nuclear reactions,understanding nuclear structure is at the basis of understanding whythe Universe looks the way it does today. Moreover, these processesare thought to involve exotic nuclei with unusual ratios of protons andneutrons that are difficult to produce at earth and are yet to be studied.

1Four fundamental interactions exist in nature, namely the strong, electromag-netic, weak and gravitational interaction in order of strength inside the nuclearmedium.

1



2 Introduction

1.1 The strong interaction bounding nucleons

The most important interaction keeping the nucleons together is thestrong interaction, which can overcome the strong electromagnetic re-pulsion between the positively charged protons. The strong interactionis described in the quantum chromodynamics (QCD) theory, but at thelow and intermediate energies that are appropriate for nucleon interac-tions the theory becomes strongly non-perturbative and, thus, difficultto use. Scattering data between free nucleons have parameterized se-veral phenomenological nucleon-nucleon one-boson-exchange (OBE) po-tentials, but they do not unambiguously define the interaction. This is afundamental difference with, e.g., the precisely known 1

r2dependence of

the electromagnetic interaction. Nonetheless, so-called ”ab-initio” calcu-lations, which make use of realistic nucleon-nucleon (NN ) potentials oreven three-nucleon (NNN ) potentials derived from the scattering data,are able to reproduce successfully the level structure and properties of nuclei up to mass A = 10, see Ref. [1] and references therein. Calcula-tions for heavier nuclear systems are hindered by the current computingcapacities and one is thus forced to rely on nuclear models to describethose.

1.2 The nuclear shell model

From the observation that nuclei with a certain number of nucleonsexhibit extra stability, i.e., at the so-called magic numbers for protons(Z ) and neutrons (N ) such as 2, 8, 20, 28, 50, 82 and 126, the shell model[2–4] has been introduced in analogy with the shell model in atoms.

The nuclear shell model describes the nucleus as a sequence of shells,which can be occupied by nucleons. A nucleus with A nucleons has aHamiltonian given by

H =Ai=1

T i +Ai=1

A j>i

V (i, j) (1.1)

where T i is the kinetic energy of the ith nucleon and V (i, j) is the strongnucleon-nucleon interaction between nucleons i and j. In the nuclearshell model, the nucleus is described in terms of a spherically symmetric



Introduction 3

mean-field potential that is generated by all nucleons and in which in-

dividual nucleons move in unperturbed states almost independently of one another. The Hamiltonian is thus rewritten as

H =Ai=1

[T i + U (ri)]+

Ai=1

A j>i

V (i, j)−Ai=1

U (ri)

= H 0+H res (1.2)

where U (ri) is the spherically symmetric mean-field potential. The firstterm, H 0, describes the motion of A nucleons, independent of each otherin the central potential U (r). The second term, H res, is the residualinteraction, which accounts for all other nuclear interactions. The mean-field potential has to be chosen such that H res can be treated as aperturbation. One of the early successes of the shell model was thereproduction of the magic numbers in an analytically solvable way byapproximating the mean-field nuclear potential by a harmonic oscillator,added with an l2-term, where l denotes the angular momentum of theorbit, and a spin-orbit term [2]. The resulting sequence of quantizedenergy levels, called orbitals, are shown in Fig. 1.1 as a function of energy. Each orbital is characterized by three quantum numbers: theshell number N , the angular momentum l (l = 0, 1, 2, 3 for s, p, d, f,. . . ), and spin j = l ± 1/2. One orbital can contain at maximum 2 j + 1nucleons of the same type.

As can be seen, between some orbitals a large energy gap exists. Agroup of orbitals in between two subsequent large energy gaps form ashell. Therefore, when a nucleus contains both as many neutrons andprotons to fill completely a shell, it will be extra stable and it is calleda double-magic nucleus.

1.3 Shell model calculations

Nowadays, shell model calculations have become a suitable tool to de-scribe experimentally-deduced spectroscopic observables. In this way,detailed spectroscopic information can be obtained. The two-body in-

teraction between nucleons depends on the specific orbitals that areoccupied. Since the interactions between all nucleons cannot be treatedsimultaneously, shell model calculations reduce the number of interac-tions by taking advantage of the presence of the nearest inert core, which



4 Introduction

1i

3p

2f 1h

1g

2p

1p

3p1/2

2f 5/23p3/2

1h11/2

2d3/2

3s1/21g7/2

2d5/2

1g9/2

2p1/2

1f 5/22p3/2

1f

1d3/2

2s1/21d5/2

1p1/2

1p3/2

1s1/2

HarmonicOscillator

potential

Figure 1.1: Shell model states as a function of energy as deducedfrom a harmonic oscillator potential at the left, with addition of anl2-term in the middle and addition of a spin-orbit term at the right,as taken from Ref. [5]. The orbitals at the right are specified by the

shell number N , the angular momentum l (l = 0, 1, 2, 3 for s, p, d,f, ...), and spin j = l ± 1/2. One orbital can contain at maximum2 j + 1 nucleons of the same type. Note the large energy gaps at 2,8, 20, 28, 50 and 82. This thesis work concentrates on N = 40, aharmonic oscillator gap, and Z = 28, the first major gap created bythe spin-orbit splitting.



Introduction 5

is typically a double-magic nucleus. In this way, one merely has to calcu-

late the residual two-body interactions between the remaining particles(and/or holes2) in the so-called valence space outside the inert core,which reduces the complexity of the calculation dramatically. In fact,the core is never completely inert and does still interact with the va-lence particles (holes). In addition, the nucleons cannot scatter freelyto states that are occupied by the core. This has to be incorporatedthrough the use of effective two-body interactions, which are often de-duced from G-matrix calculations based on the phenomenological freenucleon-nucleon interactions [6]. In general, these effective interactionsneed adjustments, which are mass-region dependent and which can onlybe obtained from experimental data. Comparison of the shell model cal-

culation with the experimental observables is an important test to verifythe used two-body interactions and the influence of the chosen valencespace.

1.4 Evolution of shell gaps and the developmentof deformation

The interactions between nucleons depend on the orbitals they occupyand thus hitherto uninvestigated nuclei can contain important experi-mental information to adjust the effective interactions in the respective

nuclear medium. The knowledge of the appropriate effective interactionsis crucial as they are the key elements to describe the evolution of shellclosures when entering regions with N/Z ratios that are different fromstable nuclei. The shell closures established from the harmonic oscilla-tor potential, added with an l2-term and a spin-orbit term, are indeedconsistent with observations for nuclei near the valley of stability, but itis not clear a priori how they evolve to more exotic nuclei.

As the number of valence nucleons increases, the residual proton-neutron interaction energy builds up. In some situations, the gain inbinding energy of the proton-neutron interactions can be sufficientlylarge that the nucleus will deviate from its spherical shape and favors a

deformed ground state. Because the residual proton-neutron interaction2The number of holes are equal to the maximum occupation number of the orbital

2 j + 1 minus the number of particles occupying the orbital and are fully equivalentto particles in the shell model [4].



6 Introduction

F i g u r

e

1 . 2 : N e u t r o n

( l e f t ) a n

d p r o t o n

( r i g h t ) N i l s s o n o r b

i t a l s a s a

f u n c t

i o n o

f t h e q u a

d r u p o

l e d e

f o r m a t i o n

p a r a m

e t e r ε 2

c a

l c u

l a t e d f r o m

a F o

l d e

d - Y

u k a w a p o t e n t i a l a n

d p r e s e n t e d i n

R e

f . [ 7 ] . T h e

f u l l l i n e s c o r r e s p o n d

t o p o s

i t i v e - p a r i t y o r b

i t a l s , t h e

d a s h e

d l i n e s t o t h o s e w

i t h n e g a t i v e p a r i t y .

T h e

N i l s s o n q u a n t u m

n u m

b e r s a r e

g i v e n

a n

d t h e m a g

i c n u m

b e r s a r e

i n d i c a t e d i n c

i r c l e s .

T h e p a r a m e t e r s λ p a

n d a p

( o r λ n

a n

d a n

) d e s c r i b e t h e

d e p t h

a n

d t h e s h a p e

d i ff u s e n e s s o

f t h e F

o l d e

d - Y u

k a w a p o t e n t i a l .



Introduction 7

energy is normally largest when the number of active valence nucleons

is maximal, deformation occurs typically at mid-shell [4]. In case of de-formation, the interaction of a valence nucleon with the underlying coredepends on the relative orientation of the nucleon’s orbit with respectto the time-averaged shape of the deformed core. Consequently, the de-generacy of the orbitals in the spherical case is partly lifted accordingto the projection of the spin j on the symmetry axis of the deformednucleus, in a way that is illustrated in Fig. 1.2. Each Nilsson orbital canbe occupied by at maximum 2 nucleons.

An example illustrating that shell closures evolve is observed in theneutron-rich N = 20 nuclei 30Ne, 31Na, 31Mg and 32Mg [8–11]. It was es-tablished from experiment that their ground states are deformed, rather

than spherical, which evidenced the vanishing of the N = 20 shell clo-sure. Theory pointed out that the deformation of their ground statesresulted from a weakening of the shell gap [12], which becomes smallerthan half of the energy gained by strong pairing and proton-neutroncorrelations [13] with configurations across the N = 20 shell gap. Be-cause the shell model space to describe the ground states lies outsidethe normal sd valence space, they are referred to as intruder states andaccordingly the region was called the ”Island of inversion” [14].

1.5 The Z = 28 and N = 40 (sub)shell gaps

In this thesis, the region around Z = 28 and N = 40 is investigated.The N = 40 subshell gap is a harmonic oscillator gap and Z = 28 isthe first major gap created by the spin-orbit splitting. More specifically,this work focusses on the low-energy structure of 65,67Co through a β -decay study of 65,67Fe. In Fig. 1.3 the 65,67Co nuclei are situated withrespect to other nuclei on the basis of their proton number Z and neutronnumber N in the chart of nuclides. As can be noticed, cobalt isotopesare only one proton hole away from the Z = 28 proton shell closure.Moreover, 67Co is only one proton hole separated from 68Ni, which liesat the crossing of Z = 28 and N = 40. In 68Ni, protons and neutrons fill

the orbitals, as schematically presented in Fig. 1.4. As will be describedin section 2.1, 68Ni exhibits properties featured by magic nuclei [15, 16],from which a subshell gap was proposed at N = 40. As a result, theregion around 68Ni has drawn a lot of attention from nuclear-structure



8 Introduction

4 8 C a

4 9 C a 5 0 C a 5 1 C a 5 2 C a 5 3 C a 5 4 C a 5 5 C a 5 6 C a

4 9 S c

5 0 S c

5 1 S c

5 2 S c

5 3 S c

5 4 S c

5 5 S c

5 6 S c

5 7 S c

5 8 S c

5 0 T

i 5 1 T i 5 2 T i 5 3 T i 5 4 T i 5 5 T i 5 6 T i 5 7 T i 5 8 T i 5 9 T i 6 0 T i 6 1 T i

5 1 V

5 2 V

5 3 V

5 4 V

5 5 V

5 6 V

5 7 V

5 8 V

5 9 V

6 0 V

6 1 V

6 2 V

6 3 V

6 4 V

5 2 C

r 5 3 C r 5 4 C r 5 5 C r 5 6 C r 5 7 C r 5 8 C r 5 9 C r 6 0 C r 6 1 C r 6 2 C r 6 3 C r 6 4 C r 6 5 C r 6 6 C r 6 7 C

r

5 3 M

n 5 4 M n 5 5 M n 5 6 M n 5 7 M n 5 8 M n 5 9 M n 6 0 M n 6

1 M n 6 2 M n 6 3 M n 6 4 M n 6 5 M n 6 6 M n 6 7 M n 6 8 M

n 6 9 M n

5 5 F e

5 4 F e

5 6 F e

5 7 F e

5 8 F e

5 9 F e

6 0 F e 6 1 F e

6 2 F e 6 3 F e

6 4 F e

6 5 F e

6 6 F e

6 7 F e 6 8 F e

6 9 F

e

7 0 F e

7 1 F e

7 2 F e

5 5 C o 5 6 C o 5 7 C o 5 8 C o 5 9 C o 6 0 C o 6 1 C o 6 2 C o 6 3 C o 6 4 C o 6 5 C o 6 6 C o 6 7 C o 6 8 C o 6 9 C o

7 0 C

o 7 1 C o

7 2 C o

7 3 C o

7 4 C o

7 5 C o

5 6 N

i 5 7 N i

5 9 N i

5 8 N i

6 0 N i 6 1 N i 6 2 N i

6 4 N i

6 3 N i

6 5 N i 6 6 N i 6 7 N i 6 8 N i 6 9 N i 7 0 N i 7 1 N

i 7 2 N i 7 3 N i 7 4 N i 7 5 N i 7 6 N i 7 7 N i 7 8 N i

5 7 C u 5 8 C u 5 9 C u 6 0 C u 6 1 C u 6 2 C u 6 3 C u

6 5 C u

6 4 C u

6 6 C u 6 7 C u 6 8 C u 6 9 C u

7 0 C u

7 1 C u

7 2 C

u 7 3 C u

7 4 C u

7 5 C u

7 6 C u

7 7 C u

7 8 C u

7 9 C u

8 0 C u

5 8 Z n 5 9 Z n 6 0 Z n 6 1 Z n 6 2 Z n 6 3 Z n

6 5 Z n

6 4 Z n

6 6 Z n 6 7 Z n 6 8 Z n

7 0 Z n

6 9 Z n

7 1 Z n

7 2 Z n

7 3 Z

n 7 4 Z n

7 5 Z n

7 6 Z n

7 7 Z n

7 8 Z n

7 9 Z n 8 0 Z n

8 1 Z n

N

Z 2 0

2 8

2 8

4 0

5 0

F i g u r

e

1 . 3 : C h a r t o

f t h e n u c

l i d e s z o o m

e d i n o n t h e c a

l c i u m

u p t o t h e z i n c

i s o t o p e s w

i t h n e u t r o n n u m

b e r s

r a n g i n

g f r o m

N

=

2 8 t o N

=

5 1

. T h e c

l a s s i c a

l s h e

l l c

l o s u r e s a r e

i n d i c a t e d w

i t h f u l l l i n e s a t Z =

2 0 ,

2 8 a n d

N

= 2

8 ,

5 0

. T h e p r o p o s e

d s u

b s h e

l l c

l o s u

r e a t N

=

4 0 i s i n d i c a t e d w

i t h d o t t e d l i n e s .



Introduction 9

Ni68

νπ

28

40

7/2f

3/2

p

5/2f

1/2

p

9/2

g

28

40

7/2f

3/2

p

5/2f

1/2

p

9/2

g

Figure 1.4: Schematical representation of the occupation of proton(π) and neutron (ν ) orbitals in the 68Ni ground state. The πf 7/2proton shell between Z = 20 and Z = 28 and the νpf 5/2 neutron shellbetween N = 28 and N = 40 is completely filled.

studies for several reasons, but so far the investigations were focussed atthe Z ≥ 28 nuclei.

• The N = 40 gap originates from the bare harmonic oscillator (HO)potential. An interesting feature of HO shells is the change inparity across a gap. Therefore, no parity-preserving excitationsare expected across N = 40, like e.g. quadrupole excitations.

• Strong proton-neutron residual interactions are present betweenthe neutrons in the νf 5/2 and νg9/2 orbitals and the protons in theπf 7/2 and πf 5/2 orbitals, which are not precisely known. Becausethe nuclear structure is sensitive to small differences in the inter-actions, it is important to deduce those interactions as accurate aspossible from experiment. The νg9/2 orbital has a high spin and

a unique parity in the major lower-spin negative-parity pf shellsbetween N = 20 and 50 facilitating the formation of isomerism.Therefore, corresponding configurations are easier to identify andthey tend to have a pure character. This is thus an ideal test-



10 Introduction

ing ground for the effective nucleon-nucleon interactions used in

large-scale shell model calculations. The region around Z = 28and N = 40 is separated from the 78Ni nucleus by 10 neutrons inthe νg9/2 orbital. A more precise knowledge of the effective in-teractions involved, allow theoretical models to make more precisepredictions toward 78Ni.

• At the prolate side, the νg9/2 orbital splits up in five Nilssonorbitals, see Fig. 1.2. The 1/2+[440] and 3/2+[431] are sharplydownsloping and might lead to deformation. Moreover, caused bythe monopole interaction, neutron occupancy in the νg9/2 orbitalinduces a lowering of the shell gap between the πf 7/2 and the πf 5/2

orbital enhancing core polarization, i.e., particle-hole excitationsacross Z = 28. For these reasons, the νg9/2 orbital is called thedeformation-driving orbital in this region.

It may become clear that, despite the apparent double-magic prop-erties of 68Ni, the influence of the N = 40 subshell gap could disappeardue to the above-mentioned mechanisms. In the following chapter, anoverview is given of the current experimental information and theoreti-cal understanding to motivate the study of the 65,67Co nuclear structure.The 65,67Co nuclei will be approached from different perspectives in theZ = 28 and N = 40 region. First, they can be viewed as nuclei with

one proton less than their respective nickel isotone, in the specific caseof 67Co this is the Z = 28, N = 40 68Ni nucleus. It will be discussed towhich extent adjacent nickel and copper isotopes have been interpretedbased on a particle and/or a hole coupled to an inert 68Ni core. Sec-ond, they can also be viewed as the prolongation of the lighter odd-masscobalt isotope chain with mass A ≤ 63. Third, they can be approachedfrom the region further below Z = 28, where an onset of deformation issuggested near N = 40.



Chapter 2

Features of nuclear

structure in the regionaround Z = 28 and N = 40

2.1 The nickel isotopes between N = 28 and N =50: the properties of 68Ni

The major proton shell up to Z = 28 is completely filled in the nickelisotopes, which results in a predominant spherical structure. The nickelisotopes span a wide region, which is experimentally known from N = 20to N = 50 including the (semi-)magic numbers 20, 28, 40, and 50. Below,properties of the N = 28 56Ni, the N = 50 78Ni and subsequently theN = 40 68Ni nuclei will be discussed.

2.1.1 56Ni at N = 28

Fig. 2.1 shows the systematics of the observed first-excited 2+1 ener-gies (a), B(E 2 : 0+ → 2+1 ) transition probabilities1 (b), and δ2n two-

1Transition probabilities from an initial state I i to a final state I f with anelectric/magnetic transition multipolarity E

M λ is defined as B(EM λ : I i → I f ) =1

2Ii+1|Ψf ||M (EM λ)||Ψi|

2, where Ψf (Ψi) denotes the total wave function of the final

(initial) state andM (EM λ) denotes the electric/magnetic multipole operator. See, e.g.,Ref. [17] for more details.

11



12 Features of nuclear structure in the region around Z = 28 and N = 40

neutron separation energy differences2 (c) in the nickel isotopes between

N = 28 and N = 50. The 56Ni isotope is situated in the neutron-deficient side and has been already intensively investigated. As can beseen in Fig. 2.1(a) and (c), the first excited 2+1 energy is about a factorof 2 larger than in the neighboring even-mass nickel isotopes and theneutron shell gap δ2n reaches a pronounced maximum at an energy of 8.37(5) MeV, which are both consistent with a double-magic behavior.On the other hand, the B(E 2) value is within uncertainties the samecompared to those of 54Ni and 58Ni [18], see Fig. 2.1(b). This is in linewith large-scale shell model calculations by the quantum Monte Carlodiagonalization method in the pf valence space, which shows that theprobability of a doubly-closed shell configuration of 56Ni is only 49%

[19]. The observed behavior is attributed to the extended possibilitiesfor creating 2+ excitations across N, Z = 28 in the f p shell by both pro-tons and neutrons [18] and to a consequence of a strong proton-neutroninteraction characterizing the N = Z nuclei [19].

2.1.2 78Ni at N = 50

Another nickel isotope with a magic neutron number, 78Ni, is situatedfar off in the neutron-rich side, where production cross sections are ex-tremely low and for this reason hard to study. Its existence has beendemonstrated by the identification of three 78Ni events [26]. More re-

cently, a half-life of 110+100−60 ms has been determined [27], but nothing isknown about the excited level structure. Because of its exotic proton-to-

neutron ratio Z/N it is not a priori obvious if 78Ni exhibits double-magicproperties. Strong residual nucleon-nucleon interactions, which are notprecisely known, exist between the neutrons in the νg9/2 orbital and theprotons in the πf 7/2 and πf 5/2 orbitals, which may alter the Z = 28and/or N = 50 shell gap drastically.

2.1.3 68Ni at a stabilizing N = 40 gap

Assuming a closely packed number of orbitals in between N = 28 andN = 50, the seniority scheme would predict a first excited 2+

1

energy thatremains constant, a parabola-like B(E 2) systematics with its maximumat mid-shell and two-neutron separation energies S 2n with a constant

2δ2n = S 2n(Z = 28, N ) − S 2n(Z = 28, N + 2)



The nickel isotopes 13

E n e r g y ( k e V )

500

1000

1500

2000

2500

3000 ) Ni+

1E(2a)

Ni56

Ni68

) ( W . u . )

1 + 2 → +

B ( E 2 : 0

2

4

6

8

10

12

14 B(E2) Nib)

Neutron number (N)26 28 30 32 34 36 38 40 42 44 46 48 50

E n e r g y ( M e V

)

012

34567

89 Ni2nδc)

Figure 2.1: Systematics of the observed first excited 2+1 energies

(a), B(E 2 : 0+ → 2+1 ) transition probabilities (b), and two-neutron

separation energy differences δ2n (c) in the nickel isotopes betweenN = 28 and N = 50. Data are taken from Refs. [20–25]




slope as a function of neutron number. However, Fig. 2.1 shows that the

2+1 energy peaks at N = 40 (E = 2033 keV) [16] and the B(E 2) valuereaches a distinct minimum at N = 40 (B(E 2) = 3.2(7) W.u.) [22, 28],which is even 3 times smaller than the 56Ni value. These propertiesappear as strong experimental indications that 68Ni is a double-magicnucleus. Moreover, the first fingerprint of magicity in 68Ni was thediscovery that its first excited state at 1.77 MeV is a 0+ state [15].Other examples of nuclei where the 0+2 level is observed as first excitedstate and, thus, at a lower excitation energy than the first excited 2+1level are 90Zr, the valence mirror at N = 50, and the well-establisheddouble-magic nuclei 16O and 40Ca. Nevertheless, mass measurements,known as the most sensitive and direct probe for (sub)shell closures, do

not reveal a clear neutron shell gap at N = 40 [25, 29]. The δ2n-valuesare known as a good indicator of shell strength and show a distinct peakat N = 28, but not at N = 40, see Fig. 2.1(c).

This apparent paradox is explained based on the uniqueness of thepositive g9/2 parity between the pf orbitals with negative parity [22, 30,31]. In order to create a 2+ state, at least two neutron particles haveto be uncoupled and excited into the g9/2 orbital. Exciting only oneneutron particle into the g9/2 orbital will form a negative-parity state.Thus, despite the relatively small neutron shell gap at N = 40, moreenergy is required compared to the other nickel isotopes. Quadrupole

excitations conserve parity and, as a consequence, are not expected tooccur between the f p and g9/2 shell. Eventually, it is due to the smallnessof the neutron shell gap, which is comparable to the pairing gap, thatneutrons are pair-scattered in the g9/2 orbital [22]. Of course, as theneutrons are chargeless particles, they do not contribute directly to theB(E 2) value, but they do by inducing core-polarization whereby protonsare excited across the Z = 28 shell gap. Without the superfluid neutroneffect in 68Ni, the B(E 2) value had even been weaker. In fact, the smallexperimental B(E 2) value to the first excited 2+ state is not regarded asa strong evidence for the double-magic character of 68Ni. This has beenargued from calculations in Ref. [32], where it is found that the main

low-energy B(E 2) strength is collected in the group of 2+ states lyingabove 4 MeV. Moreover, the calculations indicate that the N = 40 gapis small, which is confirmed in recent Penning-trap measurements [25],and that the experimental B(E 2) value is quite sensitive to the N = 40



The nickel isotopes 15

gap.

2.1.4 Systematics of 0+ states between N = 28 and N = 40

Two excited 0+ states in 68Ni are lying at remarkably low energies. Thehalf-life of the first excited, the 0+2 state at 1.77 MeV, is determined in a(14C,16O) reaction (T 1/2 = 211+60

−40 ns) [33] and in a (86Kr,Xγ ) reaction(T 1/2 = 340(30) ns) [34]. While the former half-life value is derived fromthe measurement of time-delayed coincidences between 16O and electronevents associated with the 0+2 state in 68Ni, the latter half-life valueis deduced based on coincidences between 68Ni nuclei implanted in asilicon detector and 511-keV γ rays. An unweighted average of 276(65)

ns is reported in Ref. [20]. The 0+2 state is identified as arising from

ν (2p-2h) neutron excitations across N = 40, as concluded from shell-model calculations in Ref. [31]. There exists, however, also a secondexcited (0+3 ) state at 2.511 MeV, which so far has only been observedin a β -decay study and is suggested to arise from collective excitations[35] based on Hartree-Fock Bogoliubov calculations [33].

Previous to this work, its structure could not be unambiguously de-rived solely from the lower-energy 0+ systematics in the nickel isotopes.Fig. 2.2 summarizes what is known. In 56,58,60Ni, 0+ states are observed,identified as π(2p-2h) proton excitations across Z = 28 [36, 37]. Theirexcitation energy is progressively lowering in energy when moving away

from the N = 28 neutron shell gap and they are expected to reachtheir minimal excitation energy at the middle between two shell clo-sures, where the proton-neutron residual interactions are strongest [13].If N = 40 is a good subshell closure in the nickel isotopes, the protonintruder 0+ configuration is expected at a minimal excitation energy at62Ni with 34 neutrons. The first excited 0+2 state in 62Ni, however, canbe rather attributed a vibrational character based on following observa-tions. Its excitation energy is close to the 2+2 and 4+1 state, which all lieat ∼ 2 times the 2+1 excitation energy, which is typical for a vibrationalstructure [4]. Moreover, the structure is similar to 60Ni, where the 0+2state is identified as a vibrational state [37]. This leaves the second ex-

cited 0+3 state at 2.891 MeV in 62Ni as a possible candidate for π(2p-2h)

proton intruder configuration, which is so far lowest in energy. However,experimental information is too scarce to draw definite conclusions onwhether it is a proton intruder configuration and even if so, whether it




Neutron number (N)

28 30 32 34 36 38 40

E n e r g y

( k e V )

1000

2000

3000

4000

5000

6000 Ni56

Ni68

) Ni+

2E(2

) Ni+1

E(4

) Ni+

E(0

Figure 2.2: Energy systematics of the observed low-energy 0+ (opencircles), second excited 2+

2(filled circles), and first excited 4+

1(filled

squares) states in the even-mass nickel isotopes between N = 28 andN = 40. Data are taken from Refs. [20, 35, 37].

is minimal in excitation energy at all between N = 28 and N = 40.Several 0+ states, which are not interpreted, are observed in 64−68Ni ateven lower excitation energies. The structure of 64Ni still has a vibra-tional character, but with two 0+ states close to the 2+2 and 4+1 level

energies. Anharmonicity of the two-phonon states becomes large in 66Niand the vibrational character breaks completely down in 68Ni. It is clearthat additional experimental information is needed to characterize thesecond excited 0+ state in 68Ni.

2.1.5 Enhanced collectivity beyond N = 40

Beyond N = 40, a sharp increase is observed of the B(E 2) value in70Ni indicating a strong proton core polarization [23]. This effect is con-firmed by recent Coulomb-excitation experiments in odd-mass copperisotopes, where the determined B(E 2 : 3/2−g.s. → 7/2−) transition prob-

abilities (with 7/2−

the 2+ core-coupled state) coincide with the trend of B(E 2 : 0+ → 2+1 ) values in nickel [38]. The sharp increase is explainedas arising from the strong residual interactions between neutrons in theνg9/2 orbital and protons in the πf 7/2 and πf 5/2 orbital. By filling the



68Ni-coupled structures in the adjacent nuclei 17

νg9/2 orbital, the tensor interaction raises the πf 7/2 orbital and lowers

the πf 5/2 orbital [39]. As a result, the Z = 28 gap is reduced and theproton core polarization is enhanced. Important to note here, is thatthe core polarization is more than a factor of two stronger than was an-ticipated from shell model calculations, which successfully described theB(E 2) results up to N = 40 [22]. This is illustrative for the sensitivityof the effective nucleon-nucleon interactions utilized in this region, es-pecially when proton excitations, which cannot be explicitly included inthe valence space, become more important. In line with the high B(E 2)value in 70Ni, are the observed decreasing 2+1 excitation energies up to76Ni, which is attributed to the Z = 28 core breaking [21].

2.2 68Ni-coupled structures in the adjacent nu-clei

Regardless of the nature of the double-magic properties of 68Ni, it hasprofound implications. Instead of developing a maximum of collectivebehavior at N = 40, which is mid-shell between N = 28 and N = 50,a stabilizing effect occurs and 68Ni could be, in the most extreme case,used as a rigid core to describe the adjacent nuclei. Nevertheless, thestabilizing effect is critically dependent on the neutron shell gap energy[40] and, therefore, it is not obvious a priori to what extent this idea canbe exploited.

An elaborated particle-core coupling model (PCM) [41] has been suc-cessfully developed giving an interesting alternative to the large-scaleshell model calculations, since excitations across the Z = 28 shell clo-sure (and the N = 40 subshell closure) can be accounted for. However,the model parameters require unambiguous experimental data. For thisreason, the predictive power of the model remains limited, but, once

the parameters have been reliably determined, the descriptive power ishigh. Below, the properties of the nuclei adjacent to 68Ni are discussedsummarizing the experimental information and the theoretical interpre-tation.




Ni67 ν Ni68

28

40

7/2f

3/2

p

5/2f

1/2

p

9/2g

)-

(1/2 0

)-

(5/2 694

)+

(9/2 1007 1140

1710

1970)

-(5/2 2155 2

1 5 5

6 9 4

3 1 3

s)µ=13.3(2)1/2

(T

+0 0

+0 1770

+2 2033

-

5 2849

)+

(4 3149

+0⊗

1/2

-1p ν

+0⊗5/2-1f ν

1/2

-2p ν9/2

+1g ν

+2⊗

1/2

-1p ν

Figure 2.3: Interpretation of the 67Ni low-energy structure. Onthe left hand side, a simplified picture of the shell model occupancyis shown of the 67Ni ground state. Levels above 2155 keV are notshown.

2.2.1 67Ni

The ground state of 67Ni is assigned a spin and parity of (1/2−) and ahalf-life of 21(1) s based on a β -decay study of 67Ni [42]. As depictedin Fig. 2.3, an isomeric level (T 1/2 = 13.3(2) µs [34]) exists with spinand parity (9/2+) in 67Ni at an excitation energy of 1007 keV. The g-factor of the (9/2+) state (|g(67mN i)| = 0.125(6)) has been determinedfrom a time-dependent perturbed angular distribution method [43]. Theexcited states at 694, 1007 and 2155 keV were established in a β -decaystudy of 67Co [44]. The β -decay properties revealed important structuralinformation. The state at 1710 keV has only been observed in a three-nucleon pick-up reaction 70Zn(4He,7Be)67Ni [45], while the states at 1140and 1970 keV were only observed in the quasi-elastic transfer reaction70Zn(14C,17O)67Ni [33].

In 67Ni, the ground state and first excited level are respectively as-signed a single-particle νp−1

1/2and νf −1

5/2configuration from Ref. [44], see

also Fig. 2.3. This interpretation is supported by the PCM model. The(5/2−)2 level at 2155 keV is assumed to be a member of the νp−11/2⊗

2+1 (68Ni) multiplet. A νf −15/2

⊗ 0+2 (68Ni) assignment was proposed in

Ref. [44], but this could not be reproduced in the PCM model. More-




over, the 2+1 core energy is close to that of the (5/2−)2 level and Ref. [46]

indicated already that the observed β -decay branch to the 2155-keV levelwas also consistent with a particle-vibration coupling mixed with a smallνf −1

5/2hole component. The (9/2+) state at 1007 keV is identified as the

νg+19/2νp−21/2 configuration [44], which is the lowest ν (1p-2h)3 configura-

tion in 67Ni. Furthermore, the measured g-factor of the (9/2+) stateis about a factor 2 lower compared to g-factor values calculated frommodels that ignore proton excitations across the major Z = 28 shellgap [43]. However, by including a 2% admixture of π(1p-1h) excitationsacross Z = 28, the discrepancy could be explained.

This means that 67Ni can be described in terms of a dominant 68Nicore coexisting with a low-energy ν (1p-2h) neutron-intruder configura-tion, which also contains a small admixture of π(1p-1h) excitations.

2.2.2 67Co

Based on the β -decay work of Ref. [44], the 67Co ground state is assigneda spin and parity of (7/2−). Apart from γ rays of 189 keV observed inthe β decay of 67Fe [47], there was no experimental information availableon the excited level structure prior to this work.

Due to the observed 67Co β decay towards the 9/2+ state in 67Ni, itwas concluded that the (7/2−) ground state of 67Co contains a νg+2

9/2νp−2

1/2

component [44]. QRPA calculations presented in Ref. [44] predict a νg9/2occupancy ranging from 11% up to 15%.

2.2.3 69Ni

The 69Ni ground state has a half-life of 11.4(3) s [48] with an assignedspin and parity of (9/2+) [34]. Ref. [34] reported on a long-lived isomerat 321 keV with spin and parity (1/2−) along with the levels at 915, 1959and higher energies indicated in Fig. 2.4. More recent β -decay work [49]established that the 321-keV state decays by β emission with a half-lifeof 3.5(5) s. Also levels at 915 and 1518 keV were observed in the β decayof 69Co.

3If not explicitly mentioned, ν (xp-yh) denotes particle-hole excitations across N =40, while π(xp-yh) denotes particle-hole excitations across Z = 28.




Ni69 ν Ni68

28

40

7/2f

3/2

p

5/2f

1/2

p

9/2g

)+

(9/2 0

)-

(1/2 321

)-

(5/2 915

)-

(5/2 1518

)-

(7/2 1821)

-(9/2 1959

)+

(11/2 2241

)-

(13/2 2552)-(17/2 2701

(3.5(5) s)β

(11.4(3) s)β

+0 0

+0 1770

+2 2033

-

5 2849

)+

(4 3149

+0⊗

9/2

+1g ν

Ni70 ⊗-1pf ν

+2⊗

9/2

+1g ν

Ni70 ⊗-1pf ν

Figure 2.4: Interpretation of the 69Ni low-energy structure. On theleft hand side, a simplified picture of the shell model occupancy isshown of the 69Ni ground state. All observed levels are shown.

As shown in Fig. 2.4, the low-energy structure of 69Ni consists of both positive- and negative-parity levels, denoting a single νg+1

9/2coupling

to excitations of the 68Ni core and ν (2p-1h) configurations of a νp−11/2

or νf −15/2

hole coupled to the 70Ni core, respectively [49]. The (9/2+)

ground state consists of the νg+19/2 configuration. The level at 2241 keV,

approximately at the68

Ni 2+

core energy, is assigned as (11/2+

) [50]giving strong support for a νg+1

9/2⊗ 2+1 (68Ni) structure. On the other

hand, numerous negative-parity levels have been assigned at low energy[34, 49], which are interpreted as a coupling with excited states in the70Ni core. According to the PCM model, the high density and lowenergy of these levels can be attributed to the stronger particle-vibrationcoupling, the lower energy of the 2+1 state in the subspace of 70Ni andthe higher density of single-hole, as compared to single-particle, orbitals.

2.2.4 68Cu

The 1+ assignment of the 68Cu ground state (T 1/2 = 31.1(15) s [20]) isbased on the observed feeding to the 0+ ground state of the 68Zn daugh-ter nucleus. Excited states in 68Cu have been intensively investigatedthrough the γ decay of the 68Cu isomer (T 1/2 = 3.75(5) m [51]) pro-




Cu68 νπ

28

40

7/2f

3/2

p

5/2f

1/2

p

9/2g

28

40

7/2f

3/2

p

5/2f

1/2

p

9/2g

)+

(1 0)

+(2 84

)+

(3 611)

-(6 721

)-

(3 778)

-(4 956

(3.75(5) m)β

(31.1(2) s)β

1/2

-1p ν3/2

+1pπ

5/2-1f ν

3/2

+1pπ

9/2

+1g ν3/2

+1pπ

Figure 2.5: Interpretation of the 68Cu low-energy structure. On theleft hand side, a simplified picture of the shell model occupancy isshown of the 68Cu ground state. All observed levels are shown.

duced by 68Zn(n, p) reactions [51–54]. Initially, the isomer was reportedby Ref. [52] and placed at an excitation energy of 721 keV by Ref. [55].A 68mCu decay scheme corresponding to the levels at and below 721 keV(see Fig. 2.5) was established for the first time in the work of Ref. [51],but their spin and parities were assigned in Ref. [53]. Note, however,that the 611-keV level eventually is assigned a (3+) spin and parity [54],

as shown in Fig. 2.5. The magnetic moments of the ground and isomericstate have been deduced by in-source laser spectroscopy [56]. Coulombexcitation of post-accelerated 6− beams revealed the levels at 778 and956 keV [57].

The copper isotopes contain 29 protons, which means one valenceproton is expected in the negative-parity pf orbitals. With 39 neutronsin 68Cu, positive-parity states can be assigned to single neutron holestates in the negative-parity p1/2 or f 5/2 orbitals, while negative-paritystates should arise from ν (1p-2h) intruder excitations across N = 40into the positive-parity g9/2 orbital. As shown in Fig. 2.5, the groundstate and first excited state in 68Cu is identified as the 1+, 2+ multi-plet of the πp+1

3/2νp−1

1/2coupling; the (3+) state at 611 keV as a member

of the πp+13/2

νf −15/2

coupling [54]. Intruder excitations across N = 40

are observed at 721 [56], 778 and 956 keV arising from a πp+13/2

νg+19/2




configuration [54, 57]. From the Coulomb-excitation study [57] a low

B(E 2; 6−

→ 4−

) value was extracted of 4.1(4) W.u., which is consistentwith a single-particle character of the πp+1

3/2νg+1

9/2configuration. How-

ever, the value is slightly underestimated by shell model calculationspresented in Ref. [57] pointing to a possible influence of proton excita-tions across the Z = 28 shell gap.

2.2.5 69Cu

The experimentally established level structure of 69Cu is rather ex-tended. Fig. 2.6 only shows the levels up to 1871 keV. The first spectro-scopic 69Cu information was obtained in a 70Zn(d,3He) transfer reaction

[58], which reported on the deduced spin and parity values and spec-troscopic factors of the ground state and the states at 1110, 1213, 1711and 1871 keV. The β -decay studies of the 69Ni ground state [59–61] and69mNi isomeric state [46, 49] (see also Fig. 2.4) revealed important addi-tional information. 69Ni mainly feeds higher-energy levels in 69Cu and69mNi is observed to decay solely to the 1298-keV state and the groundstate of 69Cu. While the (d,3He) transfer reaction of Ref. [58] favors thepopulation of states with a single-particle character, recent Coulomb-excitation measurements on 69Cu [38] favor the population of excitedstates with a collective character providing complementary information.

The (1/2−) isomer at 321 keV in 69Ni (see Fig. 2.4), identified as a

ν (2p-1h) intruder, is observed to decay exclusively to the 3/2−

groundstate and the (3/2−) state at 1298 keV in 69Cu [46, 49], which areshown in Fig. 2.6. Because the allowed Gamow-Teller decay involves aνp1/2 → πp3/2 transition, both states contain ν (2p-2h) configurations.

The 1298-keV state is identified as the πp+13/2⊗ 0+2 (68Ni) state and in

case the state is purely ν (2p-2h), the log f t values4 indicate that thereis a mixture of this configuration in the πp+1

3/2ground state ranging from

9(4)% [49] to 15% [46]. It is remarkable that the other N = 40 nu-cleus adjacent to 68Ni, 67Co, is predicted to have the same amount of

4The log ft value of a state is the logarithm of ft1/2, where t1/2 is the partial β -

decay half-life and f (Z,Qβ) is the known Fermi integral with Z the number of protonsin the nuclear system after the decay and with Qβ the end-point energy. Since ft1/2is proportional to |M fi |

−2, with M fi the nuclear matrix element, it is representativefor the degree of overlap between the nuclear wave functions before and after the β decay. See, e.g., Ref. [62] for more details.




Cu69π Ni68

28

40

7/2f

3/2

p

5/2f

1/2

p

9/2g

-3/2 0

-1/2 1110

-5/2 1213

)-

(3/2 1298

-7/2 1711

-7/2 1871

1 2 9 8

+0 0

+0 1770

+2 2033

-

5 2849

)+

(4 3149

+0⊗

3/2

+1pπ

+0⊗

1/2

+1pπ

+0⊗5/2+1fπ

+0⊗3/2

+1pπ7/2-1fπ

3/2

+2pπ

+2⊗

3/2

+1pπ

Figure 2.6: Interpretation of the 69Cu low-energy structure. Onthe left hand side, a simplified picture of the shell model occupancyis shown of the 69Cu ground state. Levels above 1871 keV are notshown.

ν (2p-2h) mixing (see paragraph 2.2.2). If this value is representative forthe ν (2p-2h) component in the 68Ni ground state, such a small valuesuggests double-magic character of this nucleus according to Ref. [46].However, this cannot be confirmed nor contradicted from currently avail-able experimental data.

The (d,3He) transfer reaction [58] reveals that the main configura-tion of the ground state is indeed πp+1

3/2; of the 1/2− state at 1110 keV

is πp+11/2

; the 5/2− state at 1213 keV is πf +15/2

and the 7/2− state at

1711 keV is πf −17/2

. The state at 1871 keV has no main single-particlecomponent and is interpreted in the PCM model as a member of theπp+1

3/2⊗ 2+1 (68Ni) multiplet. Its obtained B(E 2; 7/2− → 3/2−) value,

which is very similar to the B(E 2; 0+ → 2+) strength in 68Ni [38], isconsistent with the proposed interpretation. Moreover, the first excited7/2− state was not populated in the Coulomb-excitation process, whichis in line with a single-particle character of that state. Also the small

quadrupole transition strengths to the 5/2−

and 1/2−

states are con-sistent, albeit that the 1/2− state contains some amount of collectivity(B(E 2 : 3/2−g.s. → 1/2−) = 10.4(10)).

It is important to stress the occurrence of a π(2p-1h) proton intruder




state at 1711 keV [38, 41, 58]. Of all the observed intruder states in the

nuclei adjacent to 68Ni, it is the only proton excitation across the Z = 28shell closure. It is also worth mentioning that this 7/2− state comesdown in excitation energy from 2340 keV in 67Cu, to 1711 keV in 69Cuand 981 keV in 71Cu and levels off in 73Cu at 1010 keV. The intruderassignments in 71,73Cu is based on the systematics that the 7/2− intruderis not populated in the Coulomb-excitation measurements of Ref. [38].The minimum is situated at N = 42, which is near mid-shell betweenN = 28 and N = 50. This might suggest that the stabilizing effectof an N = 40 subshell gap disappears when proton excitations occuracross Z = 28. This could be caused by the reduced repulsive tensorinteraction between the πf 7/2 protons and νg9/2 neutrons when a πf 7/2

proton is removed [39], lowering the νg9/2 orbital and thus reducing theN = 40 subshell closure.

A triplet of positive-parity states are observed in the β decay of the69Ni ground state at 2550, 2696 and 2756 keV with spin J = (9/2), (7/2)and (11/2), respectively [60, 61]. Since the 69Ni ground state has aνg+1

9/2configuration, these states are suggested to be members of the

πp+13/2

νp−11/2

νg+19/2

multiplet. The 5− member of the νp−11/2

νg+19/2

configura-

tion in 68Ni lies at an excitation energy of 2849 keV, which is similar tothe three observed members in 69Cu.

To summarize 69Cu, it exhibits different coexisting structures: single-

particle and

68

Ni core-coupled states, which also includes the ν (2p-2h)and ν (1p-1h) neutron-intruder states at 1298 keV and around 2.65 MeV,respectively, and a proton-intruder state at 1740 keV.

2.2.6 70Cu

Initially, the low-energy structure of 70Cu has been studied by (n, p)[63–65] and (t,3He) reactions [66] on a 70Zn target. The (n, p) reactionsrevealed the β -decaying isomeric state at 242 keV, see Fig. 2.7, whilethe (t,3He) reaction established the levels at 101, 229, 369 and 507 keV.More recently, β -decay studies of 70Ni and 70Cu [67, 68] determined the

half-lives of the β -decaying ground state (T 1/2 = 44.5(2) s) and 242-keVlevel (T 1/2 = 6.6(2) s) more accurately and identified the 101-keV level(T 1/2 = 33(2) s) as a third β -decaying state in 70Cu. From the 70Ni β -decay work, also the 321-keV level and levels above 507 keV (not shown




Cu70 νπ

28

40

7/2f

3/2

p

5/2f

1/2

p

9/2g

28

40

7/2f

3/2

p

5/2f

1/2

p

9/2g

)-

(6 0)

-(3 101

)-

(4 229

+1 242

)+

(2 321)

-(2 369

)-

(5 507

(6.6(2) s)β

(33(2) s)β

(44.5(2) s)β

9/2

+1g ν3/2

+1pπ

9/2

+2g ν1/2

-1p ν3/2

+1pπ

9/2

+1g ν3/2

+1pπ

Figure 2.7: Interpretation of the 70Cu low-energy structure. On theleft hand side, a simplified picture of the shell model occupancy isshown of the 70Cu ground state. Levels above 507 keV are not shown.

in Fig. 2.7) were established in 70Cu. The magnetic moments of the threeisomeric states have been determined from in-source laser spectroscopy[56]. The collective properties of the 229-keV level were investigatedby Coulomb excitation of 70Cu [57]. The Coulomb-excitation processmainly populated the 229-keV level and its γ de-excitation into the 101-keV isomer was observed.

The ground state and the first excited state are identified as the6− and 3− member, respectively, of the πp+1

3/2νg+1

9/2configuration [56].

The 4− and 5− members are assigned to the 229- and 507-keV states,respectively [67]. The single-particle character of the 4− member at229 keV has been verified by the Coulomb-excitation measurement of Ref. [57]. The isomer at 242 keV is interpreted as the 1+ member of the πp+1

3/2νp−1

1/2νg+2

9/2configuration, while the 2+ member lies at 321 keV

[68]. The 2− state at 369 keV is a rather mixed state containing ν (3p-2h)configurations [68].

2.2.7 Conclusions

A lot of experimental information is available for the nickel and copperisotopes adjacent to 68Ni. From the first experimental studies on, theirlow-energy structure was interpreted as dominated by particles and/or




holes coupled to the 68Ni core. Very recently, their single-particle and

collective structure has been investigated as well through more directtechniques like g-factor measurements of 67mNi and 69mCu [43] andCoulomb excitation of 68m,69,70Cu [38, 57] and 68Ni [22, 28]. Theseexperiments deliver deeper and sometimes also unexpected insights asdiscussed above. Clearly, neutron excitations across N = 40 play alsoan important role in the nuclei adjacent to 68Ni and, e.g., in 68Cu, iteven leads to an enhanced polarization of the proton core, which cannotbe reproduced by the current shell model calculations. Nonetheless, thedominant low-energy structure consists of configurations arising from thecoupling with the 68Ni core. Furthermore, it is important to note thatthe proton intruder state in 69Cu is observed to reside at an excitation

energy of 1711 keV.

2.3 The odd-mass cobalt isotopes with A ≤ 63

The isotopes under study in this thesis work are 65,67Co. The aim isto understand their low-energy structure in the framework of nuclearmodels, for which the lighter odd-mass cobalt nuclei serve as a veryvaluable guide. Cobalt isotopes have one proton less than the nickelisotopes and thus it can be anticipated that they are interpreted as aπf −1

7/2proton hole coupled to the nickel core. Therefore, it is mandatory

to have an introduction in their low-energy structure from57

Co onwards.

2.3.1 57Co

The low-energy structure of 57Co has been extensively investigated throughdifferent reactions and β decay, see, e.g., Ref. [20]. A summarizing levelscheme is shown in Fig. 2.8. The indicated spectroscopic factors aretaken from Ref. [20] and are obtained by assuming that the 7/2− groundand excited state at 2311 keV exhaust the f 7/2 proton-hole strength,

i.e. normalizing to C 2S

(gs) + C 2S

(2311) = 2.0, and by averaging thespectroscopic factors of Refs. [69–71].

The ground state has a spin and parity of 7/2−

. Its spectroscopicfactor in the 56Fe(3He,d)57Co stripping reaction is 1.56, which meansthat the f −1

7/2proton hole configuration is by far the most dominant

component in the ground state. Below 2.3 MeV, one has observed a



The odd-mass cobalt isotopes 27

Co57

Ni58

-7/2 (1.56) 0

-9/2 1224

-3/2 (1.26) 1378

-1/2 (0.58) 1505

-11/2 1690

-3/2 (0.24) 1758

-7/2 1897

-5/2 1919

-

5/2 (1.62) 2133

+0(1.56) 0

+2

1454

+4

(1.26)

2459

+

2

(0.58)

2775

+0

2942

+0⊗7/2-1fπ

+2⊗

7/2-1fπ

7/2-2fπ

3/2

+1pπ7/2-2fπ

1/2

+1pπ

+2⊗7/2-1fπ

7/2-2fπ

5/2+1fπ

Figure 2.8: Interpretation of the 57Co low-energy structure. Spec-troscopic factors C 2S are placed between brackets next to the spinand parity notation of the state.

1/2−, 7/2−, 9/2− and 11/2− excited state and two 3/2− and 5/2−

excited states. The 1/2− state resides at an energy of 1505 keV andis strongly populated in the (3He,d) reaction indicating a large πp1/2single-particle strength. Both 3/2− states at energies of 1378 and 1758keV are populated in the reaction, but the first excited 3/2−1 state ex-hibits a significant larger spectroscopic factor. Of the 5/2− states at1919 and 2133 keV, only the 5/2−2 state at 2133 keV was populatedin the stripping reactions with an average spectroscopic factor of 1.62.The 2133-keV state has been suggested to form a doublet with a 3/2+ or5/2+ state by a 58Ni(d,3He)57Co pick-up reaction study [72], but a later(d,3He) study [73] contradicted this result. The 7/2−, 9/2− and 11/2−

states at respective excitation energies of 1897, 1224 and 1690 keV havenot been observed in the (3He,d) reaction.

The structure of 57Co can be interpreted on the basis of single-proton excitations and collective vibrations of the 58Ni core. The 9/2−,11/2−, 3/2−2 , 7/2− and 5/2−1 quintet is interpreted as originating from

the coupling of the f −1

7/2 proton hole to the first excited 2+

state in58Ni. The interpretation was originally based on models utilized in, e.g.,Ref. [74], where 57Co is merely described by coupling 1f 7/2, 2s1/2 and1d3/2 proton-hole states to core vibrations up to three quadrupole and




one octupole phonons. Despite this successful description, the model

does not account for the 1/2−

, 3/2−

1 and 5/2−

2 levels. Instead, also theproton particles in the 2 p3/2, 1f 5/2 and 2 p1/2 orbitals above the Z = 28shell gap have to be considered, which is done in the work of, e.g.,Refs. [75, 76]. Their unified model of collective vibrations and single-particle motion is capable of describing the full low-energy structure toa satisfactory extent in terms of level properties like excitation ener-gies, spins and parities, spectroscopic factors, quadrupole moments andB(E 2) values. This gives confidence that their results reflect the rightstructure of the low-energy levels. The 9/2− and 11/2− high-spin statesconsist for 76% and 75%, respectively, out of the πf −1

7/2⊗2+ configuration

according to Ref. [75]. Also the 5/2− member of the quadrupole quintet

at 1919 keV has a rather pure character with small admixtures of theπf −17/2 proton hole coupled to the two-phonon 2+ and 4+ core states. On

the other hand, the 1/2− and 3/2− low-spin states and the excited 7/2−

state are described by a strong admixture of basic states. The 7/2− stateis described by a coupling to the ground state (22%), the one-phonon2+ state (38%) and the two-phonon 0+, 2+ and 4+ states (32%). Both3/2− states are considerably mixed, but the first excited 3/2−1 statecontains a larger fraction of the πp+1

3/2component than the 3/2−2 state.

This is consistent with the spectroscopic factors in the (3He,d) reactionsand with E2 transition rates to the ground state [77]. On this basis,the 3/2−

1state was assigned the πp+1

3/2πf −2

7/2single-particle state and the

3/2−2 state the πf −17/2

⊗ 2+ state, but both states are severely mixed.

The 1/2− state at an excitation energy of only 1505 keV cannot arisefrom the πf −1

7/2coupling with a 2+ core. A 3+ or 4+ core state would be

required, but these states are already at a minimum excitation energyof 3420 and 2459 keV, respectively. Nevertheless, the model of Ref. [75]shows that the 1/2− state originates from the coupling with this 4+ stateand appears so low in energy due to significant mixing of the πp+11/2πf −27/2configuration.

2.3.2 59Co

Also the low-energy structure of 59Co has been extensively investigatedthrough different reactions and β decay, see Ref. [20]. Because 59Co is theonly stable cobalt isotope, it is the only cobalt isotope that was studied




Co59

Ni60

-7/2 (1.36) 0

-3/2 (0.44) 1099

-9/2 1190

-3/2 (1.36) 1292

-1/2 (0.74) 1434

-11/2 1460

-5/2 1482

-7/2 1745

-7/2 2062

-

5/2 (2.28) 2087

+0(1.36) 0

+2

(0.44)

1333

+2

2159

+0

(1.36)

2285

+4

(0.74)

2506

+0⊗7/2-1fπ

+2⊗

7/2-1fπ

7/2-2fπ

3/2

+1pπ

7/2-2fπ

1/2

+1pπ

+2⊗

7/2-1fπ

+2⊗

7/2-1fπ

7/2-2fπ

5/2+1fπ

Figure 2.9: Interpretation of the 59Co low-energy structure. Spec-troscopic factors C 2S are placed between brackets next to the spinand parity notation of the state.

by Coulomb excitation [78]. A summarizing level scheme is shown inFig. 2.9. The indicated spectroscopic factors are taken from Ref. [79].The level scheme and structure of 57Co and 59Co are remarkably similar.

The ground state has a spin and parity of 7/2−. Its spectroscopicfactor in the 58Fe(3He,d)59Co stripping reaction is 1.36 indicating the

dominance of the f −1

7/2 proton hole configuration. Below 2.1 MeV, onehas observed a 1/2−, 9/2− and 11/2− excited state and two 3/2−, two5/2− and two 7/2− excited states. The 1/2− state resides at an energy of 1434 keV and is strongly populated in the (3He,d) reaction. Both 3/2−

states are populated in the reaction at energies of 1099 and 1292 keV.Contrary to 57Co, it is the second excited 3/2−2 state that exhibits asignificant higher spectroscopic factor. This is consistent with the re-sults of the Coulomb-excitation study, where only the first excited 3/2−1state was populated, which indicates its enhanced collectivity. Of the5/2− states at 1482 and 2087 keV, only the 5/2−2 state at 2087 keV waspopulated in the stripping reactions with a spectroscopic factor of 2.28.

Both 7/2−

states, the 9/2−

and the 11/2−

states at respective excitationenergies of 1745, 2062, 1190 and 1460 keV have not been observed in the(3He,d) reaction. Furthermore, the 9/2− and 11/2− state are stronglypopulated in Coulomb excitation.




As in 57Co, the full low-energy structure of 59Co is explained on the

basis of single proton-particle excitations and its coupling to a vibratingcore. Unfortunately, Ref. [75] did not present their calculated wavefunctions for the 59Co levels, but the similarity of level properties in57,59Co gives strong confidence that the wave functions are similar aswell. Based on the single-particle strengths, the B(E 2) values and theresults of theoretical models [75, 76], the 3/2−1 , 9/2− and 11/2− high-spin states are interpreted as the coupling of the πf −1

7/2proton-hole to

the first excited 2+ state in 60Ni [75]. Note that the ordering is changedfrom 57Co to 59Co. The high-spin states keep their rather pure couplingcharacter. From a comparison to 57Co, the first excited 5/2−1 and 7/2−1states are interpreted as the other members of the πf −17/2

⊗2+ quintet

[80]. This interpretation is consistent with the spectroscopic factorscalculated in the model of Ref. [75], which are small and similar to thespectroscopic factors of the core-coupled 5/2− and 7/2− states in 57Co.

The single-particle states are the 1/2−, 3/2−2 and 5/2−2 states andtheir nature is exactly the same as explained in the case of 57Co. The1/2− state originates from the coupling with the two-phonon 4+ stateat 2506 keV and appears so low in energy due to strong mixing of theπp+1

1/2πf −2

7/2configuration. Although both 3/2− states are strongly mixed,

the second excited state contains a dominating πp+13/2

πf −27/2

single-particle

structure. The 5/2−2 state has a strong πf 5/2 single-particle strength in

the (3

He,d) reaction, which is reproduced in Ref. [75] and is similar to the5/2− single-particle state in 57Co. The second excited 7/2−2 state thatappears at 2062 keV can be explained as the coupling to the two-phonon2+ state at 2159 keV in 60Ni.

2.3.3 61Co

The experimental information of the odd-mass cobalt isotopes from A ≥61 on is less extensive [20]. There are, e.g., no (3He,d) data available,because the iron isotones are not stable. This means there is no directexperimental single-particle information available. However, 61Co has

been studied in several pick-up reactions on nickel isotopes [81, 82],in the β decay of 61Fe [83], and in a deep-inelastic reaction [84]. Asummarizing level scheme is shown in Fig. 2.10.

A firm spin and parity of 7/2− has been assigned to the ground state




Co61

Ni62

-7/2 0

-3/2 1027

)-

(3/2 1205

-9/2 1286

)-

(1/2 1325

-7/2 1619

)-

(5/2 1646

-11/2 1664

)-

,7/2-

(5/2 1889

)-(1/2 1953

)-

(3/2 2011

+0 0

+2

1173

+2

2049

+0

2302

+4

2336

+0⊗7/2-1fπ

+2⊗

7/2-1fπ

7/2-2fπ

3/2

+1pπ

+2⊗

7/2-1fπ

7/2-2fπ

1/2

+1pπ

+2⊗7/2-1fπ

+,4+,)2+(0⊗7/2-1fπ

+4⊗7/2-1fπ

+,4+2⊗7/2-1fπ

Figure 2.10: Interpretation of the 61Co low-energy structure.

and 1620-keV state based on the combined analysis of the 59Co(t, p)61Coand 62Ni(t,α)61Co reactions [85]. Furthermore, they unambiguouslycould assign the 1027-keV state a spin and parity of 3/2−. The states at1286 and 1664 keV have been strongly populated in a 16O(48Ca, p2n)61Codeep-inelastic reaction [84]. From angular γ correlations, they were ableto confirm the previously suggested 9/2− and 11/2− assignment of the1286-keV and 1664-keV level [82], respectively. Furthermore, the 1325-keV level was suggested a 1/2− assignment, which is consistent with theproposed assignment in Ref. [80]. The spin and parities of the other low-energy levels have been assigned on the basis of their angular momentumL deduced from angular distributions in (t,α) and (d,3He) reactions, the61Fe β decay and the γ branchings. The 1205-keV state, however, is notobserved in the pick-up reactions and systematics of the 57,59Co low-energy structure was used to discriminate between the experimentallyassigned 3/2− and 5/2− spin and parities [80].

As could be anticipated from systematics, the ground state is inter-preted as the coupling of the πf −1

7/2proton-hole to the 0+ ground state of

its nickel isotone core, 62Ni. This is also supported by its large spectro-

scopic factor of 4.47 in the 62Ni(d,3He)61Co reaction [81]. The membersof the 2+ coupling are identified at 1027, 1286, 1619 and 1646 keV [80]and at 1664 keV [84]. The (3/2−) state with single-particle character isassigned to the 1205-keV state. This is consistent with the spectroscopic




factors in the (d,3He) pick-up reaction [81], since the 1205-keV state is

not observed, while the 1027-keV state is relatively strongly populated.This can be understood from the perspective that, when a proton istaken out of the 62Ni core, preferentially proton-hole states are popu-lated in the resulting 61Co nucleus. For the same reason and also fromexcitation energy systematics [80], the (1/2−) states at 1325 keV and1953 keV are interpreted as the πp+1

1/2πf −2

7/2and 4+-coupled states, re-

spectively. The states at 1889 and 2011 keV have not been interpretedexplicitly in the literature, but it is very tempting to understand themas two-phonon couplings. Contrary to the 57,59Co isotopes, there is nostate present in 61Co at low energy with a dominant πf +1

5/2πf −2

7/2configu-

ration. Also the 1889-keV level can not be a candidate due to its strong

population in the (d,3He) reaction [81].

2.3.4 63Co

The heaviest cobalt isotope, for which experimental pick-up reactiondata from the nickel isotopes are available, is 63Co. It is not a coinci-dence that 64Ni is the heaviest stable nickel isotope. Additional exper-imental information was obtained from a 63Fe β -decay study [86] andthe deep-inelastic 16O(48Ca, p2n)61Co study [84]. It is important to notethat 63Co is also the heaviest cobalt isotope, for which its low-energystructure could be interpreted in the framework of weak-coupling and

single-particle excitations, see Fig. 2.11.In 63Co, a controversy existed about the states at 1384, 1427 and

1495 keV from (d,3He) [87] and (t,α) reactions [88]. Ref. [87] noted thatthese ambiguities were due to the insufficient energy resolution to re-solve the triplet, which amounted to ∼ 100 keV and ∼ 50 keV for therespective studies. This issue is overcome, however, in the (d,3He) workof Ref. [89], where they complemented the results of a low-resolution(FWHM = 130 keV) polarized deuteron reaction with a high-resolution(FWHM = 20 keV) unpolarized deuteron reaction. From this work,firm spins and parities of 7/2−, 3/2−, 1/2− and 7/2− have been de-duced for the ground state and the 995-, 1889- and 2128-keV states,

respectively, in 63Co. Moreover, the energy resolution was sufficient todeduce angular momenta of L = 1 and 3 for the respective states at1427 and 1495 keV from the angular distributions. The proposed L = 3assignment for the 1384-keV state has been contradicted, however, by a




Co63

Ni64

-7/2 0

-3/2 995

-9/2 1384

)-

(3/2 1427

)-

,7/2-

(5/2 1495

)-

(1/2 1577

-11/2 1672

-1/2 1889

)-

,7/2-

(5/2 2077

-

7/2 2128

+0 0

+2

1346

)+

(2

2277

+4

2610

)+

(0

2867

+0⊗7/2-1fπ

+2⊗7/2-1fπ

7/2-2fπ

3/2

+1pπ

+2⊗7/2-1fπ

7/2-2fπ

1/2+1pπ

+2⊗

7/2-1fπ

+4⊗

7/2-1fπ

Figure 2.11: Interpretation of the 63Co low-energy structure.

firm 9/2− spin and parity assignment from angular γ -correlations in thedeep-inelastic study [84]. In Ref. [89], it can be seen that the 1384-keVstate is populated considerably less than the 1427-keV state hamperingan unambiguous angular momentum assignment for the former state.The 1427-keV level has also been established in the β decay of 63Fe [86],which has a 5/2− ground state. It is directly β fed with a log f t of 5.9 and subsequently decays towards the 7/2− ground state. This rules

out a (1/2

−

) assignment and leaves (3/2

−

) as the only option. The1577-keV state is fed with a large log f t value of 7.5. Furthermore, itsubsequently decays only to the 3/2− states at 995 and 1427 keV andnot to the 7/2− ground state. The latter restricts the spin and parity toJ π ≤ 3/2−. Because the large log f t value indicates a forbidden decayand from systematics only two 3/2− states are expected at low energy,a (1/2−) assignment is proposed here. From the deep-inelastic reaction,the 1672-keV state was assigned a 11/2− spin and parity. The 2077-keVlevel, finally, was observed in the (d,3He) reactions of Ref. [89] and wasproposed a L = 3 character, which was confirmed by its γ -decay studiedin the extended work with (d,3Heγ ) coincidence experiments [90].

The large spectroscopic factor of 4.53 in the (d,3

He) reaction [89]for the 7/2− ground state supports the πf −17/2 ⊗ 0+ interpretation one

expects from systematics. From the strong population of the 3/2−

state at 995 keV in pick-up reactions, it can be assigned a dominant




πf −17/2⊗ 2+ configuration. The (3/2−) state at 1427 keV, on the other

hand, is only weakly populated, which indicates a more pronouncedsingle-particle πp+1

3/2πf −2

7/2character. The (5/2−, 7/2−), 9/2− and 11/2−

states at 1495, 1384 and 1672 keV, respectively, are also significantlypopulated in pick-up and thus should contain an important contributionfrom the πf −17/2 ⊗ 2+ configuration. It is remarkable that one member

of the quadrupole quintet is missing. Of the two observed 1/2− states,only the 1889-keV state has been populated in the (d,3He) reaction. Onthis basis, the 1889-keV state should arise from a dominant πf −1

7/2⊗ 4+

configuration and the 1577-keV state from a dominant πp+11/2πf −27/2 single-particle configuration. The states at 2077 and 2128 keV are good can-didates to consist of configurations with a πf −1

7/2

proton hole coupled

to the two-phonon core states at 2277, 2610 and/or 2867 keV. In fact,the experimental (d,3He) strength distribution in 63Co is found in verygood agreement with a calculated strength distribution based on a sim-ple phonon-hole coupling model [90].

2.3.5 65Co

The experimental information for the low-energy structure of 65Co priorto this work is very scarce. The ground state is assigned a (7/2−) statebased on the strong direct β decay to the 5/2− ground state of 65Ni (log

f t = 4.4) [91], which is believed to be the allowed νf 5/2 → πf 7/2 Gamow-Teller decay. The (7/2−) assignment is consistent with the systematicsof the lighter odd-mass cobalt isotopes.

The excited structure in 65Co has been investigated by one 65Fe β -decay study [92]. More than 50% of the β strength was missing in the γ activity and, accordingly, this β strength was attributed to direct decaytowards the (7/2−) ground state. Allowed Gamow-Teller decay givespossible spin and parities of 5/2−, 7/2− and 9/2− for the ground stateof 65Fe. Because only 5/2− makes sense in a shell model picture, theground state was assigned (5/2−). In turn, the established states at882, 1222, 1960, 1993 and 2183 keV, which exhibit low log f t values as

well, are assigned spin and parities of (3/2−

, 5/2−

, 7/2−

). Two γ raysare emitted from the 1222-keV level, one with an energy of 340 keV tothe 882-keV level and another of 1222 keV to the (7/2−) ground state.Their respective γ intensities are indicative for an M1 340-keV transition




and an E2 1222-keV transition. On this basis, the 1222-keV level was

assigned a (3/2−

) spin and parity and the 882-keV level a (5/2−

). Aninterpretation of the 65Co structure was not given.

2.3.6 67Co

Analogous to 65Co, the (7/2−) assignment of the ground state in 67Co isbased on the strong direct β decay to the 5/2− ground state of 67Ni (logf t = 4.7) [44]. Again, this assignment is consistent with systematics. Astrong γ ray at 189 keV has been observed in the decay of 67Fe [47], butno excited states have been established prior to this work.

2.3.7 Conclusions

The cobalt isotopes that are well known, i.e., for A ≤ 63, all have a re-markably similar low-energy structure, see Fig. 2.12. In fact, knowledgeof 57Co is sufficient to understand qualitatively 63Co. All the isotopeshave in common the 2+-coupled multiplet with spins ranging from 3/2−

to 11/2− and excitation energies spread around the 2+ core state exci-tation energy. However, the 3/2− member is severely mixed with an-other low-energy 3/2− state with a dominant πp+1

3/2πf −2

7/2single-particle

character. A 1/2− state is present at a surprisingly low energy, due tosubstantial mixing of the πp+1

1/2πf −2

7/2single-particle configuration into

the πf −17/2⊗ 4+ configuration. States at higher energies reside typically

around the two-phonon core states energies and are interpreted also assuch.

Intruder states at relatively low excitation energies are typically ex-pected to be deformed states, because they have to come along withsignificant proton-neutron residual interactions [4], which together withpairing correlations account for a gain in binding energy comparable tothe shell gap [13]. However, the 1/2− and 3/2− states labeled a single-particle structure in the odd-mass cobalt isotopes are strongly mixed

with the πf −17/2 core-coupled states. As a result, the development of de-

formed bands is prevented, which is consistent with the fact that noexperimental indications have been reported on band structures on topof the single-particle states.




Neutron number (N)30 32 34 36

E n e r g y

( k e

V )

0

1000

2000

3000

) Ni+E(4) Ni+E(2

cc) Co--11/2-E(5/2sp) Co

-E(1/2

cc) Co-

E(3/2sp) Co

-E(3/2

Figure 2.12: Systematics of the odd-mass cobalt isotopes rangingfrom mass A = 57 to A = 63. The 2+ and 4+ nickel core states aremarked with open circles and squares, respectively. The filled symbolsmark states in the cobalt isotopes: the 1/2− state with single-particlecharacter (sp) by the red star; the 3/2− state with single-particlecharacter (sp) by the red tip-up triangle; the 3/2− state with 2+ core-

coupled character (cc) by the blue tip-down triangle; the other stateswith 2+ core-coupled character (cc) by the circles.

2.4 Onset of deformation below Z = 28 in theN = 40 region

From paragraphs 2.1–2.3 it may have become clear that, although theenergy gap between the pf shell and the g9/2 orbital is not substantial,68Ni features a stabilizing effect due to the parity change across N = 40.This effect is strong enough to allow the adjacent nickel and copper

isotopes to be interpreted to a large extent as arising from a particleand/or hole coupling to a spherical 68Ni core, see paragraph 2.2. It wasalso observed though that neutron excitations across N = 40 appear atlow energies. When entering the region below Z = 28 around N = 40 it



Onset of deformation below Z = 28 37

is not a priori obvious if the odd-mass cobalt structures still arise from

the coupling of a πf −

17/2 proton-hole with the adjacent nickel isotonestructure, like is the case for the odd-mass cobalt isotopes with N ≤ 36(see paragraph 2.3). The core-coupled states coexist with single-particleπf −2

7/2 p+13/2

, πf −27/2

f +15/2

and πf −27/2

p+11/2

states, but the intruder characteris too strongly mixed with the core-coupled configurations to developdeformation. One has to take into account that, with respect to thelighter odd-mass cobalt isotopes, the νg9/2 orbital approaches the Fermilevel and that, with respect to the nickel isotopes, a strong proton-neutron residual interaction is at work between the πf 7/2 protons andνf 5/2 and νg9/2 neutrons [39]. By removing protons in the πf 7/2 orbital,the νf 5/2 orbital is shifted up in energy and the νg9/2 is shifted down

in energy [93]. As a result, the N = 40 gap, which is rather small innickel already, is further reduced and the enhanced population of theνg9/2 orbital facilitates deformation.

The qualitative picture discussed above explains a lot of features be-low Z = 28. However, the strength of the tensor interactions and thusthe magnitude of the gap reduction and νg9/2 occupancies are not pre-cisely known. Therefore, the currently available experimental data ispresented in this section to get an idea of the importance and implica-tions of the proposed mechanism. Is the effect strong enough to developdeformation and if so, will it set in abruptly in the cobalt nuclei or isthere a gradual onset of collectivity present toward lower Z nuclei?

Fig. 2.13 shows the excitation energy E (9/2+) of the 9/2+ statein the odd-mass nickel, iron and chromium isotopes. In a simple shellmodel interpretation, this corresponds to the first excited state with oneneutron in the νg9/2 orbital. The 350-keV value of the (9/2+) state in63Fe is an upper limit, which is based on deep-inelastic reaction data bycomparing its unobserved γ decay with the observed γ decay from the9/2+ state in 61Fe [94, 97]. The 400-keV value of the (9/2+) state in67Fe is an approximate value, which is based on the β -decay scheme of 67Mn evidencing the presence of an isomer (T 1/2 = 62(23) µs) at ∼ 400keV [98] and a comparison with the 65Fe level structure where a 9/2+

isomer was discovered at an excitation energy of 402 keV [95, 99].Two effects are noticed in the E (9/2+) systematics. On the one

hand, it shows that the excitation energies of the isotopes drop whenapproaching N = 40, as a consequence of the νg9/2 orbital approaching




Neutron number (N)29 31 33 35 37 39 41 43

) +

E

( 9 / 2

0

500

1000

1500

2000

2500

3000

3500

4000

( )

Ni

Fe

Cr

Figure 2.13: E (9/2+) systematics of the odd-mass nickel, iron andchromium isotopes ranging from neutron number N = 29 to N =43. The data on nickel are taken from Refs. [20, 60], on iron fromRefs. [20, 94, 95] and on chromium from Refs. [20, 96].

the Fermi level when the pf shell is filled. On the other hand, theexcitation energies of the isotones drop typically with a energy differenceof ∼ 500 keV when moving away from Z = 28, which can be associatedwith the tensor interaction. At N = 33, the chromium E (9/2+) value

deviates from the observed trend as it is very similar to the iron E (9/2+

)value. Another deviation is seen for 67Fe. While the 9/2+ state becomesthe ground state in 69Ni, it levels off at ∼ 400 keV in 67Fe. Although it isvery speculative, it might point to an enhanced collectivity in 67Fe withrespect to 69Ni altering the spin and parity sequence of their respectivelevel structures.

A lot of information can be obtained from the systematics of theeven-even nickel (Z = 28), iron (Z = 26), chromium (Z = 24) andtitanium (Z = 22) isotopes. The top panel of Fig. 2.14 shows the sys-tematics of the first excited 2+ energies E (2+) of the even-even nickel,iron, chromium and titanium isotopes. At N = 28, all isotopes exhibit a

peak in E (2+), which is consistent with the expected closed shell struc-ture. At N = 32, no peak is observed for the nickel and iron isotopes, asmall peak appears for chromium and in titanium the peak at N = 32becomes even as large as at N = 28. This effect is attributed to a gap




in the effective single-particle energies between νp3/2 and νf 5/2 states

created by the gradual monopole migration of the νf 5/2 orbital as pro-tons are removed from the πf 7/2 orbital [100, 101]. The anti-correlation

with measured B(E 2; 0+ → 2+1 ) reduced transition probabilities in the52−56Ti even isotopes [102] and in the 54−58Cr even isotopes [103], shownin the middle panel of Fig. 2.14, placed the above interpretation on evenfirmer ground. The fact that E (2+) and B(E 2) values observed in 54Tiare comparable to those in 50Ti confirmed that the N = 32 titaniumisotope is as good a semi-magic nucleus as its N = 28 counterpart. TheE (2+) systematics of the even-mass chromium isotopes indicate that theeffect of the N = 32 subshell gap is less pronounced. Nevertheless, theirB(E 2) systematics show a minimum at N = 32, which is comparable

with the value at N = 28. Important to note is that the E (2+) of 56Ti(N = 34) comes down in energy again at the level of the E (2+) of 52Ti[104, 105]. Hence, the monopole migration of νf 5/2 is not that large thata subshell closure arises between the νp1/2 and νf 5/2 orbital.

Large-scale shell model calculations were carried out for the chromiumand titanium isotopes making use of the recently developed GXPF1Ainteraction, which takes into account the f p valence space but not g9/2[109]. It was found to be able to reproduce the E (2+) systematics of chromium and titanium isotopes up to N = 34 and to account for theN = 32 gap as resulting from the strong tensor interaction between πf 7/2protons and νf

5/2neutrons. It also predicts a N = 34 subshell closure

in the calcium isotopes, which have an empty πf 7/2 orbital. Contraryto the successful reproduction of the chromium and titanium E (2+) sys-tematics, the GXPF1A interaction falls short in reproducing the B(E 2)systematics. Despite the variations in E (2+) from N = 30 to 34, thecorresponding B(E 2) values are almost constant, which illustrates thelimitations of the calculations.

Beyond N = 34, the available experimental data are more scarce.Nevertheless, a striking contrast is revealed between the E (2+) system-atics of nickel isotopes and iron and chromium isotopes. While the 2+

energies of the nickel isotopes go again to a maximum at N = 40, those

of iron and chromium drop steadily. In first instance, this feature wasinterpreted in terms of strong deformation in the region near N = 40[106, 107]. The N = 40 gap in 68Ni is known to be very subtle al-ready as discussed in previous paragraphs. When protons are removed




) ( k e V )

+

E ( 2

500

1000

1500

2000

2500

Ni (Z=28)

Fe (Z=26)Cr (Z=24)

Ti (Z=22)

) ( W . u . )

+ 1 2

→ +

B ( E 2 : 0

2

4

6

8

10

12

14

1618

20 Ni (Z=28)

Fe (Z=26)

Cr (Z=24)

Ti (Z=22)

Neutron number (N)28 30 32 34 36 38 40 42

) +

) / E ( 2

+

E ( 4

1.5

2

2.5

3

Ni (Z=28)

Fe (Z=26)

Cr (Z=24)

Ti (Z=22)

Figure 2.14: E (2+) (top panel), B(E 2 : 0+ → 2+1 ) (middle panel)and E (4+)/E (2+) (bottom panel) systematics of the even-even nickel,

iron, chromium and titanium isotopes ranging from neutron numberN = 28 to N = 42. The data on nickel are taken from Refs. [20, 22,23, 28], on iron from Refs. [20, 97, 106], on chromium from Refs. [20,103, 107] and on titanium from Refs. [20, 102, 104, 105, 108].




from the πf 7/2 orbital, the N = 40 gap is even further reduced and

the deformation-driving νg9/2 orbital gets a more significant popula-tion. Moreover, the ν 2d5/2 orbital, which carries two units of spin lessthan the νg9/2 orbital, is also pulled down by the tensor interaction andenhances greatly the development of quadrupole collectivity [40]. Bothprocesses, the stronger population of the deformation-driving νg9/2 or-bital and the enhanced quadrupole correlations, thus increase collectiv-ity. Therefore, the interpretation of the observed E (2+) systematics wasthat the increased collectivity was sufficient to drive 66Fe and 64Cr tostrong deformation.

The bottom panel of Fig. 2.14 shows the systematics of the energyratio E (4+)/E (2+) of the first excited 4+ state to the first excited 2+

state for the nickel, iron, chromium and titanium isotopes. This ratiois a good indicator for the collective properties of a nucleus and rangesfrom values smaller than two for near magic nuclei towards the limit-ing value of 3.33 for strongly deformed nuclei. Values near 2.0, 2.5 and3.33 are all typical of different types of macroscopic collective behav-ior: spherical harmonic vibrator, axially asymmetric rotor and axiallysymmetric rotations, respectively [4].

The E (4+)/E (2+) values of the N = 28 isotones are less than twoand are thus consistent with a closed N = 28 subshell. In betweenN = 28 and N = 40 the nickel isotopes generally behave as sphericalvibrators and at N = 40 the small value is consistent with the magicfeatures of 68Ni.

The E (4+)/E (2+) values of the titanium isotopes are known up toN = 34 and are consistent with the N = 32 subshell gap.

For the chromium isotopes, the E (4+)/E (2+) value levels off atN = 32 and rises steadily from 2.06 to 2.65 at N = 38. The latter valueis still well below the rotational limit of 3.33, but is large enough to pro-vide evidence for the development of static deformation in 62Cr [108].Concerning 64Cr, a very interesting result is obtained in the recentlyperformed 9Be(68Ni,66Fe)X and 9Be(66Fe,64Cr)X two-proton knockoutreactions experiment [110]. It was found that the cross section of the

former reaction is consistent with calculations using the GXPF1 inter-action in the pf shell-model space, while the cross section of the latterreaction is unexpectedly small. This is a strong indication that theground states of 68Ni and 66Fe have a similar configuration, while a




structural change occurs when going from 66Fe to 64Cr, which suggests

that 64Cr is a well-deformed nucleus. This result draws special attentionfor further experimental efforts to extend the E (4+)/E (2+) systemat-ics toward 64Cr. Also the less neutron-rich 58,60Cr isotopes turn out tobe very peculiar. The experimental E (4+)/E (2+), E (6+)/E (2+) andE (8+)/E (2+) values in 58Cr are nearly identical to the values expectedby the E (5) dynamical symmetry [111]. Ref. [112] has shown that thissymmetry corresponds to the critical point of the shape phase transitionfrom a spherical vibrator to a γ -soft rotor. The E (4+)/E (2+) value in60Cr does not increase much. Despite the small enhancement in collec-tivity, its structure is suggested to be similar to the one of 58Cr.

The iron isotopes, which are situated between nickel and chromium,

exhibit different systematics. Up through N = 40, the E (4+)/E (2+)values are rather constant and typical for axially asymmetric rotors (∼2.5 values), except for N = 32 (2.07). In the latter case, one couldconsider some stabilizing effect from the N = 32 gap, despite the lowE (2+) energy and high B(E 2) value. As discussed above, there is astrong indication that the ground states of 68Ni and 66Fe have a similarconfiguration [110]. On the other hand, the rather high E (4+)/E (2+)value of 2.47 suggests a large collectivity in the excited states. TheE (4+)/E (2+) value in 68Fe rises to 2.66, which is comparable to thevalue of the deformed 62Cr. It is therefore tempting to assign as well astatic deformed structure to 68Fe.

2.5 The relevance of studying the 65,67Fe β decay

The 65,67Co isotopes form a bridge between the spherical nickel isotopesand the region of deformation below Z = 28 that is observed to set ingradually in excited states of 66Fe [106, 110] and is proposed for the64Cr ground state [107, 108, 110]. Because the onset of deformationbelow Z = 28 is understood only qualitatively, it is not clear a priorihow the cobalt isotopes are behaving, since the deformation mechanismdepends critically on the energy of the N = 40 and N = 50 shell gaps

[40]. Nuclear structure of the cobalt isotopes was until recently knownup to N = 37 and all of them can be interpreted as a πf −1

7/2proton

hole coupled to its adjacent nickel neighbor. Moreover, the low-energystructure of 67,69Ni and 68−70Cu could be explained as a coupling with



65,67Fe β decay 43

excited levels of the 68Ni core, even though neutron excitations across

N = 40 also play an important role [41].In the β decay of 65,67Fe, states of 65,67Co are fed in a selective way

and the deduced decay schemes will reveal important information ontheir nuclear structure. Consequently, they are a good testing groundfor the eventual magic character of the 68Ni core and the onset of de-formation. The results will also serve as a crucial test for the effectiveinteractions in the cobalt isotopes adjacent to 68Ni. More precise inter-actions allow more reliable extrapolations on the evolution of the Z = 28shell closure toward N = 50 and shed light on the question how magic78Ni is.





Chapter 3

Experimental setup

The 65,67Fe, 65,67Co and 71Co isotopes have been produced at the LISOLfacility [113, 114] at the Cyclotron Research Center (CRC) at Louvain-La-Neuve in a 30-MeV proton-induced fission reaction of 238U. The setupis schematically presented in Fig. 3.1, which is taken from Ref. [5]. Thetwo 10 mg/cm2-thick 238U targets were placed inside a gas cell in orderthat the recoiling fission products were stopped and thermalized in argonbuffer gas at 500-mbar pressure. As the fission products, dragged bythe argon flow, nearly reached the exit hole of the gas cell, they wereirradiated by two excimer-pumped dye lasers that resonantly ionized

the desired element to a 1+

charge state. The ions leaving the cellwere transported through a SextuPole Ion-Guide (SPIG) [115] to a highvacuum region, where they were accelerated over a potential difference of 40 kV. After separation according to their mass-over-charge ratio A/Q,the ions were implanted into a moveable tape, which was surroundedby three thin plastic ∆E β detectors and two MINIBALL γ -detectorclusters [116], as depicted in Fig. 3.2. The β particles are detected withan efficiency of about 50% by the three plastic detectors that cover 68%of 4π. The γ rays are detected by two MINIBALL clusters with a photo-peak efficiency of about 5.5% at 1332 keV. For an extensive descriptionof the experimental setup, the reader is referred to Ref. [5] and references

therein.An important issue in the discussion of the applied correlation tech-

nique (see appendix A) is the beam structure at the LISOL facility, whichis schematically shown in Fig. 3.3 as taken from Ref. [5]. For half-life de-

45



46 Experimental setup

G a s C e l l

B u f f e r

G a s

C y c l o t r o n

3 0 M e V

P r o t o n B e a m

2 3 8 U T a r g e t s

( 1 0 m g / c m

2 )

M a s s S e p a r a t o r

I o n G u

i d e

( S P I G )

β −

β −

β −

β −

D e t e c t i o n S e t - u p

L e u v e n I s o t o p e S e p a r a t o r - O n - L i n e L

a s e r - i o n

i z e d

r e a c t i o n p r o d u c t s

L a s e r s

A A *

A +

+ e

-

D a t a - a c q u i s i t i o n

S y s t e m

X I A

D G F - 4 C

I G O R

Figure 3.1: A schematic drawing of the LISOL facility as taken fromRef. [5].



Experimental setup 47

b e a m

implantation chamber

implantation into tapemylar windows

plasticdetectors

MINIBALLleft

MINIBALLright

1 cm

Figure 3.2: Schematic drawing of the top view of the detection setupas also shown in paper I. The two MINIBALL clusters and threeplastic detectors are indicated. Electric segmentation is indicated bydotted lines.

termination purposes data were acquired in an implantation-decay cyclewhere in a first period the proton beam was on and the mass separator

open (Macro ON in the figure), followed by a period when the protonbeam was switched off and the separator closed (Macro OFF in the fig-ure). After a fixed number of such cycles, the implantation tape wasmoved in order to remove long-lived daughter and contaminant activity.This information is conventionally written as timp/tdec/ctape, where timp

is the ”macro beam on time”, tdec the ”macro beam off time” and ctapethe ”number of implantation-decay cycles per tape move”. During themacro beam on period, the proton beam is, however, not constantly im-pinging on the 238U target, but there is a micro time structure present.The proton beam hits the target during 100 ms (micro ON in the figure)and is subsequently switched off for the next 100 ms (micro OFF in the

figure). The SPIG is closed when the proton beam is switched on andis opened after a delay of 2 ms after the proton beam is switched off.Consequently, ion extraction from the gas cell lasts only 98 ms duringone micro cycle. The reason for running in such a micro cycle is the large



48 Experimental setup

amount of charges created in the gas cell by the proton beam impact

leading to a reduced selectivity of the ion source. Additionally, there isa beam-related background radiation due to prompt neutrons, see alsosection A.4 in appendix A. The laser beams are constantly deliveredinto the gas cell at a repetition rate of 200 Hz.

Protonbeam

Separator

SPIG

Lasers

Secondarybeam

Zoomx20

(microON)

(microOFF)

Figure 3.3: The time structure of the LISOL beam. Picture takenfrom Ref. [5].



Chapter 4

Results

In order to determine the 65,67Co structure, different measurements arecarried out on the respective masses. Data are recorded with the lasersswitched off and with the lasers tuned to the iron and cobalt resonances.By comparing those data, the γ lines following the 65,67Fe and 65,67Co β decay can be identified. Using β -γ -γ coincidences, the 65,67Fe and 65,67Codecay schemes are obtained. Furthermore, the β decay of 71Co and 71Niis revisited in this thesis work. The results have been concentrated infour papers, of which two have been published and two are submitted.

In the 67Fe and 67Co decay, an isomeric transition is observed at 492

keV in the singles γ -ray spectrum, but not in the β -gated γ -ray spec-trum. Because of the absence of γ coincidences, the 492-keV transitioncannot be unambiguously placed in the A = 67 decay chain. To corre-late the 492-keV line in longer time ranges with β , γ , and β -coincident γ events, a novel correlation technique is developed aimed for applicationsat ISOL facilities. The formalism, limitations and possibilities of thetechnique are discussed in paper I. The developed correlation techniqueunambiguously established and fully characterized an isomeric state in67Co residing at an unexpected low excitation energy of 492 keV andinterpreted as a 1p-2h proton intruder state, which is subject of paperII. In paper III, the construction of the β -decay schemes of 65,67Fe and65

Co is discussed in full detail. Paper IV describes a collective state at454 keV in 71Cu that is directly fed in the β decay of the (1/2−) isomerin 71Ni.

In section 4.1, the newly developed correlation technique is intro-

49



50 Results

duced, which is subject of paper I and which is extensively discussed in

appendix A. Section 4.2 refers to the β -decay results of the 65,67Fe and65,67Co nuclei, which are discussed in papers II and III. One paragraphin this section is also devoted to the obtained results of the performed67Co β -decay analysis. Section 4.3 introduces paper IV.

4.1 Correlations

I. Decay correlations in the seconds range with laser-ionized,

mass-separated beams,D. Pauwels, O. Ivanov, J. Buscher, T. E. Cocolios, J. Gentens, M. Huyse,A. Korgul, Yu. Kudryavtsev, R. Raabe, M. Sawicka, I. Stefanescu, J. Vande Walle, P. Van den Bergh, P. Van Duppen,Nuclear Instruments and Methods in Physics Research Section B 266 (2008) 4600

In order to establish the 67Fe β -decay scheme, β , γ and β -coincidentγ events had to be correlated with each other in long time ranges upin the order of seconds. This has led to the development of a novelcorrelation technique, which is aimed for application on weakly pro-duced exotic nuclei through the ISOL scheme. The presented techniquediffers with other known correlation techniques in the fact that no ad-

vantage can be taken from an unambiguous implantation signal, like atIn-Flight separators or with post-accelerated ISOL beams, nor charac-teristic charged-particle signals like with α particles, β -delayed nucleons,and direct nucleons. Because the events in this case are less characteris-tic, the accurate knowledge of the random correlations becomes manda-tory. The formalism, limitations and possibilities are discussed in thispaper. The limitations are determined by two conditions, which havebeen derived from statistical principles and simulations based on theMonte-Carlo method:

N cyc 1 (4.1)

and

AcR2 + Ac

bg <

α2 − 1

∆t· N trtrue

N tr− Atr

true

εtr

· I bεc (4.2)



β decay of 65,67Fe and 65,67Co 51

where the definition of the different parameters is given in paper I and

appendix A. The parameter α2 is constrained to a maximum value of 5as deduced from the simulations. For a detailed report on all aspects of the correlation technique and its application at the LISOL facility, thereader is referred to appendix A.

4.2 β decay of 65,67Fe and 65,67Co

4.2.1 β decay of 67Fe

II. Shape isomerism at N = 40: Discovery of a proton intruder

state in

67

Co,D. Pauwels, O. Ivanov, N. Bree, J. Buscher, T. E. Cocolios, J. Gentens,M. Huyse, A. Korgul, Yu. Kudryavtsev, R. Raabe, M. Sawicka, I. Ste-fanescu, J. Van de Walle, P. Van den Bergh, P. Van Duppen, W. B. Wal-ters,Physical Review C 78 (2008) 041307(R)

The application of the correlation technique to the obtained 67Fe β -decay data turned out to be crucial to establish an isomeric state in 67Co(N = 40) at an unexpected low excitation energy of 492 keV. A (1/2−)spin and parity of the isomer is assigned on the basis of its long half-life

(T 1/2 = 496(33) ms) and a (7/2−

) ground state. Only the presence of aproton π1p-2h intruder configuration, which is associated with a prolatedeformation, can account for such a structure. Furthermore, good can-didates are found for the 3/2− and 5/2− members of a rotational bandbuilt on top of the shape isomer at excitation energies of 680 and 1252keV, respectively.

The paper compares the low-energy structure of 67Co with the lighterodd-mass cobalt isotopes, which have been introduced in section 2.3.While the energies of the first excited states in the nickel core rise ap-proaching N = 40, a π1p-2h intruder state decreases in energy and findsits minimum excitation energy at N = 40. The core-coupled states

are sufficiently separated in energy from the intruder state to preventsignificant configuration mixing resulting in a pronounced prolate defor-mation. The fact that the intruder state finds its minimum at N = 40means that the N = 40 subshell gap is considerably weakened with re-



52 Results

spect to 68Ni. This is consistent with what one expects from the strong

proton-neutron residual interactions between the protons in the πf 7/2orbital and neutrons in the νf 5/2 and νg9/2 orbitals. It is, however, sur-prising that the effect sets in so abruptly by removing only one protonfrom the 68Ni nucleus.

The excitation energy of the proton intruder state in 68Ni is esti-mated from summing the excitation energy of the proton intruder statesin 69Cu (E ∗ = 1711 keV) and 67Co (E ∗ = 492 keV). The result of 2203keV makes the (0+3 ) 68Ni state observed in the 68Co β decay a goodcandidate for the π(2p-2h) intruder state. Such an interpretation hassome consequences that are discussed in section 5.2.

4.2.2 β decay of 65,67Fe and 65Co

III. Structure of 65,67Co studied through the β decay of 65,67Fe

and a deep-inelastic reaction,D. Pauwels, O. Ivanov, N. Bree, J. Buscher, T. E. Cocolios, J. Gentens,M. Huyse, A. Korgul, Yu. Kudryavtsev, R. Raabe, M. Sawicka, I. Ste-fanescu, J. Van de Walle, P. Van den Bergh, P. Van Duppen, W. B. Wal-ters,(Submitted to Physical Review C)

While in paper II the intruder configuration in 67Co is extensively

discussed, this paper contains a detailed description of the results ob-tained in the 65,67Fe and 65Co β -decay experiments performed at LISOL.The 65Co structure is studied in detail from the combined analysis of 65Fe and 65Co β decay and complementary deep-inelastic data, whichwere taken at Argonne National Laboratory (USA).

The 65Co ground state has a spin and parity of (7/2−). The observedβ decay towards the 1274-keV level in 65Ni [91], which was previouslyassigned a spin and parity of 1/2− [117], raised the question for a pos-sible low-spin β -decaying isomer in 65Co. An earlier 64Ni(n, γ ) study[118], however, did not observe the level at 1274 keV, which stronglyindicates that the 1274-keV level in 65Ni has spin J ≥ 5/2. Apart from

the wrongly assigned 883- and 340-keV transitions, which are now un-ambiguously placed in the 65Fe decay scheme, the 65Co decay scheme isfound to be consistent with Ref. [91] and the 1274-keV level in 65Ni isnow assigned a spin and parity of (5/2−).




Recently, a long-lived isomer (T 1/2 > 150 ms) was discovered in 65Fe

at an excitation energy of 402 keV in Penning-Trap mass measurements[95, 99]. From the 65Fe β -decay data, two independent level structuresare deduced without any interconnecting transitions. The structurescorrespond to the decay of the (1/2−) ground state and the (9/2+)isomer in 65Fe, where the spin and parities were assigned in Refs. [95, 99].As such, the β -decay data confirm the measured isomer in 65Fe andprovides evidence that the isomer decays by β emission. By gatingon any two coincident γ rays observed in the 65Fe β -decay work, thetriple coincidence data from the deep-inelastic reactions reveal the near-yrast structure of 65Co. The spin and parities of the near-yrast levelsare deduced from a comparison with the near-yrast levels in 59,61,63Co

populated in other deep-inelastic reactions [84, 119]. This provides abasis to confirm the 65Fe β -decay scheme, as established from the LISOLdata, and to extend the 65Co level structure. Moreover, the near-yraststructure can be attributed to the decay of the high-spin (9 /2+) isomer(T 1/2 = 1.12(15) s) in 65Fe and the second level structure to the decayof the low-spin (1/2−) ground state (T 1/2 = 0.81(5) s) in 65Fe. Bothstructures are placed on top of the (7/2−) ground state. The observed65Co level structure is interpreted as arising from the coupling witha 66Ni core coexisting with proton intruder states at 1095 and 1223keV, analogous to the 492- and 680-keV states in 67Co, see paper II.Because both low- and high-spin 65Co levels are fed in the β decay of

65Fe, a rather complete 65Co level scheme is revealed at low energy. Allobserved levels below 1.7 MeV are interpreted and are assigned to thefive members of the πf −17/2 ⊗ 2+ quintet, coexisting with the 1095- and1223-keV states interpreted as proton intruder configurations.

A more detailed 67Fe decay scheme is presented and discussed. Theground state of 67Fe is assigned a spin and parity of (1/2−) and its β decay features similarities with the decay of the (1/2−) ground stateof 65Fe. Strong feeding is observed to three high-energy (1/2−), (3/2−)nickel core-coupled states and to a (3/2−) level suggested to arise froma proton intruder configuration. However, there is also evidence for

structural changes between 65Co and 67Co. A strong transition wasobserved in 65Co from the 1959-keV level to the spherical (7/2−) groundstate, whereas the analogous ground state transition was not observedfrom any of the ∼ 2.75-MeV levels in 67Co.



54 Results

Energy (keV)400 500 600 700

C o u n t s / k e V

1000

2000

3000

4000

5000

6000

7000

8000

492

511

694

Time (ms)2 00 0 2 20 0 240 0 26 00 28 00

C o u n t s / 1 0 0 m s

210

492-keV decay fit

Figure 4.1: Singles γ -ray spectrum during the last 85 ms of mi-cro beam off periods and during the beam off period in the 2s/2s/3implantation-decay cycle. The lasers are tuned resonantly on cobaltand the mass separator tuned on mass A = 67. The 492- (67mCo de-cay) and 694-keV (67Co decay) lines are indicated. The insert showsthe decay behavior of the 492-keV peak with multiplicity M = 1 (seetext) during the first 900 ms of the beam off period.

4.2.3 β decay of 67Co

Apart from the 65,67Fe and 65Co β -decay results that have been presented

in papers I-III, also the β decay of 67

Co was investigated and the decayscheme that was already established in the work of Ref. [44] was verified.States have been established at excitation energies of 694, 1007 and 2155keV, see Fig. 2.3 of this work and Fig. 4 of Ref. [44]. The 2155-keVlevel is observed to decay solely to the ground state. The 1007-keVstate is isomeric (T 1/2 = 13.3(2)µs [34]) and decays through the 313-keVtransition toward the 694-keV state, which subsequently decays to theground state.

With the lasers tuned resonantly on cobalt and the mass separa-tor tuned on mass A = 67, data have been acquired in a 2s/2s/3implantation-decay cycle. Fig. 4.1 shows the spectrum of single γ events

during the last 85 ms of micro beam off periods and during the beamoff period. The 492- (67mCo decay) and 694-keV (67Co decay) lines arepresent. Since the 492-keV γ peak corresponds to the γ decay of the492-keV isomer in 67Co, the half-life of the isomer can be deduced from




Energy (keV)0 1000 2000

C o u n t s / k e V

0

200

400

600

800

1000

1200

1400

1600

511

694

Energy (keV)1500 2000 2500

C o u n t s / k e V

0

5

10

15

20

25

30

1460

Tc)106

1970 (

2155

2706

Figure 4.2: Vetoed β -gated γ -ray spectrum in the 2s/2s/3implantation-decay cycle. The lasers are tuned resonantly on cobaltand the mass separator tuned on mass A = 67. The insert zooms inon the energy region from 1400 to 2750 keV.

a single exponential fit of the 492-keV decay behavior. The inset of thefigure shows the fitted decay behavior of integrals of multiplicity M = 1single 492-keV γ rays1, from which a half-life value of 503(42) ms wasdetermined. This is consistent with the value of 483(56) ms determinedfrom the correlations. These values have been combined into a weightedaverage value of 496(33) ms, which is reported in paper II as the final

half-life value. The half-life of the 67Co ground state (T 1/2 = 329(28)ms) has been deduced from the correlations only, because fitting the694-keV mother-daughter decay behavior is much less sensitive to itshalf-life value, even when the half-life of the isomer is fixed to 496 ms.Instead, it has been checked that the 694-keV mother-daughter decaybehavior is consistent with the correlation half-life results and directproductions of the 67Co ground and isomeric state.

To suppress the true summing of β particles with γ rays in the ger-manium crystals, prompt γ events are vetoed if the β event occurredat the same side of the detection setup [120]. The vetoed, β -gated γ spectrum is presented in Fig. 4.2. The spectrum contains γ lines origi-

nating from 67Co β decay at 694 and 2155 keV [44], a γ line originating

1A γ event was registered by one core signal, while none of the other 5 core signalsnor one of the 3 β detectors fired within a prompt window of ±500 ns.



56 Results

Table 4.1: Transitions in 67Ni from 67Co β decay are indicated bytheir energy E (keV), the corresponding β -gated peak count rate Aγ

and transition intensity Irel relative to the 694-keV transition (100 %).Multiply I rel by 0.942(12) to get absolute intensities. The γ -ray ener-gies of coincident events are listed in the last column with the numberof observed β -γ -γ coincidences between brackets.

E (keV) Aγ (cts/h) Irel (%) Coincident γ -events313.0 (1)a 3.1 (3) 1.9 (4) 694(15)a

694.4 (1) 124 (2) 100 313(17)a, 1460(3)1460.4 (3)b 1.6 (3) 2.3 (6) 694 (2)2154.5 (3) 3.3 (4) 6.2 (13) -a Observed in the delayed coincidence window of 0.35− 50 µs after

the β event.b The 1461-keV line is tentatively attributed to the 67Co decay

on the basis of the energy difference between the states at 2155

keV and 694 keV. See text for a discussion on the weak β -γ -γ

coincidences.

from 106Tc β decay at 1970 keV and the 511-keV line. The 511-keV lineoriginates from high-energy γ rays undergoing pair production in var-ious materials of the detection setup resulting in β -coincident 511-keVevents [5]. The source of the high-energy γ rays is twofold:

1. the soft component of the cosmic radiation producing high-energyBrems-strahlung, based on the fact that the β -coincident 511-keVline is observed in background spectra [5];

2. neutron-induced high-energy γ rays, based on the observed β -coincident 511-keV count rate, which is during the micro ON pe-riods (see Fig. 3.3) ∼ 9 times higher than the background countrate. Note that during the micro and macro OFF periods its countrate is consistent with the background count rate. The neutronsoriginate from the cyclotron beam, which induces proton reactionson the gas cell windows, the uranium target, and the beam dump.

Most of the materials in our detection setup consists of materi-als with high neutron-capture or neutron-scattering cross sections(e.g., isotopes of hydrogen, aluminum, silicon, iron, copper, andgermanium).




C o u n t s / k e V

1

2

3

4

5

6

7 s)µ(350 ns- 50γ s)-µ-313(350 ns- 50βa)

694 (15)

Energy (keV)500 1000 1500

C o u n t s / k e V

0

2

(350 ns)γ s)-µ-313(350 ns- 50βb)

Figure 4.3: Energy spectra of γ rays coincident with β -gated 313-keV events in a delayed coincidence window of 0.35−50 µs after the β event. In panel (a), the γ rays are in prompt coincidence with the 313-keV events, while in panel (b), the γ rays are in prompt coincidencewith the β events.

The 106Tc nuclei could reach the detection setup by the formation of a A = 132 molecule in a double-charged state, e.g. (106TcCO)2+. Theweak γ lines at 1460 and 2706 keV could not be attributed to a con-

taminating β -decaying nucleus and, therefore, one could consider it as atransition following 67Co β decay. The energies of the observed transi-tions following 67Co β decay, including the 1460-keV line, are listed inTable 4.1. Also their count rates, γ intensities relative to the 694-keV γ ray (I rel = 100), and coincident γ lines are indicated.

The 1460-keV line matches exactly the energy difference between thestates at 2155 keV and 694 keV, see Fig. 4 of Ref. [44]. In this case,one expects 6(2) coincidences between β -gated 694-keV and 1460-keVevents. However, only 2(2) coincident 694-keV γ rays are observed incoincidence with β -gated 1460-keV events. On the other hand, its decaybehavior in the implantation-decay cycle is consistent with the one of

the 694-keV line. There is a large uncertainty though due to the lowstatistics in the 1460-keV line. On this basis, it is tempting to placethe 1460-keV line as a transition in 67Ni, but it is realized that the datado not provide strong evidence either. From the β -gated γ spectrum



58 Results

with a delayed coincidence window of 0.35 − 50 µs after the β event,

the isomeric 313-keV transition (T 1/2 = 13.3(2) µs [34]) following 67Codecay as suggested in the work of Ref. [44] is unambiguously established.

In Fig. 4.3, energy spectra are shown of γ rays coincident with β -gated 313-keV events with the 313-keV γ rays in a delayed coincidencewindow of 0.35 − 50 µs after the β event. Fig. 4.3(a) shows the γ raysin prompt coincidence with the 313-keV events. A coincident peak of 15counts is observed at 694 keV, which is in agreement with the 313-keVtransition feeding the 694-keV level. Fig. 4.3(b) shows the γ rays inprompt coincidence with the β events. Peaks in this spectrum wouldcorrespond to transitions feeding the isomeric 1007-keV level, but noclear peaks could be identified.

In conclusion, the 67Co data confirm the decay scheme established byRef. [44]. In addition, there is an indication that a 1460-keV transitioncan be placed as de-exciting the 2155-keV level into the 694-keV level.The 492-keV decay behavior reveals a half-life value of 503(42) ms of the 492-keV state in 67Co, which is consistent with the half-life valueof 483(56) ms extracted from the correlations in the iron data. As aresult, this supports the reliability of the extracted half-life values fromthe correlations.

4.3 β decay of 71Ni and 71Co

IV. Evidence for a 1/2− β -decaying isomer in 71Ni,I. Stefanescu, D. Pauwels, N. Bree, T. E. Cocolios, J. Diriken, S. Fran-choo, M. Huyse, O. Ivanov, Yu. Kudryavtsev, N. Patronis, J. Van deWalle, P. Van Duppen, W. B. Walters,(Submitted to Physical Review C)

This paper reports on the investigation of the population mechanismfor the 454-keV level in 71Cu. This level was identified for the first timein a recent Coulomb-excitation measurement with a radioactive beamof 71Cu [38]. The selective nature of the Coulomb-excitation process as

well as nuclear-structure considerations constrain the possible spin andparity values for the newly observed state to (1/2−).

The proposed spin value of (1/2−) for the 454-keV level in 71Cuout of the Coulomb-excitation study rules out the possibility of a direct



β decay of 71Ni and 71Co 59

β branch from the 9/2+ ground state of 71Ni. Furthermore, the lack

of γ -ray coincidences in the β -decay study of Ref. [60] also excludesindirect feeding from the ground state of 71Ni. Reanalyzing the β -γ andγ -γ coincidences obtained in the 71Ni [60] and 71Co β -decay studies atLISOL, revealed evidence that the γ intensity of the 454-keV level in thedecay of 71Ni is enhanced when the source of 71Ni is obtained from theβ decay of 71Co. This is explained by the fact that 71Co feeds a (1/2−)isomer in 71Ni [121], which subsequently decays by β emission and feedsthe (1/2−) state at 454 keV and the 3/2− ground state in 71Cu. Inthis work, the half-life of the (1/2−) isomer in 71Ni was determined as2.3(3) s.





Chapter 5

Discussion

In chapter 2, the 65,67Co nuclei were approached from three differentperspectives in the Z = 28 and N = 40 region: from the spherical nickelisotopes, from the lighter odd-mass cobalt isotopes, and from the onsetof deformation below Z = 28. This chapter is devoted to a discussionof new insights in nuclear structure features in the Z = 28 and N = 40region based on the 65,67Fe, 65,71Co and 71Ni β -decay studies that aredescribed in the respective papers presented in this work. In section 5.1,the low-energy structures of 65,67Co are discussed from the perspectiveof the lighter odd-mass cobalt nuclei. Section 5.2 focusses on intruderstates in 68Ni and a comparison with 90Zr, the Z = 40 counterpart of 68Ni. This section contains also further considerations concerning theevolution of intruder states and the onset of deformation near Z = 28and beyond N = 40, as well as near N = 40 and below Z = 28. In thefinal section 5.3, the β decay of the (1/2−) isomer in 71Ni toward the(1/2−) state at 454 keV in 71Cu is discussed. Additional informationcan be found in the respective articles.

5.1 The odd-mass cobalt isotopes with A ≤ 67

In section 2.3, the low-energy structure of the odd-mass cobalt isotopes

with A ≤ 63 could be discussed in great detail, while prior to this workthe 65,67Co isotopes were poorly known. A remarkable similar low-energystructure was noticed for the odd-mass cobalt isotopes of mass A ≤ 63.Their low-energy structure is composed of a 2+-coupled multiplet with

61



62 Discussion

spins ranging from 3/2− to 11/2− and a 1/2− and a 3/2− state with

πp+11/2πf −

27/2 and πp+13/2πf −

27/2 single-particle character, respectively. Thelatter 1/2− and 3/2− states are strongly mixed with the πf −1

7/2core-

coupled states preventing the development of deformed bands. Becauseof the stabilizing effect of the N = 40 gap in the nickel isotopes, onewould expect that the number of valence neutrons in cobalt isotopesdecreases when approaching 67Co (N = 40). In the N = 49 isotonescounterpart the analog stabilizing effect of the Z = 40 subshell gap isobserved. The intruder configuration is at a minimal excitation energyat 34Se, mid-shell between Z = 28 and Z = 40 and goes to a maxi-mum again towards 40Zr, consistent with a sub-shell closure at Z = 40[13, 122]. As a consequence, proton-intruder configurations in the cobalt

isotopes, like πp+11/2πf −27/2 and πp+13/2πf −27/2, are expected to go up in exci-tation energy again when approaching N = 40.

Fig. 5.1 is the extended version of Fig. 2.12 from section 2.3 using thesame conventions. The additional data points are based on the new re-sults for the 65,67Co isotopes. The filled circles mark the 2+1 core-coupledstates with spins (J = 5/2) or higher and the filled tip-up triangles markthe 2+1 core-coupled (3/2−) states. The 67Co level at 1859 keV has notbeen explicitly discussed in paper III, but it is tentatively indicated inthe figure as a 2+1 core-coupled (3/2−) state. This tentative interpreta-tion is solely based on the (1/2−, 3/2−) assignment from experimental

information and the excitation energy of the 1859-keV state, which isclose to the excitation energy of the 2+1 state in 68Ni. The filled starsmark the 1/2− states with single-particle character.

As illustrated in Fig. 5.1 and discussed in paper II, exactly the op-posite feature is observed as expected from a stabilizing N = 40 gap.While the core-coupled multiplets of 65,67Co follow the energy trend of the 2+ and 4+ core states, the (1/2−) proton intruder configurationcomes down in energy. In 67Co, there exists a rather large energy differ-ence between the (1/2−) intruder state at 492 keV and the lowest-energycore coupled state preventing large configuration mixing like is the casein the lighter cobalt isotopes. Based on the Nilsson diagram of Fig. 1.2

[7], a large quadrupole deformation parameter of 0.25 < ε2 < 0.4 couldbe attributed to the 492-keV state. Moreover, band members built ontop of the (1/2−) state are assigned at 680 and 1252 keV, see paper II.The (1/2−) intruder level sets already in in 65Co at 1095 keV (see paper



The odd-mass cobalt isotopes with A ≤ 67 63

Neutron number (N)30 32 34 36 38 40

E n e r g y

( k e

V )

0

1000

2000

3000

) Ni+

E(4

) Ni+

E(2cc) Co--11/2-E(5/2

sp) Co-

E(1/2

cc) Co-

E(3/2

sp) Co-

E(3/2

Figure 5.1: Systematics of the odd-mass cobalt isotopes rangingfrom mass A = 57 to A = 67. The 2+ and 4+ nickel core states aremarked with open circles and squares, respectively. The filled symbolsmark states in the cobalt isotopes: the 1/2− state with single particlecharacter (sp) by the red star; the 3/2− state with single particlecharacter (sp) by the red tip-up triangle; the 3/2− state with 2+ core-

coupled character (cc) by the blue tip-down triangle; the other stateswith 2+ core-coupled character (cc) by the circles.

III), 482 keV lower in energy than the first excited (1/2−) level in 63Co.For 68Ni, it is known that Z = 28 is at a pronounced proton shell gapof 5.3(3) MeV (see section 5.2) and the observation of a proton intruderconfiguration in 67Co so low in excitation energy implies strong pairingand proton-neutron residual interactions [4, 13], see next section 5.2 fora more elaborate discussion. This means that many valence neutronshave to be present to account for its low excitation energy. It was no-

ticed already in 68Ni that neutrons are easily pair scattered across theN = 40 gap [22]. By taking away one proton from the πf 7/2 protonorbital, the tensor interaction causes a further reduction of the N = 40gap facilitating pair scattering across, which illustrates the subtlety of



64 Discussion

the N = 40 gap.

Furthermore, it is noticed in paper III that the 65Fe and 67Fe groundstates feature similar β -decay patterns. Strong feeding is observed tothree high-energy (1/2−), (3/2−) nickel core-coupled states arising fromνp−1

1/2f −15/2

and νg+29/2

p−11/2

f −15/2

neutron configurations, respectively, and to

a (3/2−) level suggested to arise from a proton intruder configuration,which in the case of 65Co is strongly mixed with the 2+ core-coupledconfiguration. However, there is also evidence for structural changesbetween 65Co and 67Co. A strong transition was observed in 65Co, forinstance, from the 1996-keV level to the spherical 7/2− ground state,whereas the analogous ground state transition was not observed fromone of the

∼2.75-MeV levels in 67Co. The structure could not be dis-

cussed quantitatively due to the lack of reliable large-scale shell modelcalculations.

5.2 Intruder properties of 68Ni compared to 90Zr

The established (1/2−) isomeric state at 492 keV in 67Co, interpreted asa π(1p-2h) excitation (see paper II), provides a basis for further consid-erations on the Z = 28 and N = 40 gap in the immediate neighborhoodof 68Ni. As discussed in paper II, the (0+3 ) state in 68Ni at 2.511 MeV canbe interpreted as the proton π(2p-2h) intruder state based on the protonintruder excitation energies in 67Co and 69Cu. The low-lying 68Ni struc-ture is thus dominated by excitations across the N = 40 (the 0+2 stateat 1770 keV) [31] and the Z = 28 (the 0+3 state at 2511 keV) (sub)shellgaps. Starting from this observation the discussion is extended to the0+ states in 68Ni as well as in the equivalent Z = 40 90Zr nucleus.

5.2.1 Shell gaps and intruder states at Z = 28, N = 40 andZ = 40, N = 50

As discussed in Ref. [13], intruder states result from particle-hole ex-citations across the major closed shells. Nevertheless, they can appearat low excitation energies because of both strong pairing and proton-

neutron correlations. For the case of 2p-2h 0+ intruder states, this isexpressed [123] as

E intr(0+) = 2(ε p − εh)−∆E pairing + ∆E πν , (5.1)



Intruder properties of 68Ni compared to 90Zr 65

where E intr(0+) is the excitation energy of the 0+ intruder state, ε p−εh

the shell gap energy1, ∆E pairing the nucleon pairing energy, and ∆E πν the energy of the proton-neutron residual interactions. The shell gapenergy can be deduced from measured nucleon separation energies [123,124]. In the nucleus A(Z, N ), the proton separation energy is a goodestimate for the proton single-hole energy, i.e., εh(Z, N ) = −S p(Z, N ).Now, S p(Z + 1, N ) will not, in general, be a good estimate for ε p(Z, N ),since residual interactions can perturb the shell gap. Therefore, in thedetermination of the unperturbed particle-hole energy, one needs both ε pand εh in the same nucleus. A graphical method [125] has been suggestedfor obtaining the value ε p − εh from nucleon separation energies nearclosed shells. This is done by extrapolating from above the shell closure

and thereby correcting for the difference in energy it takes to remove anucleon from a given orbital above the Fermi level in a nucleus A(Z, N )compared to the nucleus A + 1(Z + 1, N ), i.e. the expression

ε p − εh = S p(Z, N )− S p(Z extr., N ) (5.2)

is used.The nucleon pairing energy for a 2p-2h configuration at a closed shell

is according to Ref. [123] best determined by

∆E pairing = ∆E pairing( p) + ∆E pairing(h), (5.3)

with (for protons)

∆E pairing(h) = 2S p(Z, N )− S 2 p(Z, N ), (5.4)

∆E pairing( p) = −2S p(Z + 1, N ) + S 2 p(Z + 2, N ), (5.5)

where (Z, N ) denote the closed-shell proton number and neutron num-ber. Remark that the definition of ∆E pairing( p) has opposite sign com-pared to the definition published in Ref. [123].

In the shell model framework, the proton-neutron residual interac-tion is considered in a multipole expansion, of which typically the firsttwo terms are taken into account, i.e. the monopole and quadrupole term[4]. Fig. 5.2 shows a schematic representation of the quadrupole proton-neutron energy ∆E Q [123] as a function of neutron (proton) numberbetween the closed shells at N (Z ) = 28 and N (Z ) = 50 assuming two

1The subscripts p and h denote particles and holes, respectively.



66 Discussion

N,Z30 35 40 45 50

( a

. u . )

Q

E ∆

-1

-0.8

-0.6

-0.4

-0.2

-0N=40 is closed

N=40 is open

Figure 5.2: Schematic representation of the quadrupole proton-neutron energy ∆E Q [123] as a function of neutron (proton) numberbetween the closed shells at N (Z ) = 28 and N (Z ) = 50 assuming twoextreme cases: N (Z ) = 40 is a closed (dashed lines) and N (Z ) = 40is an open (full line) shell configuration.

extreme cases: Z (N ) = 40 is a closed (dashed lines) and open (full line)shell configuration. In the case that Z (N ) = 40 is open, the contributionof quadrupole correlations is strongest around N = 39. On the otherhand, if Z (N ) = 40 is a shell closure, the contribution of quadrupole

correlations becomes negligible around Z (N ) = 39.In Table 5.1, neutron and proton shell gap and pairing energies are

listed as deduced from equations 5.2 and 5.3, respectively, for the 68Ni(Z = 28, N = 40) and the 90Zr (Z = 40, N = 50) nuclei. The requiredseparation energies are taken from Ref. [24] or were obtained from mea-sured masses of 70−73Ni [25]. The excitation energies of the 2p-2h 0+

intruder states are listed in the third column. The proton-neutron resid-ual energy is calculated from equation 5.1, where it should be noted thatmixing with other 0+ states is not taken into account. The contributionof each term in equation 5.1 for the respective intruder states in 68Niand 90Zr is depicted in Fig. 5.3. Several features can be noticed.

The ν (2p-2h) and π(2p-2h) intruder states in 68Ni reside at respectiveexcitation energies of 1770 and 2511 keV, which are rather similar, whilethe Z = 28 shell gap is about 2.2 MeV larger than the N = 40 subshellgap. For both gaps, a large pairing energy exists and in case of N =




Table 5.1: 68Ni and 90Zr are compared for their excitation energies of the intruder 0+ states E intr(0+) arising from 2p-2h excitations acrossthe indicated neutron and proton gaps. Also their unperturbed protonand neutron shell gap energies ε p − εh, neutron and proton pairingenergies ∆E pairing , and the energy of proton-neutron correlations inthe respective intruder states ∆E πν are compared.

Isotope Gap E intr(0+) ε p − εh ∆E pairing ∆E πν (keV) (keV) (keV) (keV)

68Ni Z = 28 2511 5270(320) 4500(700) -3500(1000)68Ni N = 40 1770 3050(100) 4705(14) 380(200)90Zr Z = 40 1761 2670(90) 3593(8) 20(190)90Zr N = 50 4126 4445(8) 4093(12) -670(20)

4424 4445(8) 4093(12) -370(20)

40 it explains the low ν (2p-2h) excitation energy, while proton-neutroninteractions are not important. The latter is consistent with a rigid Z =28 shell closure without proton valence particles that can interact withthe neutrons. However, the low excitation energy of the π(2p-2h) staterequires a strong gain in binding energy from the proton-neutron residualinteractions (−3.5(10) MeV). This means that many valence neutronsare available accounting for such a strong proton-neutron interaction.

In90

Zr, the π(2p-2h) intruder state arising from proton excitationsacross Z = 40 appears at an excitation energy that is remarkably similarwith that of the ν (2p-2h) intruder state in 68Ni. This is caused, however,by a reduction of both the Z = 40 shell gap energy and the pairingenergy. So, although the excitation energies of both intruder states arealmost identical, the situations at N = 40 and Z = 40 are different. Aswas the case for the ν (2p-2h) intruder state in 68Ni, the low excitationenergy of the π(2p-2h) intruder state in 90Zr is solely explained by thegain in pairing energy, which is consistent with a rigid N = 50 shellclosure.

Based on the neutron ν (1p-2h) intruder excitation energy in 89Zr

(1627 keV) combined with the ν (2p-1h) excitation energy in 91Zr (2914keV) and observed 0+ states in 90Zr, the ν (2p-2h) configuration in 90Zr issuggested to be located at an excitation energy of 4126 (0+3 ) or 4424 keV(0+4 ) [20]. Both excitation energies are significantly higher than the



68 Discussion

Ni68(2p-2h) (N=40) ν (2p-2h) (Z=28)π

Zr90(2p-2h) (N=50) ν (2p-2h) (Z=40)π

E (

k e V )

6100

1770

0

νπE∆

pairingE∆

) h

ε - p

ε

2 (

νπE∆

pairingE∆

) h

ε - p

ε

2 (

νπE∆

pairingE∆

) h

ε - p

ε

2 (

pairingE∆ ) h

ε - p

ε

2 (

Figure 5.3: The contribution of each term in equation 5.1 is depictedto scale for the proton and neutron (2p-2h) intruder states in 68Ni andin 90Zr. The intruder state is indicated by a thick line.

analog energy of the π(2p-2h) state in 68Ni (2511 keV). However, theN = 50 shell gap is about 0.8 MeV smaller than the Z = 28 shellgap, while the pairing energies are rather similar. This implies that theproton-neutron residual interactions are much weaker in the ν (2p-2h)state of 90Zr than in the π(2p-2h) state of 68Ni. This difference can beexplained from the fact that pairing correlations are more important at

N = 40 than at Z = 40: at N = 40, the pairing energy is about 1.65MeV larger than the shell gap, while at Z = 40, this amounts only about0.9 MeV. Consequently, more neutrons are pair scattered across N = 40than protons across Z = 40 that can interact with the valence protonsor neutrons, respectively. The strong pair scattering across N = 40 wasinferred already from the measured B(E 2 : 0+1 → 2+1 ) value in 68Ni [22].Ref. [31] also noted that the reason for the observed smooth behaviorof δ2n(Z = 28, N = 40) (see Fig. 2.1(c)) and δ2 p(Z = 40, N = 50) hasbeen found to be different for 68Ni and 90Zr, respectively. In 68Ni, it isattributed to the large energy gain due to J = 0 pairing correlations inthe νg9/2 subshell. In 90Zr, it is attributed to the large energy gain due

to J > 0 residual interactions.The fact that the pairing energy is higher in 68Ni (∆E pairing =

4705(14) keV) than in 90Zr (∆E pairing = 3593(8) keV) can be under-stood from two features [4]. The coupling constant G of the pairing




force decreases with mass A in heavier nuclei where the outer nucleons

are generally further apart and so spatial overlaps are likely to be less.G may also be different for protons and neutrons, being lower for theformer because of Coulomb repulsion. Commonly used prescriptions areG p = 17

A MeV and Gn = 23A MeV for proton and neutron scattering,

respectively. Both features favor stronger pair scattering across N = 40in 68Ni than across Z = 40 in 90Zr.

Although the unperturbed Z = 40 shell gap is smaller than theunperturbed N = 40 gap, pairing correlations cause a Z = 40 subshellclosure that is more rigid than the N = 40 subshell closure. This isillustrated by the respective excitation energies of the ν (2p-2h) state in90Zr and of the π(2p-2h) state in 68Ni. The gain in binding energy from

proton-neutron residual interactions is large in 68Ni and, as depicted inFig. 5.2 by the full line, this indicates that N = 40 behaves rather as anopen shell configuration. In 90Zr, proton-neutron residual interactionscontribute significantly less to the excitation energy of the ν (2p-2h) stateindicating that Z = 40 behaves rather as a closed shell configuration,as depicted in Fig. 5.2 by the dashed lines. A closed Z = 40 and anopen N = 40 gap for the intruder configurations is consistent with theobserved energy systematics of 1p-2h intruder states in the N = 49isotones and in the Z = 27 isotopes, which was discussed already inprevious section 5.1 and in paper II. In the N = 49 isotones, theirexcitation energies show a maximum toward zirconium (89Zr), while in

the Z = 27 isotopes a (preliminary) minimum is observed at N = 40(67Co), see also Fig. 5.1. Note that the dependence of the proton-neutroninteraction on specific proton and neutron orbitals should be furtherconsidered.

5.2.2 Monopole ρ2(E0) and quadrupole B(E2) transitionstrengths

In 58,60Ni, B(E2) transition strengths and monopole strengths ρ2(E0)have been measured between the lowest-lying 0+ and 2+ states [37].Strong E0 transitions (ρ2(E0) = 80(30), 77(42) · 10−3 in 58,60Ni, resp.)

were observed from the π(2p-2h) 0+ intruder state to the ground state.In 68Ni, only the monopole transition strength from the 0+2 state at1770 keV to the ground state is known (ρ2(E0) = 4.4(10) · 10−3) [126].Unfortunately, there is no information available on monopole transition



70 Discussion

strengths from intruder states in the 62,64,66Ni isotopes. On the other

hand, the ρ2(E0;0+2 → 0+1 ) value is known in the Z = 40 counterpart90Zr (3.46(14)·10−3) [126], with the 0+2 state at 1761 keV identified as theπ(2p-2h) state. This value is remarkably similar to the 68Ni ρ2(E0) valueand is significantly less compared to the π(2p-2h) E0 decays in 58,60Ni,which supports the ν (2p-2h) assignment of the 0+2 state in 68Ni [31].The 2+1 to 0+2 transition in 68Ni has never been observed, but should notbe considered as a direct indication of a low B(E2; 2+1 → 0+2 ) transitionstrength, since from Weisskopf estimates an E2 γ ray of 2.033 MeV(2+1 → 0+1 ) is 2.8 · 104 times faster than one of 0.263 MeV (2+1 → 0+2 ).In fact, calculations, as shown in Ref. [31], predict a B(E2;2+1 → 0+2 )value of 12 W.u. and a B(E2;2+1

→0+1 ) value of 3.2 W.u. The former

is in agreement with the B(E2;2+2 → 0+2 ) value in 58Ni, where the 0+2state is believed to be the ν (2p-2h) state.

The considerations given above call for the determination of theρ2(E0;0+3 → 0+1 ) transition strength in 68Ni to compare with the ρ2(E0)transition strengths of the proton intruder states in 58,60Ni into theirground states.

5.2.3 The Z = 28 gap towards N = 50

Beyond N = 40, an interesting interplay will occur. On the one hand,the number of available valence neutrons is reduced hampering proton

excitations across Z = 28 [13]. On the other hand, the Z = 28 shellgap is reduced through the strong monopole interaction between theneutrons populating the νg9/2 orbital and protons in the πf 7/2 and πf 5/2orbitals [39]. Indirect experimental indications for the reduction of theZ = 28 gap beyond N = 40 are found in 70Ni [23], 70,71,73Cu [38, 57]and 74Zn [23], where increased collectivity is observed from measuredB(E 2) values in Coulomb excitation experiments. In addition, it is seenfrom the Coulomb excitation work of Ref. [38] that the 7/2− protonintruder state goes steeply down from 1711 keV in 69Cu to 981 keVin 71Cu and levels off at 1010 keV in 73Cu. Note, however, that the(7/2−) spin assignment in 73Cu is weak [59]. Nevertheless, if such a

steep reduction in excitation energy of the intruder configuration in thecobalt isotopes going from N = 40 to N = 42 exists, it means thatthe (1/2−) deformed proton intruder state becomes the ground state in69Co: an unexplored ”Island of inversion” might be out there. Moreover,



Discovery of a collective (1/2−) state in 71Cu 71

in case that the intruder state effectively lowers further in energy beyond

N = 40, β -decaying isomerism is expected in these cobalt isotopes dueto the reduced energy difference with the coexisting 7/2− single-particlestate.

5.2.4 The N = 40 gap towards Z = 20

Below Z = 28, the occupation of the πf 7/2 proton orbital is reducedinducing a reduction of the N = 40 gap through a strong monopoleinteraction of the πf 7/2 protons with the neutrons in the νf 5/2 andνg9/2 orbitals [93]. From the observation that a deformed intruder stateexists at an excitation energy of only 492 keV in 67Co, ground state

deformation is expected to set in rather quickly in N = 40 isotoneswith lower Z . In section 2.4, the onset of deformation below Z = 28near the N = 40 gap was discussed. Although the first excited 2+1excitation energy in 66Fe is low [106], the 66Fe ground state is assigneda structure similar to the spherical 68Ni ground state [110]. This canbe interpreted in terms of intruder configurations at low energy, but notlow enough to drive the ground state to a deformed shape. A small9Be(66Fe,64Cr)X two-proton knock-out cross section [110] and the lowfirst excited 2+ energy in 64Cr [107] provide strong indications that the64Cr (Z = 24) ground state is well-deformed. Unfortunately, other N =40 nuclei below Z = 28 are not experimentally known. Spectroscopic

studies of the nuclei below Z = 28 and near N = 40 like, e.g., in the61−66Fe isotopes [97] would yield valuable information concerning theonset of deformation in this region.

5.3 Discovery of a collective (1/2−) state in 71Cu

Remarkable similarities are observed between the A = 69 and A = 71decay chains from cobalt to copper. In both nickel isotopes, the groundstate is the 9/2+ single particle state arising from an odd number of neutrons in the νg9/2 orbital and a β -decaying (1/2−) isomer exists

arising from a νp−1

1/2neutron-hole configuration. The isomer in 69Ni is

observed to decay predominantly into the (3/2−) state of 69Cu at 1298keV (log f t = 4.3(2)) arising from a πp+1

3/2⊗ 0+2 (68Ni) configuration and

to the πp+13/2⊗ 0+1 (68Ni) ground state (log f t = 5.3(2)) [49]. The 71Ni



72 Discussion

isomer decays into the 454-keV level, which, in contrast to the A = 69

case, has a spin and parity of (1/2−

), and to the 3/2−

ground state of 71Cu. As discussed in Ref. [38], the large B(E 2) value measured forthe 454-keV transition excludes a single-particle character of πp+1

1/2type

for the 454-keV level. Instead, the increased collectivity indicates thatthe observed β -decay branch from the 1/2− isomer in 71Ni to the 454-keV level in 71Cu can be explained by assuming that the odd protonoccupies the K = 1/2 downsloping orbit of the πp3/2 orbital, on theprolate side, while the neutron part of the wave function is, depending ondeformation, dominated by νp+2

1/2g+29/2

or νp−21/2

g+49/2

configurations. Hence,

the β decay of the 1/2− isomer in both 69,71Ni isotopes is interpretedto proceed via a fast Gamow-Teller transition but in the case of 71Ni,

the spin of the final state in the daughter nucleus is changed by thedeformation.

In fact, the structure of the 454-keV level in 71Cu is similar to the(1/2−) proton intruder state in 67Co, which is also understood fromthe population of the odd proton in the K = 1/2 downsloping orbitof the πp3/2 orbital. The onset of collectivity is associated with thequenching of both Z = 28 and N = 40 gaps through the combinedeffect of the attraction and repulsion between the f p protons and g9/2neutrons [23, 39, 57], which supports the suggested ”Island of inversion”below Z = 28 and beyond N = 40.

It is also worthwhile to notice that the ground state of both 69,71Co

was assigned a spin and parity of (7/2−), while in previous section a pos-sible inversion of the (1/2−) proton intruder state and (7/2−) groundstate was considered. Because the energy difference between both statesis expected to decrease with respect to the situation in 67Co, one has tokeep in mind that a β -decaying 1/2− (isomeric or ground) state in the69,71Co isotopes is nevertheless possible. Penning-trap mass measure-ments and/or β -decay studies of 69,71Fe are necessary to shed light onthis issue.



Chapter 6

Conclusions and outlook

In this thesis, the neutron-rich region around Z = 28 and N = 40 hasbeen investigated with a specific focus on the low-energy structure of the65,67Co isotopes. They were investigated in the β decay of 65,67Fe and65,67Co isotopes, which were produced at the LISOL facility in Louvain-La-Neuve, Belgium. Crucial results could be achieved after the success-ful development of a new correlation technique aimed to be applied atISOL facilities. The 65,67Fe decay schemes have been established andevidence was found for some adjustments of the previously established65Co decay scheme [91]. Furthermore, combining the conclusions fromCoulomb excitation on 71Cu with a re-investigation of 71Co and 71Ni

data taken some time ago at LISOL revealed a β -decaying isomer in71Ni.

6.1 A new correlation technique

Thanks to the availability of weak, yet pure beams in low-backgroundconditions at the LISOL facility, correlations between single γ and β -coincident γ events were established in long time windows ranging upin the order of seconds. The technique was presented and its limita-tions were formulated amongst others through a systematic investiga-

tion of Monte-Carlo simulations. Finally, the application of the correla-tion technique was presented for the specific experimental conditions atLISOL. It has been demonstrated that correlations can be safely inter-preted in the acquired 67Fe β -decay data, but not in the acquired 67Co

73



74 Conclusions and outlook

β -decay data.

As today’s nuclear-structure study is mainly aimed at regions farfrom the line of stability, where the typical β -decay half-lives are in theorder of seconds or even smaller, the correlation technique can exten-sively be exploited to investigate their respective ground and isomericstates.

6.2 Discovery of a low-energy proton intruderin 67Co and β decay of 67Co

Application of the developed correlation technique on the 67Fe β -decay

data, revealed the presence of a (1/2−

) isomeric state in67

Co (T 1/2 =496(33) ms) at an unexpected low excitation energy of 492 keV. Thisnewly established isomer has been interpreted as a prolate ([321]1/2−)proton intruder state coexisting with a spherical (7/2−) ground state.A (3/2−) and a (5/2−) state at excitation energies of 680 and 1252 keV,resp., are interpreted as the first band members built on top of the (1/2−)band head. Taking away one proton from 68Ni induces a weakening of the N = 40 subshell gap facilitating neutron pair scattering across. Thelow excitation energy of the (1/2−) proton intruder state in 67Co marksa drastic change in structure with the odd-mass cobalt isotopes withA ≤ 63. The analogous (1/2−) proton intruder state is also observed

and identified in65

Co. While the N = 40 gap provides a stabilizingeffect in the nickel isotopes, there are strong indications for the presenceof many valence neutrons in 67Co illustrating how subtle the N = 40subshell gap is. 67Co sets in a region of deformation below Z = 28 and,based on the experimental observation of increased collectivity beyondN = 40 at Z = 28 [23], 29 [38, 57], and 30 [23] and the lowering of the (7/2−) proton intruder state in copper isotopes beyond N = 40, theobserved (1/2−) proton intruder state in 67Co opens perspectives for apossible ”Island of inversion” beyond N = 40 and below Z = 28.

The 67Co β -decay study confirmed the previously established decayscheme [44] and the 1460-keV transition, de-exciting from the 2155-keV

level into the 694-keV level, is tentatively placed. The 492-keV decaybehavior reveals a half-life value of 503(42) ms of the 492-keV state in67Co, which is consistent with the half-life value of 483(56) ms extractedfrom the correlations in the iron data.



Conclusions and outlook 75

6.3 Intruder properties of 68Ni

The observation of a proton intruder state in 67Co allowed further con-siderations on the 0+ intruder states in 68Ni, which were compared withthe 0+ intruder states in the 90Zr valence counterpart. The unperturbedshell gaps and pairing energies of both nuclei were determined frommeasured one- and two-nucleon separation energies following the pre-scriptions of Ref. [123]. On this basis, the excitation energies of thesuggested ν (2p-2h) and π(2p-2h) intruder states revealed informationon the strength of proton-neutron residual interactions and, hence, in-directly also on the number of valence nucleons involved. The resultswere interpreted in terms of well-established Z = 28 and N = 50 shell

closures in 68Ni and in 90Zr, respectively. The N = 40 and Z = 40 gapsin the respective nuclei were found to be not completely rigid. However,this effect is much more pronounced in 68Ni where the proton-neutroninteraction strength amounts to 3.5(10) MeV, which is attributed to thestrong neutron pair scattering across N = 40. When the N = 40 gap isfurther weakened below Z = 28, more pair scattered valence neutronsbecome available that bring the proton intruder state to lower excitationenergies, which is consistent with the observed onset of deformation atN ∼ 40 below Z = 28.

6.4 The β decay of 65,67

FeTwo β -decaying states in 65Fe were identified through the observation of two level structures without any interconnecting transitions, one fed bythe (1/2−) ground state, the other by the (9/2+) isomeric state. The twolevel structures are suggested to decay into one common (7/2−) groundstate. Important information from deep-inelastic reaction data taken atArgonne National Laboratory was used to fully establish the presented65Fe decay scheme. The deduced 65Co structure can be interpreted asarising from the coupling of a πf −1

7/2proton-hole state with core levels of

66Ni, coexisting with a (1/2−) proton intruder state at 1095 keV, which

is analogous to the (1/2−

) proton intruder state in67

Co.Also the subsequent β decay of 65Co has been revisited. Apart from

the wrongly assigned 883- and 340-keV transitions, which are now un-ambiguously placed in the 65Fe decay scheme, the 65Co decay scheme is




found to be consistent with Ref. [91]. The observed low-energy structure

of 65Ni is interpreted as arising from νf −

15/2, νp−

11/2 and νp−

13/2 neutron-holeconfigurations coupled to the 66Ni core structure.

It is noticed that the β -decay patterns of the 65Fe and 67Fe (1/2−)ground states feature both remarkable structural similarities and changes.Both 65Co and 67Co low-energy structures are interpreted as the coexis-tence of core-coupled states with a deformed proton intruder band. Onthe other hand, a strong transition was observed in 65Co from the 1959-keV level to the spherical (7/2−) ground state, whereas the analogousground state transition was not observed from any of the ∼ 2.75-MeVlevels in 67Co. This indicates that 65Co exhibits a transitional structuregoing from the odd-mass cobalt isotopes with A

≤63 towards the 67Co

isotope.

6.5 The β decay of the 71Ni isomer

Evidence for the β decay of the (1/2−) isomer in 71Ni is presented anddiscussed. The key observable for this study is the newly observed(1/2−) level at 454 keV in 71Cu [38]. The results of the Coulomb-excitation measurement with radioactive beams [38] are combined withresults of a 71Co β -decay experiment at NSCL (National SuperConduct-ing Laboratory) [121] and the results of two decay experiments at LISOL

aiming to the investigation of the β decay of 71

Co and71

Ni. The anal-ysis of the β decay of 71Ni indicates that the 454-keV state observed in71Cu is fed by the 1/2− β -decaying isomer in 71Ni (T 1/2 = 2.34(25) s).The large B(E 2) value measured in Ref. [38] for the 454-keV transitiondepopulating the (1/2−) state in 71Cu indicated a deformed structurefor this level. This means that in both 69,71Ni isotopes the main β -decay branch of the (1/2−) isomer goes to the level dominated by theπp+1

3/2νg+2n

9/2configuration in the daughter nuclei, where n = 1 for 69Cu

and n = 1 or 2 for 71Cu. In 71Cu, however, due to deformation, thenuclear properties of the level receiving the main β -feeding are dictatedby the K = 1/2 downsloping orbit of the πp3/2 orbital.

Instead, this structure is similar to the (1/2−

) proton intruder statein 67Co, which is also understood from the population of the odd protonin the K = 1/2 downsloping orbit of the πp3/2 orbital. The onset of collectivity above Z = 28 and beyond N = 40 is associated with the



Conclusions and outlook 77

quenching of both Z = 28 and N = 40 gaps through the combined

effect of the attraction and repulsion between the f p protons and g9/2neutrons [23, 39, 57]. This supports the suggested ”Island of inversion”below Z = 28 and beyond N = 40.

6.6 Outlook

This thesis work leaves an open question for the isotopes beyond N = 40and below Z = 28 with special attention for cobalt and iron isotopes.Because of the low excitation energy of the (1/2−) intruder state in 67Co,β -decaying 1/2− (isomeric or ground) states in the 69,71Co isotopes can

be expected. On the other hand, the β decay of 69,71,73

Co isotopes havebeen already studied [49, 121] and their ground states have been assigneda spin and parity of (7/2−). Nevertheless, Penning-trap mass measure-ments and/or β -decay studies of the corresponding iron isotopes arenecessary to establish or to rule out the presence of β -decaying isomersin the odd-mass cobalt isotopes beyond N = 40. In fact, beam time isscheduled at the ISOLDE facility of CERN in Geneva, Switzerland, toperform 61−70Mn β -decay studies. The manganese isotopes feed levels inthe corresponding 61−70Fe daughter nuclei, which subsequently populatelevels in 61−70Co. The correlation technique developed in this work canbe applied on the data serving as an important means to disentangle the

decay chains in case of isomerism.The 65,67Co structures could not be discussed quantitatively due to

the lack of reliable large-scale shell model calculations, e.g., none of the presently used calculations succeed to predict the low-lying (1/2−)state in 67Co. This is not only due to the very large shell model spaceneeded (e.g., a 48Ca core with a πpf , νpf 5/2g9/2 valence space), butalso because of the lack of proper effective interactions. On the otherhand, their level schemes obtained in this work offer a well-suited testingground for adjusting the effective interactions in this region. This thesiswork particularly illustrated how subtle the stabilizing effect is of theN = 40 gap arising from the energy difference between the νp1/2 and

νg9/2 orbital. 68Ni has semi-magic properties and can to a certain extentbe used as a core nucleus for the adjacent nickel and copper nuclei, butby removing only one proton already a proton intruder state appears atan excitation energy of only 492 keV. This demonstrates that there is a




need for accurately known effective interactions, especially with the νg9/2

orbital, in order to describe the studied 65,67Co. In a subsequent step,these interactions could be used for regions near Z = 28 and beyondN = 40. As such, predictions can be made for the possibility of thesuggested ”Island of inversion” in the heavier cobalt and iron isotopes.They could alternatively also be used to explore the N = 40 regionbelow Z = 28 to investigate the observed onset of deformation.



Paper I: Decay correlationsin the seconds range withlaser-ionized,

mass-separated beams

79





Nuclear Instruments and Methods in Physics Research B 266, 4600-4605(2008)

Decay correlations in the seconds range with

laser-ionized, mass-separated beams

D. Pauwels,1, ∗ O. Ivanov,1 J. Buscher,1 T.E. Cocolios,1

J. Gentens,1 M. Huyse,1 A. Korgul,2 Yu. Kudryavtsev,1

R. Raabe,1 M. Sawicka,1 I. Stefanescu,1, 1 J. Van

de Walle,1 P. Van den Bergh,1 and P. Van Duppen1

1Instituut voor Kern- en Stralingsfysica, K.U. Leuven,

Celestijnenlaan 200D, B-3001 Leuven, Belgium 2 Institute of Experimental Physics, Warsaw University,

ul.Ho˙ za 69, 00-681 Warszawa, Poland

Abstract

The upgraded LISOL β -decay detection setup, which was used for the mea-surement of the mass A = 67 Fe-Co-Ni decay chain, is presented. A new decaycorrelation technique has been developed in order to characterize an isomeric492 keV transition, observed in this decay chain. Correlating single β and γ

events and β -coincident γ events with each other in the seconds range, allowedfor the placement of this isomeric transition in 67Co. A new half-life for the67Co ground state was determined. The technique and its possibilities andlimitations are discussed.

PACS numbers: 07.05.Kf, 23.35.+g, 23.40.-s, 27.50.+e

∗[email protected]



82 Paper I

I. INTRODUCTION

Implantation-decay correlations are a very powerful technique at in-flight separators to reach out far in the region of unstable nuclei, seee.g. [1–3]. With the advent of post-accelerated ISOL beams this tech-nique has also successfully been used for the observation of rare charged-particle decay channels, see [4]. At low-energy ISOL systems, however,the acceleration voltage (typically 60 kV) is not high enough to givean unambiguous implantation signal and often the beam of interest isoverwhelmed by unwanted radioactive or stable contaminants. Instead,the decays are classically studied on the basis of coincidences of a parti-cle (beta, neutron, proton, alpha) with a γ -event, two γ -events or evenhigher multiplicity combinations, where the coincidence time window

ranges in the order of nanoseconds up to at maximum milliseconds.Longer coincidence time windows are restricted by the amount of ran-dom coincidence events hampering the true correlations and thus causinga loss in sensitivity.

For decay studies at ISOL facilities, this puts a severe restrictionto investigate the properties of supra-milliseconds isomeric states. Thelonger the half-life is, the larger the coincidence window has to be chosenand the more the coincident events are getting drowned in the randomcounts. However, with the decay correlation technique that will be pre-sented here, combined with weak but pure sources and the flexibility of element selectivity using lasers, it becomes possible to accurately sub-

tract the random activity for decays up into the seconds range. In thatway, the exponential decay of the physically correlated events are maderandom-free. As today’s nuclear structure study is mainly aimed at re-gions far from the line of stability, where the typical β -decay half-livesare in the order of seconds or even smaller, the correlation techniquecan extensively be exploited to investigate their respective ground andisomeric states.

This technique has been used for the first time on data recordedduring the 67Fe β -decay experiment at the Leuven Isotope SeparatorOn Line (LISOL) facility in Louvain-La-Neuve, Belgium, [5, 6]. Thesegmented detection system, digitally read-out, in combination with

selective laser-ionization and on-line mass separation has created thepossibility at low-energy ISOL separators for decay correlations in theseconds range. Performing a sequence of experiments with the lasersselectively tuned to Fe, Co and Ni, respectively, and making use of the



Nucl. Instrum. Methods Phys. Res. B 266 , 4600-4605 (2008) 83

new technique of mother, daughter and even granddaughter correlationsin the seconds time domain, allowed us to disentangle this complicated

decay chain and identify an isomer with a half-life in the order of 0.5 sin 67Co, while its ground state has a half-life of 329(28) ms. The correla-tion technique allowed us to deduce the 67Co level scheme, the half-livesinvolved and their β branching ratios.

II. THE DETECTION SETUP

The current LISOL detection setup, shown in figure 1, is based onthe setup described in [7]. The mass-separated ions are implanted inthe implantation tape, where their subsequent β -decay is detected bythe surrounding β - and γ -detectors. Typically one runs in cycles of a specific implantation time period followed by a specific decay timeperiod when the cyclotron beam is closed. The implantation and decaytimes are chosen according to the half-life of the investigated nucleus.To suppress the effect of long-lived contaminants the implantation tapeis moved after a certain number of such implantation-decay cycles. Thedetection setup has been upgraded and some important differences arediscussed below.

Firstly the two coaxial Ge γ -ray detectors with 70% and 75% relativeefficiency are replaced by two MINIBALL clusters [8], each composed of three HPGe crystals. One crystal has a relative efficiency of 55% and iselectrically six-fold segmented as indicated by the dotted lines in figure1. The solid angle that is covered by one MINIBALL crystal from theimplantation spot is on the order of 9% of 4π. For the total of six crystalsthis is very similar to the total solid angle covered by the two coaxialGe detectors (in the order of 60% of 4π). The reason for the similartotal covered solid angle is mainly the larger distance of the MINIBALLGe crystals from the implantation spot and, to a smaller degree, thegeometry. Despite the fact that there is no gain in total solid angle,there is a gain in photo-peak efficiency, because of the reduction of truesumming. The probability of two coincident γ -rays entering the samecrystal is 0.8% for the MINIBALL setup, while it is 9% for the coaxialdetector setup. With this MINIBALL setup the photo-peak efficiencyof a multiplicity 1 γ -ray of 1332 keV is 5.8%.

A second difference is the new electronics and data-acquisition sys-



84 Paper I

b e a m

implantation chamber

implantation into tapemylar windows

plasticdetectors

MINIBALLleft

MINIBALLright

1 cm

Figure 1: A schematic drawing of the top view of the detection setup. Thetwo MINIBALL clusters and three plastic detectors are indicated. Electric

segmentation is indicated by the dotted lines.

tem. To read-out the 42 Ge signals1 digital electronics are used. TheMINIBALL preamplifier signals are digitized and processed by XIA-DGF4C modules [9] on an event-by-event basis. Each module has fourpreamplifier signal inputs and an internal 40 MHz clock. The modulesare initialized and synchronized by the IGOR software package [10]. Ourdata-acquisition system is running in the format of storing energy andtime information for each event.

The β -particles are detected with an efficiency of 50 % by three thinplastic scintillators that cover 68 % of 4π. Lower energy particles in theβ -distribution are only partially registered causing an overall intrinsic

1 Each crystal has 7 signals (6 segment signals and 1 core signal, which collects allthe energy deposited in the total crystal), and in total there are 6 crystals. Howeverthere are also MINIBALL clusters available with an additional two-fold segmenta-tion in the longitudinal direction. In total this means 13 signals per crystal.




efficiency that stays constant at about 73 % for decays with a β -endpointenergy larger than 4 MeV. The plastic detectors serve as a β trigger only

and the energy information is not registered, see [7] for more details.

III. THE CORRELATION TECHNIQUE

With the LISOL detection setup, there are three possible event typesthat can be correlated with each other: single γ -events, single β -events,and β -coincident γ -events inside a time window of 50 ns < tγ − tβ <

400 ns (the βγ -events). Three steps are required for building a random-free correlation spectrum.

In the first step, the exact trigger event with the γ -energy gate, incase a γ -signal is involved and the correlation event type have to be spec-ified. All the trigger events that are present in the data are scanned.Every time a valid trigger event is found, correlated histograms are builtin equal time slices before and/or after the trigger event, within a corre-lation time window of typically two to four times the correlation half-life,but outside the prompt trigger event window (typically 0.5 µs). The re-sult is a set of histograms with the desired correlations, but still drownedin random correlations.

The random correlations can accurately be approximated though inthe second step, even with the specific implantation-decay cycles atLISOL, where isobaric contaminants with different half-lives have dif-ferent growing-in and decay structures. Every trigger event occurred ata specific time inside the implantation-decay cycle. The time windowswithin the cycle of the corresponding correlated histograms are thereforealso determined. Since the implantation-decay structure is identical foreach cycle, the randomly correlated activity in the correlated histogramscan accurately be approximated by the events within these specific timewindows for the total statistics of all cycles, normalized to the numberof cycles.

In the final third step, the histograms containing the approximatedrandomly correlated events are subtracted from the correlated his-tograms. The results are the random-free correlated histograms, whichshow the evolution of the physically correlated events as a function of time with respect to the trigger event.

Different kind of correlation techniques have become a common issuein today’s nuclear physics. The presented technique differs with otherknown techniques in the fact that the trigger event is not an implantation



86 Paper I

b

g1 g1’

g3 g3’g2’’g3’’

g1’’’ g1’’’’E1

E2

E3

E0

T1/2

True R1 R2 Escape

E4

Escape

g4’’’

Figure 2: An example of five hypothetical consecutive γ -ray decay cascadesis shown. An isomeric state at energy E 3 de-excites with a half-life T 1/2. In

the text the situation is discussed for the correlation time window that isopened by γ 1.

signal or a characteristic charged-particle signal like alphas, β -delayednucleons, and direct nucleons, but rather a less specific signal like asingle γ - or β -signal, or a βγ -signal. Because the trigger is in this caseless characteristic, the accurate knowledge of the random correlationsbecomes mandatory.

IV. LIMITATIONS

Obviously the presented technique has its limitations. Before goinginto more details, definitions are needed for the different types of corre-lation and trigger events. For convenience this will be done making useof figure 2. Suppose all events within the γ 1 photo-peak energy windoware specified as trigger events and its correlation with the γ 3-transitionis investigated. In the following the situation is discussed for the corre-lation time window ∆t that is opened by the γ 1-trigger observed at timet0.

• The true correlation event (indicated as ”True” in the figure) isthe detection within this correlation time window of γ 3. All othercorrelation events are random correlations.

• The first type of random correlations, indicated as ”R1” and ”R2”in the figure, is the detection within the correlation time windowof γ 3, respectively, γ 3 coming from another decaying nucleus of the same type fed through the preceding γ 1, respectively, γ 2 . In




the ”R2” case, it is more generally required that the randomlycorrelated event is an event of the same type as a truly correlated

event, but belonging to a decay cascade that does not contain thetransition of the type of the trigger event.

• The second type of a random correlation, labeled in the text bythe subscript ”bg”, but not shown in figure 2, is the detectionwithin the correlation time window of a background event insidethe correlation energy window.

So far, the different types of correlated events are discussed, but alsothree different types of trigger events exist.

•A true trigger event is a trigger event that is followed by the

investigated correlated event, irrespective of the fact that the cor-related event gets detected or not. In figure 2 only γ 1 and γ 1 aretrue trigger events.

• The first type of a faulty trigger event is the detection of transi-tions, like γ 1 and γ 1 in the figure, which are not followed by theinvestigated correlation event. One can speak of an escape out of the (γ 1 − γ 3) correlation scheme.

• The second type of a faulty trigger event (not shown in figure2) is a background event inside the trigger photo-peak energywindow.

The total number of true correlations N ctrue can be expressed by theequation:

N ctrue = N trtrueI bεc

1 − e−λ∆t

(1)

where N trtrue is the number of true trigger events, I b is the branching

ratio, εc the detector efficiency for the correlation events, λ = ln(2)T 1/2

the

decay constant and ∆t the correlation time window.The total number of experimental correlations N cexp as built in the

first step can be expressed by the equation:

N cexp = N tr ·

Atrtrue

εtrI bεc + Ac

R2 + Acbg

∆t

+ N trtrue · I bεc

1 − e−λ∆t

(2)



88 Paper I

where N tr is the total number of triggers, Atrtrue is the count rate of the

true trigger events, AcR2 of randomly correlated events of the type ”R2”,

Acbg of background events and εtr the trigger detection efficiency. The

right-hand side of this equation represents exactly the total number of random correlations.2

The total number of experimentally deduced random correlations

N rexp as built in the second step can be expressed by the equation:

N rexp =

N cyci=1

N tr ·

Atrtrueεtr

I bεc + AcR2 + Ac

bg

∆ti

N cyc

+N trtrue · I bεc

1 − e−λ∆t

N cyc

(3)

where N cyc is the total number of implantation-decay cycles.The true correlations are experimentally estimated by subtracting

the deduced random correlations N rexp from the experimental correlatedevents N cexp:

N csub = N cexp − N rexp (4)

leading to

N csub = N ctrue ·

1 − 1

N cyc

. (5)

A systematic error term of 1N cyc appears. This means that as a firstcondition N cyc 1 has to be fulfilled.

The second condition is related to the count rates of trigger andcorrelated events. The experimentally estimated true correlations willonly be an accurate estimate as long as its statistical uncertainty δN csubis small enough with respect to the statistical uncertainty δN ctrue of thetrue correlations. This is formulated as

δN csub < α · δN ctrue (6)

with α a factor that is deduced from simulations based on the Monte-Carlo method. Using the first condition that N cyc

1, equation 2

2 More complete would be writing (N trtrue− 1)/∆tmeas instead of Atrtrue, with ∆tmeas

the total measuring time, in order to take into account the true correlation that isneglected here.




and the assumption that the correlation time window ∆t is chosen largeenough such that e−λ∆t becomes negligibly small, this results in the

second condition:

AcR2 + Ac

bg <

α2 − 1

∆t· N trtrue

N tr− Atr

true

εtr

· I bεc. (7)

From the simulations it is shown that α <√

5 is a safe limit in orderthat half-life fits are still reliable.

The first two terms at the left-hand side of the inequality are relatedto the purity of the beam and the background conditions for the cor-

related events, while the ratioN trtrueN tr in the first term at the right-hand

side of the inequality is related to the purity of the beam and the back-

ground conditions for the trigger events. The ratioAtrtrueεtr

in the second

term at the right-hand side of the inequality will make the correlationtechnique obsolete when the beam intensity is too high. The correlationtime window ∆t is chosen in function of the correlation half-life. A typ-ical choice is ∆t = 4 · T 1/2. Then, in perfect conditions, which meansthat Ac

R2 = Acbg = 0 Hz and all trigger events are true trigger events

(N tr = N trtrue), equation 7 reduces to

Atrtrue

εtr<

1

T 1/2. (8)

V. EXPERIMENTAL RESULTS: A CASE STUDY

The correlation technique as described in section III has been appliedfor the first time on LISOL data of the mass A = 67 Fe-Co-Ni decaychain, where the lasers had been tuned subsequently on resonance toFe, Co and Ni and turned off (called lasers off). From comparing thelasers on Co with the lasers off data, prompt β -γ coincidences confirmedthe intense 694 keV γ -ray transition in 67Ni (see figure 3) as was seenalready in [11], in which the reported 67Co half-life is 425(20) ms.

However, for both the Fe and Co data sets, an intense 492 keV γ -raywas observed in the single γ spectrum, while it disappeared completelyrequiring coincidences with a β -particle. Neither were found gammas incoincidence with the 492 keV γ -events. As a result, at this stage, it wasalready clear that the 492 keV transition is not situated in Fe, but therewas still no way to conclude whether the transition takes place in Co orNi. Therefore, the described correlation technique has been applied.



90 Paper I

40Co

67

27

39Ni

67

28

329(28) ms

~500 ms

-β

0

491.6

694.4

4 9 1

. 6 ( 1 )

6 9 4

. 4 ( 1 )

Figure 3: Mass 67 decay chain resulting from the present study.

Figure 4 shows the three consecutive steps of building a random-freecorrelated histogram for single γ -events in a time window of 1 µs to200 ms before β -694 keV trigger events. The spectra were built fromthe data taken with the lasers tuned resonantly on Fe and in a cycle of 10 s implantation, 0 s decay and a tape move after every cycle. Thetop spectrum shows all correlated events, the middle spectrum showsthe approximated randomly correlated events and the bottom spectrum

shows the random-free correlations. In the first step the spectrum showsa 492 keV line, the uncorrelated 511 keV line, other background lines andeven the 694 keV line itself. The presence of the last two lines is alreadyevidence that the spectrum contains randomly correlated events and itis not clear if the observed 492 keV line is physically correlated. In thesecond step the same lines appear again as the approximated randomlycorrelated events, but the ratio of the 492 keV line intensity to theintensity of any other line is clearly different compared to the spectrumcontaining all correlations. Note also that the statistical fluctuations aremuch smaller in the second spectrum, because by definition the statisticsis higher by a factor N cyc = 19, 409, the total number of cycles in the Fe

data. After subtraction of the middle spectrum from the top spectrum,only the 492 keV line remains on a zero background level, shown in thebottom spectrum. This proves that the 492 keV transition takes placebefore a β -694 keV event and thus in 67Co. Because the spectrum only




C o u

n t s / k e V

20

40

60

80

100 eventsγ -694 keV correlated singleβa)

Fe67492,

-e

+511, e

T l

2 0 8

5 8 3 ,

B i

2 1 4

6 0 9 ,

C o

6 7

6 9 4 ,

C o u n t s / k e V

20

40

60

80

100 eventsγ -694 keV randomly correlated singleβb)

Energy (keV)0 100 200 300 400 500 600 700 800

C o u n t

s / k e V

-20

-10

0

10

20

30

40

50eventsγ -694 keV randoms subtracted singleβc)

Figure 4: Different steps of the correlation technique illustrated for theexample of single γ -events in a time window of 1 µs to 200 ms before β -694

keV trigger events.

shows a 492 keV line, this proves also that the isomeric state decays

internally through γ -emission to the ground state as shown in figure 3.Apart from proving that the correlation exists, one can also deducethe half-life of the ground state of 67Co by fitting the random-free corre-lated 492 keV peak integrals as a function of the time difference t694−t492between the correlated 492 keV events and the trigger β -694 keV events,as shown in figure 5. Each data point represents the 492 keV peak in-tegral in the corresponding random-free correlation histogram, e.g., the492 keV integral from spectrum 4c is the first data point. The cor-relations satisfy the two conditions that were deduced in section IV:N cyc = 19, 409 1 and working out numerically the left and righthand-side of inequality 7 for ∆t = 2 s gives 0.08 Hz < 0.15 Hz. Note

that the integrals are statistically fluctuating around zero for the lastsix data points indicating a good control of the random correlations. Inthis way it was possible to determine the half-life of the ground state of 67Co as 329(28) ms with a simple single exponential relationship. The



92 Paper I

Integral 202.1/ ndf2χ 8.676 / 8

Activity 9.15±85.71Halflife 27.6±329.1

(ms)492-t694t0 200 400 600 800 1000 1200 1400 1600 1800 2000

C o u n t s / 2 0

0 m s

-20

0

20

40

60

80

100Integral 202.1

/ ndf2χ 8.676 / 8

Activity 9.15±85.71Halflife 27.6±329.1

Figure 5: Single exponential fit of the 492 keV events coming before β -694keV trigger events on a reversed time axis.

disagreement with the half-life of 425(20) ms [11] stems from the factthat in [11] the presence of the isomeric level was unknown.

A third application of the correlation technique is the determinationof branching ratios.

VI. CONCLUSIONS

A new segmented gamma setup consisting of two MINIBALL clus-ters and a new data-acquisition system, based on digital XIA-DGF4Celectronics, in the βγ -detection setup at LISOL, has been discussed.

A new correlation technique has been developed and its limits arespecified. In combination with weak, yet pure beams and low back-ground conditions, the technique offers the possibility to correlate sig-nals containing a large non-correlated component like single betas orgammas, or β -coincident gammas up into the seconds range. The purityof the beam is realized by making use of resonant laser-ionization, incombination with mass separation. The correlations are able to deliver

information on the placement of long-lived isomers in a decay chain, onthe half-life of isomeric and ground states in a simple single exponentialrelationship and on branching ratios.

Experimental results, showing the strength of the technique, have




been presented on the mass A = 67 Fe-Co-Ni decay. Using the cor-relations, a long-lived isomeric state at 492 keV has been identified in67

Co, making an internal γ -ray transition to the ground state, whichsubsequently β -decays with a half-life of 329(28) ms.

This correlation technique in the seconds range could be used pro-vided that the beams are weak and pure enough and the backgroundlevel is low enough, as formulated by equation 7.

Acknowledgments

We acknowledge the support by the European Commission within theSixth Framework Programme through I3-EURONS (contract no. RII3-CT-2004-506065), BriX-IUAP P6/23, FWO-Vlaanderen (Belgium),GOA/2004/03 and the Foundation for Polish Science (AK).

[1] A. N. Andreyev, et al., Nucl. Instr. and Meth. A 533 (2004) 409.[2] E. S. Paul, et al., Phys. Rev. C 51 (1995) 51.[3] O. Sorlin, et al., Nucl. Phys. A 669 (2000) 351.[4] D. Smirnov, et al., Nucl. Instr. and Meth. A 547 (2005) 480.[5] Yu. Kudryavtsev, M. Facina, M. Huyse, J. Gentens, P. Van den Bergh,

Nucl. Instr. and Meth. B 204 (2003) 336.[6] M. Facina, et al., Nucl. Instr. and Meth. B 226 (2004) 401.

[7] L. Weissman, et al., Nucl. Instr. and Meth. A 423 (1999) 328.[8] J. Eberth, et al., Prog. in Part. and Nucl. Phys. 46 (2001) 389.[9] http://www.xia.com/DFG-4C.html.

[10] http://www.wavemetrics.com/products/igorpro/igorpro.htm.[11] L. Weissman, et al., Phys. Rev. C 59 (1999) 59.





Paper II: Shape isomerismat N = 40: Discovery of aproton intruder state in

67Co

95





Physical Review C 78 041307(R) (2008)

Shape Isomerism at N = 40: Discovery of a ProtonIntruder in 67Co

D. Pauwels,1, ∗ O. Ivanov,1 N. Bree,1 J. Buscher,1 T.E. Cocolios,1

J. Gentens,1 M. Huyse,1 A. Korgul,2 Yu. Kudryavtsev,1

R. Raabe,1 M. Sawicka,1 I. Stefanescu,1, 3 J. Van de Walle,1

P. Van den Bergh,1 P. Van Duppen,1 and W.B. Walters3


Celestijnenlaan 200D, B-3001 Leuven, Belgium 2 Institute of Experimental Physics, Warsaw University,

ul.Ho˙ za 69, 00-681 Warszawa, Poland 3 Department of Chemistry and Biochemistry,

University of Maryland, College Park, Maryland 20742, USA

Abstract

The nuclear structure of 67Co has been investigated through 67Fe β decay.The 67Fe isotopes were produced at the LISOL facility in proton-induced fissionof 238U and selected using resonant laser ionization combined with mass sepa-ration. The application of a new correlation technique unambiguously revealeda 496(33) ms isomeric state in 67Co at an unexpected low energy of 492 keV.A 67Co level scheme has been deduced. Proposed spin and parities suggest aspherical (7/2−) 67Co ground state and a deformed first excited (1/2−) stateat 492 keV, interpreted as a proton 1p-2h prolate intruder state.

PACS numbers: 23.35.+g, 23.40.-s, 21.60.Cs, 27.50.+e




98 Paper II

Atomic nuclei in the neighborhood of closed shells often exhibit in-triguingly low-energy excitations whereby particle-hole configurations

across major shell gaps give rise to so-called intruder states [1, 2]. Al-though expected at an excitation energy of at least the size of the shellgap, the strong energy gain in both pairing and proton-neutron interac-tions can bring them close to the ground state. In odd-mass nuclei with±1 nucleon outside a closed shell, the possible unique spin/parity of theintruder orbitals combined with the difference in deformation comparedto the normal states can lead to isomerism. Their excitation energybecomes minimal where the proton-neutron correlations are maximal,typically in the middle of the open shell. Intruder states, through theirisomeric character, are excellent experimental and theoretical probesto study the relation between individual and collective excitations in

atomic nuclei revealing information on shell gaps, pairing correlationsand proton-neutron interactions. The rich variety in orbitals, shell gapsand shapes available in exotic nuclei makes intruder states an ideal lab-oratory for a more general study of mesoscopic systems.

Through the use of a novel correlation technique applied to the β decay of 67Fe, we report on the existence of a proton-intruder isomerin 67Co40 at an excitation energy of 492 keV. The 67Co nucleus is onlyone proton-hole separated from the semidoubly magic 68Ni [3] and oneproton-particle beyond 66Fe, whose low 2+ energy hints to a reduced gapat N = 40 [4, 5]. On the other hand, the nickel and copper nuclear struc-tures adjacent to 68Ni have been successfully interpreted as dominated

by particle/hole coupled to the68

Ni core [6–10]. Nevertheless, severalexamples of low-energy neutron-isomers have been observed arising fromexcitations across N = 40 into the g9/2 unique-parity orbital [8, 9, 11–13], but so far no single low-energy proton-isomer has been reported inthis region and in the odd-mass cobalt isotopes up to mass A = 65.

In previous 67Fe decay studies the half-life of 470(50) ms was reported[14] and a single gamma ray at 189 keV was identified [15]. Low produc-tion yields far away from the line of stability and difficulties to producethe short-lived cobalt and iron isotopes using conventional ISOL tech-niques hamper detailed studies. However, much improved data for thedecay of neutron-rich iron and cobalt nuclei can now be obtained with

high selectivity using the laser-ion source at the LISOL facility [16]. The67Fe nuclei were produced in a 30 MeV proton-induced fission reactionon two 10 mg/cm2 thick 238U targets, placed inside a gas cell. The fis-sion products, recoiling out of the targets, were stopped and thermalized





100 Paper II

Energy (keV)200 400 600

C o u n

t s / k e V

0

500

1000

1500

2000

2500189

4 9 2

6 9 4

γ Single(b)

C o u

n t s / k e V

100

200

300

400

500

189

296 511 6 8 0

6

9 4

γ -gatedβ(a)2×

Time (ms)1500 2000 2500 3000

C o u n t s / 1 0 0

m s

1

10

210

Figure 1: γ -ray spectra at A = 67. (a) β -gated spectra with the laser-on (upper-black on-line) and laser-off (lower-red on-line). (b) Singles γ -ray spectra withthe laser-on (upper-black on-line) and the laser-off (lower-red on-line). Linesmarked by a star are laser-enhanced lines and the 296-keV line is from 102Nbβ decay reaching the detection setup in the doubly charged molecular form102NbO++

2 . The lines that are not marked are background lines. The upperinsert in (a) is the fitted decay behavior of the 189-keV line.

67Co and the 694-keV transition in 67Ni. Fig. 2(a) shows all corre-lated single γ events in a time window from 1 µs to 200 ms after aβ -gated 189-keV event from data taken in cycles of 10 s implantationafter which the detection tape is immediately moved. The randomlycorrelated events present in the spectrum can be estimated by taking allstatistics in the specific time windows over all 19409 implantation-decaycycles, normalized to this number of cycles, see Fig. 2(b). In Fig. 2(c)



Phys. Rev. C 78 , 041307(R) (2008) 101

C o u

n t s / k e V

20

40

60

80

100 eventsγ -189 keV correlated singleβa)

F e

6 7

4 9 2 5 1

1

C o 6 7

6 9 4

C o u n t s / k e V

20

40

60

80

100 eventsγ -189 keV randomly correlated singleβb)

Energy (keV)0 100 200 300 400 500 600 700

C o u n t s / k

e V

-20

-10

0

10

2030

40eventsγ -189 keV randoms-subtracted singleβc)

Energy (keV)

0 100 200 300 400 500 600 700

C o u n t s / k e V

-20

-10

0

10

20

30

40

50 eventsγ -694 keV randoms-subtracted singleβd)

Figure 2: Single γ -events coming after β -gated 189-keV events in a 1 µs to200 ms window (a), the corresponding randomly correlated events (b) andrandoms-subtracted histogram (c). The randoms-subtracted histogram in (d)corresponds to single γ events before β -gated 694-keV events in a 1 µs to 200ms window.

the estimated randomly correlated events are subtracted leaving onlythe 492-keV peak present, indicating that the transition takes place af-ter the β -gated 189-keV transition. Combined with the presence of the

492-keV line in Fig. 2(d), showing all the events correlated in a timewindow 1 µs to 200 ms before a β -gated 694-keV event after subtractionof random correlations, the isomeric transition can firmly be placed in67Co.



102 Paper II

The half-life of this newly established isomeric state in 67Co wasdetermined by two independent methods: the 492-keV γ -ray decay be-

havior in a data set with the lasers tuned on cobalt, revealing a half-lifeof 503(42) ms and by fitting the decay behavior of correlated 492-keVevents after β -gated 189-keV trigger events in the iron data set, reveal-ing a half-life of 483(56) ms. These results indicate the reliability of the half-life values obtained from the correlation technique [18]. Thehalf-life value of 496(33) ms, shown in Fig. 3, is the weighted average of the two methods. Additionally, from the correlated 492-keV events afterβ -gated 189-keV trigger events, the isomeric state at 492 keV is found todecay by a lower limit of 80 % through the 492-keV γ -transition, leavingroom for at maximum 20 % β -decay. The half-life of the 67Co groundstate was obtained with the same correlation technique as described in

Ref. [18].The level scheme for 67Co, shown in Fig. 4, has been constructed

from βγ γ -coincidences. The γ -ray intensities in 67Co are relative to the189-keV transition (I γ = 100). Assigned spins and parities are based ona 7/2− ground state of 67Co [10]. Weisskopf estimates for the half-lifeof an E3, M3 and E4 492-keV transition are 0.63 ms, 33 ms and 500 s,respectively. Hence, the extracted half-life indicates an M3 multipolarityfor the 492-keV transition, which, in turn, leads to (1/2−) proposedspin and parity values for the 492-keV isomer in 67Co. The expectedprobability ratio for an M1 189-keV to an E2 680-keV transition is theonly possible match that is of the same order of magnitude as their

intensity ratio. Hence, (3/2−

) spin and parity values are proposed forthe 680-keV level and (5/2−) values are proposed for the 1252-keV levelon the basis of the observed decay to both the (7/2−) ground state and(3/2−) level at 680 keV. The 67Fe decay pattern supports a low-spin andnegative-parity for its ground state.

The level structures for the ground state and low-energy 1/2−, 3/2−

and 9/2− levels in odd-mass 57−67Co nuclei are shown in Fig. 5, alongwith the energy of the 2+

1 level in the adjacent even-even nickel corenucleus. The data on mass 65 were obtained from another experiment atLISOL [19] and the results are consistent with previous studies [20, 21].Higher-spin levels in 65Co were deduced using the same data set and

methods of Ref. [22].As can be seen, the energies of the 9/2− levels, representative also for

the 11/2− levels that are not shown in the figure, follow the energies of the core 2+ levels quite closely. This behavior provides strong support for



Phys. Rev. C 78 , 041307(R) (2008) 103

40Co67

39Ni67

41Fe67 416(29) ms

-β

)-

(7/2

)-

(1/2 496(33) ms)-

(3/2

329(28) ms -

β

(<20%)-

β

6 8 0

. 4

1 8 8

. 9

4 9 1

. 6

E2

M1

M3

)-(1/2

)-

(5/2 6 9 4

Figure 3: Partial A = 67 β -decay chain.

the description of these nuclei as a single πf −17/2 hole in the Z = 28 closed

shell coupled to excited levels that arise from excitations in the adjacenteven-even nickel core nucleus [23]. Two 3/2− levels and a single 1/2−

level are also shown that have both core-coupled and πp+13/2

and πp+11/2

configurations, respectively, as deduced from proton transfer [24–26] andCoulomb excitation studies [27, 28]. Note that a 1/2− core-coupled statecan only be obtained by coupling a πf −1

7/2hole to a 4+ state.

All four of these levels follow the energy trend of the core levels upthrough N = 34. As additional neutrons are added, first the 3/2− leveldrops in energy for N = 36 and beyond and the (1/2−) level for N = 38and particularly N = 40 where the core 2+ and 4+ energies are 2.033 and3.149 MeV, respectively. Hence, particularly for the (1/2−) level, core-coupled configuration admixtures should be negligible for 67Co, leavingproton π(1p-2h) excitations across Z = 28 as the only possible configu-ration. The strong decrease in excitation energy of the (1/2−) state can

be described by strong proton-neutron correlations inducing deforma-tion [1]. According to calculated Nilsson orbitals presented in Ref. [29],a prolate-deformed 67Co nucleus with a quadrupole deformation value of 0.25 < ε2 < 0.4 leads in a very natural way to a first excited [321]1/2−



104 Paper II

40Co6727

41Fe67

26=9.4(5) MeV

βQ

-β

0 416(29) ms

(%)βI

<28

<2449(9)

<5

<2

24(6)

13(4)13(4)

log ft

>5.4

>5.45.0(3)

>5.8

>6.0

4.8(2)

5.0(2)5.0(2)

)-

(7/2 329(28) ms

)-

(1/2 496(33) ms)

-

(3/2

)-

(5/2

-β

-β <20%

0

491.6680.5

1251.9

1859.1

2734.82760.62769.2

2 0

8 8

. 7

1 6 ( 5 )

2 0 7 9

. 8

8 ( 3 )

1 5 0 8

. 9

8 ( 3 )

2 0 5 4

. 2

1 8 ( 5 )

1 4 8 3

. 2

7 ( 2 )

8 7 6 .

9

5 ( 2 )

1 3 6 8

1 . 1

( 9 )

1 1 7 8

. 9

3 . 3

( 1 4 )

1 2 5 1

. 9

1 0 ( 4 )

5 7 1

. 4

3 . 7

( 1 4 )

6 8 0

. 4

8 ( 3 )

1 8 8

. 9

1 0 0

4 9 1

. 6

9 9 ( 2

9 )

Figure 4: 67Fe β -decay scheme. The γ -ray intensities are indicated relative tothe 189-keV transition (I γ = 100). The upper limits of the β -decay feeding(67Fe to 67Co) are 1σ limits on the missed γ -ray intensities. The log f t valuesare lower limits due to possibly missed γ rays. The upper limit of β -decay outof the 492-keV isomer is deduced from the correlations.

state obtained by promoting one proton particle from the f 7/2 into the p3/2 orbital. Also the neutrons favor this configuration due to the sharplydownsloping 1/2+[440] and 3/2+[431] orbitals. It is tempting to assignthe (3/2−) and (5/2−) states at 680 and 1252 keV as the first membersof a rotational band built on the (1/2−) state. Such a rotational bandoccurs in the indium isotopes [1], where the Coriolis decoupling is evenstrong enough to bring the 3/2+ state below the π[431]1/2+ band head.Fig. 5 also indicates that already in 65Co the (1/2−) intruder level setsin at 1095 keV [19], 482 keV lower in energy than the first excited (1/2−)

level in63

Co, while the corresponding Ni 4+

1 state goes up by 575 keV.In the N = 49 isotones counterpart, the neutron-intruder configura-tion can be followed as a function of the filling of the proton orbitals,showing a maximum excitation energy towards 40Zr, consistent with a



Phys. Rev. C 78 , 041307(R) (2008) 105

Neutron number (N)30 32 34 36 38 40 42

E n e r g y

( k e V )

0

500

1000

1500

2000

) Ni+

E(2) Co

-E(9/2

) Co-

E(3/2

) Co-E(1/2

Figure 5: Odd-mass cobalt systematics of low-lying 1/2−, 3/2−, and 9/2−

states relative to the 7/2− ground state [32]. The 2+ energy in the even nickelisotones are indicated by open circles [32].

subshell closure at Z = 40 [1, 30]. The situation is completely differentin the odd-mass cobalt isotopes as the (1/2−) proton-intruder state is

up till now lowest at N = 40, evidencing that for the Z = 27 isotopesthe N = 40 subshell gap is washed out, as is the case in the iron [4]and chromium isotopes [31]. In the lighter odd-mass cobalt isotopes theintruder configuration is more difficult to localize due to the strong frag-mentation of its strength over different states. It is, remarkably enough,the semimagic behavior of the 68Ni core that allows a pure character of the intruder state not mixed up with core-coupled configurations. Therapid onset of deformation below Z = 28 can thus be explained by thestrong proton-neutron residual interactions between the protons in theπf 7/2 orbital and neutrons in the νf 5/2 and νg9/2 orbitals [4, 31].

Combining the energy measured for this newly identified proton in-

truder in 67Co with that of the previously known 7/2− π(2p-1h) intruderstate in 69Cu at 1711 keV [6, 7], allows us to estimate the energy of the0+ π(2p-2h) intruder state in 68Ni using the prescription of Ref. [33].At Z = 50 and Z = 82 the estimated 0+2 energies from summing the



106 Paper II

intruder excitation energies of the Z ± 1 isotones are reproduced onaverage within ∼ 200 keV. The 2.2 MeV estimate for 68Ni makes the

(0+

3 ) state at 2.511 MeV therefore a good candidate for the π(2p-2h)configuration. This state was observed in β -decay work and could notbe described by shell model calculations not allowing excitations acrossZ = 28 [13], while it was properly predicted by Hartree-Fock-Bogoliubovcalculations from collective excitations [34]. The low-lying 68Ni struc-ture is thus dominated by excitations across the N = 40 (0+2 state at1770 keV) [35] and the Z = 28 (0+3 state at 2511 keV) (sub)shell gap.

In conclusion, a (1/2−) isomeric state with a half-life of 496(33) mshas been identified in 67Co using a new correlation technique. Thisnewly established isomer has been interpreted as a prolate ([321]1/2−)proton intruder state coexisting with a spherical (7/2−) ground state.

Taking away only one proton from68

Ni already induces the obliterationof the N = 40 subshell gap and sets in a region of deformation belowZ = 28. The identification and further study of intruder states in heaviercobalt, nickel, and copper isotopes beyond N = 40 will deliver crucialinformation on the Z = 28 gap toward 78Ni.

We acknowledge the support by the European Commission within theSixth Framework Programme through I3-EURONS (contract no. RII3-CT-2004-506065), BriX-IUAP P6/23, FWO-Vlaanderen (Belgium),GOA/2004/03, the Foundation for Polish Science (A.K.), the US De-partment of Energy, and the Alexander von Humboldt Foundation(W.B.W.).

[1] K. Heyde, P. Van Isacker, M. Waroquier, J. L. Wood, and R. A. Meyer,Phys. Rep. 102, 291 (1983).

[2] J. L. Wood, K. Heyde, W. Nazarewicz, M. Huyse, and P. Van Duppen,Phys. Rep. 215, 101 (1992).

[3] R. Broda et al., Phys. Rev. Lett. 74, 868 (1995).[4] M. Hannawald et al., Phys. Rev. Lett. 82, 1391 (1999).[5] P. Adrich et al., Phys. Rev. C 77, 054306 (2008).[6] A. M. Oros-Peusquens and P. F. Mantica, Nucl. Phys. A 669, 81 (2000).[7] I. Stefanescu et al., Phys. Rev. Lett. 100, 112502 (2008).

[8] J. Van Roosbroeck et al., Phys. Rev. C 69, 034313 (2004).[9] W. F. Mueller et al., Phys. Rev. Lett. 83, 3613 (1999).

[10] L. Weissman et al., Phys. Rev. C 59, 2004 (1999).[11] R. Grzywacz et al., Phys. Rev. Lett. 81, 766 (1998).



Phys. Rev. C 78 , 041307(R) (2008) 107

[12] J. Prisciandaro et al., Phys. Rev. C 60, 054307 (1999).[13] W. F. Mueller et al., Phys. Rev. C 61, 054308 (2000).[14] F. Ameil et al., Eur. Phys. J. A 1, 275 (1998).[15] O. Sorlin et al., Nucl. Phys. A669, 351 (2000).[16] M. Facina et al., Nucl. Instrum. Methods Phys. Res. Sect. B 226, 401

(2004).[17] J. Eberth et al., Prog. in Part. and Nucl. Phys. 46, 389 (2001).[18] D. Pauwels et al., Nucl. Instrum. Methods Phys. Res. Sect. B (Accepted),

DOI: 10.1016/j.nimb.2008.05.083.[19] D. Pauwels et al., to be published.[20] L. Gaudefroy, Ph.D. thesis, Universite de Paris XI Orsay (2005).[21] M. Block et al., Phys. Rev. Lett. 100, 132501 (2008).[22] N. Hoteling et al., Phys. Rev. C 74, 064313 (2006).[23] P. H. Regan, J. W. Arrison, U. J. Huttmeier, and D. P. Balamuth, Phys.

Rev. C 54, 1084 (1996).

[24] B. Rosner and C. H. Holbrow, Phys. Rev. 154, 1080 (1967).[25] A. G. Blair and D. D. Armstrong, Phys. Rev. 140, B1567 (1965).[26] K. W. C. Stewart, B. Castel and B. P. Singh, Phys. Rev. C 4, 2131 (1971).[27] R. Nordhagen, B. Elbek, and B. Herskind, Nucl. Phys. A104, 353 (1967).[28] Jose M. G. Gomez, Phys. Rev. C 6, 149 (1972).[29] P. Moller et al., At. Data Nucl. Data Tables 66, 131 (1997).[30] R. A. Meyer, O. G. Lien, and E. A. Henry, Phys. Rev. C 25, 682 (1982).[31] O. Sorlin et al., Eur. Phys. J. A 16, 55 (2003).[32] URL: http://www.nndc.bnl.gov/ensdf/.[33] P. Van Duppen, E. Coenen, K. Deneffe, M. Huyse, K. Heyde, and P. Van

Isacker, Phys. Rev. Lett. 52, 1974 (1984).[34] M. Girod, P. Dessagne, M. Bernas, M. Langevin, F. Pougheon, and

P. Roussel, Phys. Rev. C37

, 2600 (1988).[35] K. Kaneko, M. Hasegawa, T. Mizusaki, and Y. Sun, Phys. Rev. C 74,024321 (2006).





Paper III: Structure of 65,67Co studied through theβ decay of 65,67Fe and a

deep-inelastic reaction

109





Submitted to Physical Review C

Structure of 65,67Co studied through the β decay of 65,67Feand a deep-inelastic reaction

D. Pauwels,∗ O. Ivanov, J. Buscher, T.E. Cocolios,

M. Huyse, Yu. Kudryavtsev, R. Raabe,

M. Sawicka, J. Van de Walle, and P. Van Duppen

Instituut voor Kern- en Stralingsfysica, K.U. Leuven,

Celestijnenlaan 200D, B-3001 Leuven, Belgium

A. Korgul

Institute of Experimental Physics, Warsaw University,

ul.Ho˙ za 69, 00-681 Warszawa, Poland

I. Stefanescu, A.A. Hecht, N. Hoteling, and A. Wohr

Department of Chemistry and Biochemistry,

University of Maryland, College Park, Maryland 20742, USA and

Physics Division, Argonne National Laboratory,

Argonne, Illinois 60439, USA

W.B. Walters

Department of Chemistry and Biochemistry,

University of Maryland, College Park, Maryland 20742, USA

R. Broda, B. Fornal, W. Krolas, T. Pawlat, and J. Wrzesinski

Niewodniczanski Institute for Nuclear

Physics, Krakow, PL-31342, Poland

M.P. Carpenter, R.V.F. Janssens, T.

Lauritsen, D. Seweryniak, and S. Zhu

Physics Division, Argonne National Laboratory,

Argonne, Illinois 60439, USA

J.R. StoneDepartment of Chemistry and Biochemistry,

University of Maryland, College Park, Maryland 20742, USA and

Department of Physics, University of Oxford,



OX1 3PU Oxford, United Kingdom

X. WangPhysics Division, Argonne National Laboratory,

Argonne, Illinois 60439, USA and

Department of Physics, University of Notre Dame,

Notre Dame, Indiana 46556, USA

Abstract

The neutron-rich isotopes 65,67Fe and 65Co have been produced at the LISOLfacility, Louvain-La-Neuve, in the proton-induced fission of 238U. Beams of these isotopes have been extracted with high selectivity by means of resonantlaser ionization combined with mass separation. Yrast and near-yrast levels of 65Co have also been populated in the 64Ni+238U reaction at Argonne National

Laboratory. The level structure of 65

Co could be investigated by combining allthe information from both the 65Fe and 65Co β decay and the deep-inelasticreaction. The 65Fe, 65Co and 67Fe decay schemes and the 65Co yrast structureare fully established. The 65,67Co level structures can be interpreted as resultingfrom the coexistence of core-coupled states with levels based on a low-energyproton-intruder configuration.

PACS numbers: 23.40.-s,23.20.Lv,21.10.-k,27.50.+e




113

I. INTRODUCTION

The region around Z = 28 and N = 40 has drawn considerableinterest in nuclear-structure research since the observation in 68Ni of a0+ level as the first excited state [1] and the high excitation energy of the first excited 2+ level [2]. Both properties were regarded as strongindications for the double-magic character of 68Ni. However, despite allthe additional information that was acquired over the last decade, thespecific role of the N = 40 subshell closure and the Z = 28 closure onthe structure of nuclei around 68Ni is not yet understood. Especiallythe occurrence of single-particle and collective phenomena close to 68Nideserves further attention. Therefore, this region remains challengingfrom both an experimental and a theoretical perspective.

Most early studies were aimed at the structure of the more easilyproduced nickel and copper isotopes using in-beam γ -ray studies [2–4],β -decay investigations [5–9], and (d,3He) pickup reactions [10]. Recently,more exotic nuclei with Z ≥ 28 have provided experimental informationproviding a more direct connection with single-particle and collectiveconfigurations, e.g., g-factor measurements of 69mCu and 67mNi [11] andtransition probabilities from Coulomb excitation experiments in 68Ni[12, 13] and 67−71,73Cu [14, 15]. These results provide complementary,but often also unanticipated and crucial insights, such as the admixtureof (1p− 1h) excitations across Z = 28 in 67mNi [11], the superfluidcharacter of 68Ni [12] and the collectivity present in 69Cu [15]. While

experiments on the nickel and copper isotopes are currently experiencinga new boost, information on the cobalt isotopes around and beyondN = 40 remains scarce. On the other hand, the levels of the lighter odd-mass cobalt isotopes up through 63Co appear to be readily described bytreating the observed structures as resulting from a single πf 7/2 proton-hole coupled to the adjacent even-even nickel cores [16].

Until recently, the known experimental observables for the heaviercobalt nuclei near 68Ni were isomeric γ decay in 66Co [4], a 189-keV γ transition in 67Co [17] and ground state half-life values determined in66−71,73Co β decay [6–8, 18, 19]. 65Co is the heaviest odd-mass cobaltisotope for which, prior to this work, a level scheme was proposed [20],

albeit one that could not be interpreted. The 65Co level scheme pre-sented in the present paper results from a study of 65Fe β decay, as wellas of deep-inelastic data that were initially dedicated to the yrast struc-ture of 64Fe [21]. Also, the study of the subsequent 65Co β decay turned





Submitted to Phys. Rev. C 115

MeV) [34], although the error bar is large in the latter case. Underthe influence of the tensor interaction between protons in the πf 7/2 or-

bital and neutrons in the νf 5/2 and νg9/2 orbitals [35], the closure isexpected to decrease even further for the N = 40 isotones with lower Z.The N = 50 energy shell gap in 78Ni is not experimentally determinedyet, but the systematics of the N = 50 isotones with Z = 31 − 40 in-dicate the persistence of this gap towards nickel [36]. Nuclear structureof the cobalt isotopes was until recently known up to N = 37 and thestructure of all of the nuclei can be interpreted as originating from aπf −1

7/2proton hole coupled to its adjacent nickel neighbor. Moreover, the

dominant low-energy structure of 67,69Ni and 68−70Cu can be explainedas due to a coupling with excited levels of the 68Ni core [37]. It came,therefore, as a surprise that the first excited level in 67Co arises from

excitations across Z = 28 [23]. The complementarity of the β -decay anddeep-inelastic experiments allows to interpret the 65Co structure. Also,a more detailed 67Fe β -decay scheme is presented and will be discussedextensively.

II. EXPERIMENTAL SETUP

A. β decay at LISOL

Short-lived 65,67Fe and 65,67Co isotopes have been produced at the

LISOL facility [38, 39] installed at the Cyclotron Research Center (CRC)at Louvain-La-Neuve (Belgium) with the 30-MeV proton-induced fissionreaction on 238U. The two 10 mg/cm2 thin 238U targets were placed in-side a gas catcher in order to stop and thermalize the recoiling fissionproducts in an argon buffer gas with 500 mbar pressure. As the fissionproducts, dragged by the argon flow, come close to the exit hole of thegas cell, they are irradiated by two excimer-pumped dye lasers that res-onantly ionize the desired element. The ions leaving the cell are trans-ported through a SextuPole Ion Guide (SPIG) [40] to a high-vacuumenvironment, where they are accelerated over a potential difference of 40 kV. After separation according to their mass-to-charge ratio A/Q,

the ions are implanted into a detection tape surrounded by three thinplastic ∆E β detectors and two MINIBALL γ -detector clusters [41].Important features of the detection setup, described in [42], are the

MINIBALL’s granularity and the data acquisition through digital elec-



116 Paper III

tronics. The granularity reduces substantially the loss in photo-peakefficiency due to true γ summing. In the data acquisition, all β and γ

events get an absolute time stamp by a 40-MHz clock, so that no timinginformation gets lost. The β -gated γ spectra contain the γ events thatoccurred in a prompt time window of 350 ns after a β event. To suppressthe true summing of β particles with γ rays in the germanium crystalsprompt γ events are vetoed if the β event occurred at the same sideof the detection setup [43]. The combination of digital electronics andhigh selectivity by the laser ion source coupled to mass separation offersthe possibility to correlate single γ events and/or β -gated γ events witheach other up into the seconds time range [42], which turned out to becrucial to disentangle the A = 67 decay scheme from iron down to nickel[23].

For half-life determinations, data were acquired in a cycle where,in a first period, the cyclotron beam was on and the mass separatoropen, followed by a period where the beam was switched off and theseparator closed. After a fixed number of such cycles, the implantationtape was moved in order to remove long-lived daughter and contaminantactivities. The cycles used are specified in Table I, which also containsproduction rates at the exit hole of the gas cell as obtained from theobserved γ intensities. Despite the high purity of the argon buffer gas (atthe ppb-level) and the careful preparation of the gas cell, the productionyield is very sensitive to the impurity level of the buffer gas. Due toslightly different conditions, the 67Fe production rate was a factor of 3

higher in data set IV than was the case in data set VI.The γ -energy and efficiency calibrations were performed by placing

standard 133Ba, 137Cs, 152Eu and 60Co sources at the implantation spotof the detection tape as well as by on-line implantation of 90Rb (withintense γ lines up to 3.317 MeV) and of 142Ba isotopes, which wereproduced in large amounts. The activity could be calculated from the β rate, but at mass A = 142 the large production of 142Cs isotopes had tobe coped with. Advantage was taken of the large difference in half livesbetween 142Cs (T 1/2 = 1.7 s) and 142Ba (T 1/2 = 10.7 min) by acquiringdata in a 600s/600s/1 implantation-decay cycle and by not consideringthe implantation period and the first 10 s of the decay period. The latter

notation denotes a cycle of 600 s implantation and 600 s decay and theimplantation tape is moved after 1 cycle. The γ efficiencies were fitted




T a

b l e I : L i s t o

f t h e

d i ff e r e n t d a t a s e t s w

i t h i n d i c a t i o n

o f t h e m a s s A ,

t h e

l a s

e r r e s o n a n c e ,

t h e c y c

l e ( b e a m

O N / b e a m

O F F / n u m

b e

r o

f c y c

l e s p e r t a p e m o v e

) , t h e t o

t a l d a t a - a c q u

i r i n g t i m e

∆ t , t h e p r o

d u c t i o n r a t e P

o f t h e

l i s t e d i s o t o p e a n

d

t h e p a r a m e t

e r s o

f e q u a t i o n

1 ,

w h i c h d e t e r m

i n e t h e γ - r a y p

h o t o - p e a

k e

ffi c

i e n c y .

D a t a s e t

A

L a s e r s

C y c l e

∆ t ( h )

I s o t o p e

P

( a t / µ C )

C 1

D 1

C 2

D 2

I

6 5

F e

2 . 4 s / 2 . 4 s / 5

4 9 . 9

6 5 F e

1 . 2

3 ( 8 )

8 5 ( 1 1 ) · 1 0 − 5

− 7 9 2 ( 1 9 ) · 1 0 − 3

8 0 0 ( 1 0 0 0 )

2 . 1

6 ( 2 9 )

6 5 m F e

1 . 2

0 ( 1 7 )

I I

6 5

C o

2 . 4 s / 2 . 4 s / 5

2 8 . 6

6 5 C o

6 . 6

( 1 6 )

8 5 ( 1 1 ) · 1 0 − 5

− 7 9 2 ( 1 9 ) · 1 0 − 3

8 0 0 ( 1 0 0 0 )

2 . 1

6 ( 2 9 )

I I I

6 5

o ff

2 . 4 s / 2 . 4 s / 5

4 . 4

6 5 C o

<

1 . 1

8 5 ( 1 1 ) · 1 0 − 5

− 7 9 2 ( 1 9 ) · 1 0 − 3

8 0 0 ( 1 0 0 0 )

2 . 1

6 ( 2 9 )

6 5 F e

<

0 . 0

5

6 5 m F e

<

0 . 0

5

I V

6 7

F e

1 . 4 s / 1 . 6 s / 3

9 . 9

6 7 F e

1 . 3

7 ( 1 3 )

3 . 1

( 4 ) · 1 0 − 3

− 5 8 ( 2 5 ) · 1 0 − 2

0

V

6 7

o ff

1 . 4 s / 1 . 6 s / 3

5 . 3

6 7 C o + 6 7 m C o

0 . 4

0 ( 8 )

3 . 1

( 4 ) · 1 0 − 3

− 5 8 ( 2 5 ) · 1 0 − 2

0

6 7 F e

<

0 . 0

2

V I

6 7

F e

1 0 s / 0 s / 1

5 3 . 9

6 7 F e

0 . 4

5 ( 1 3 )

1 . 7

( 2 ) · 1 0 − 3

− 6 5 ( 2 ) · 1 0 − 2

0

V I I

6 7

o ff

1 0 s / 0 s / 1

8 . 2

6 7 m C o

0 . 5

1 ( 1 4 )

1 . 7

( 2 ) · 1 0 − 3

− 6 5 ( 2 ) · 1 0 − 2

0

6 7 C o

0 . 2

5 ( 7 )

6 7 F e

<

0 . 0

2



118 Paper III

by the function

εγ =

1

C 1E D1γ + C 2E D2

γ (1)

and the parameters determined with this expression are given in Table Ifor the respective data sets. Note that for data sets IV-VII the secondterm in the denominator, which fits the low-energy behavior, was fixedto 0, since there are no γ transitions with low energy in the 67Fe decay.

B. Deep-inelastic reaction at ANL

Complementary information for the 65Co level structure was ex-

tracted from an experiment performed at Argonne National Laboratory.The prime objective of that experiment was to study excited levels inthe neutron-rich iron isotopes populated in deep-inelastic reactions of a430-MeV 64Ni beam with a 55 mg/cm2 isotopically-enriched 238U target[21, 44]. The uranium target was located in the center of the Gammas-phere array [45] consisting of 100 Compton suppressed HPGe detectors.The nickel beam was produced in bunches separated by 82 ns, but for thedeep-inelastic experiment reported here, only one out of five pulses wasallowed to hit the Gammasphere target. This resulted in prompt burstsseparated by a 410-ns gap within which delayed γ -ray decays emittedby the reaction products could be studied.

Events were recorded on the basis of three-fold or higher-order coin-cidences. Data were sorted offline into single γ spectra, γ -γ matrices andγ -γ -γ cubes. More details about the sorting procedure are given in Refs.[21, 44]. Four types of coincidence cubes PPP (prompt-prompt-prompt),DDD (delayed-delayed-delayed), PDD (prompt-delayed-delayed) andPPD (prompt-prompt-delayed) were created by selecting different γ -ray times with respect to the prompt beam bursts. The PPP cube wasobtained by selecting only the events recorded within ±20 ns of thebeam burst. These events correspond to γ rays emitted by excited lev-els populated directly in the deep-inelastic reaction. The DDD cubewas constructed by selecting only the delayed events (but with the three

γ rays within a prompt coincidence window of 40 ns) acquired duringthe beam-off period. These events consist of γ rays emitted by isomericstates (10 ns to 10 µs range) and/or β -delayed transitions. The PDDand PPD cubes were built by combining the prompt and delayed events




and were used to identify transitions above or below isomeric levels. Anexample of the latter is described in Ref. [44].

III. RESULTS

A. 65Co decay to 65Ni

Fig. 1 presents the vetoed, β -gated γ spectra of data set I with thelasers tuned on the iron resonance in black and of data set II withthe lasers on the cobalt resonance in red. Using the same cycle, datawith the lasers switched off have also been collected (data set III), onlyshowing a line at 511 keV in the vetoed, β -gated γ spectrum. In dataset II, significant contaminant lines are observed at 838 and 1223 keV,

originating from the β decay of 130mSb and 98Y, respectively. 130mSband the molecule 98YO2 are able to reach the detection tape in a doubly-charged state. In Fig. 1, the full circles indicate lines from the 65Fe to65Co decay, open squares from 65Co to 65Ni and open triangles fromcontaminant β decay. The observed transitions, count rates and relativeintensities in 65Ni from data set II are listed in Table II, while thisinformation for the transitions observed in 65Ni and 65Co from data setI is summarized in Tables III and IV, respectively.

Table II: Transitions in 65Ni from 65Co β decay (data set II) are indicated by

their energy E (keV), the corresponding off-resonant subtracted β -gated peakcount rate Aγ and transition intensity I rel relative to the 1141.1-keV transition(100 %). Multiply I rel by 0.027 (7) to get absolute intensities. The γ -rayenergies of coincident events are listed in the last column with the number of observed β -γ -γ coincidences between brackets.

E (keV) Aγ (cts/h) I rel (%) Coincident γ -events

63.4 (4) 0.9 (2) 65 (18)a 1210(3)

310.4 (1) 9.2 (7) 82 (11) 963(16)

963.4 (2) 3.7 (5) 79 (13) 310(16)

1141.1 (2) 4.2 (4) 100 -

1210.6 (2) 1.5 (3) 39 (9) 63(3)

1273.2 (3) 1.6 (3) 42 (9) -

a The relative intensity also includes the correction for electron conversion.



120 Paper III

E n e r g y

( k e V

)

0

2 0 0

4 0 0

6 0 0

8 0 0

1 0 0 0

C o u n t s / 1 k e V - 5 0 0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

C o u n t s / 1 k e V

0 5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

4 5 0

- e + e

E n e r g y

( k e V

)

1 2 0 0

1 4 0 0

1 6 0 0

1 8 0 0

2 0 0 0

2 2 0 0

2 4 0 0

2 6 0 0

2 8 0 0

C o u n t s / 1 k e V - 4 0

- 2 0 0

2 0

4 0

6 0

8 0


0 2 0

4 0

6 0

8 0

1 0 0

1 2 0

F i g u r e

1 :

T h e v e t o e

d β - g a t e d γ s p e c t r u m

w i t h t h e

l a s e r s t u n e

d t o i o n

i z e

i r o n

( u p p e r -

b l a c

k o n - l i n e

) a n

d c o

b a

l t ( l o

w e r - r e

d

o n - l i n e

) . T h

e l i n e s

f r o m

6 5 F e t o 6 5 C o

d e c a y a

r e i n d i c a t e d b y

f u l l c

i r c l e s , t h o s e

f r o m

6 5 C o t o 6 5 N i d e c a y

b y o p e n

s q u a r e s

a n

d c o n t a m

i n a n t l i n e s

b y o p e n t r i a n g

l e s .

T h r e

e d o u

b l e t s a r e p r e s e n t : a t 8 3 7 ( o f

6 5 F e a n

d 1 3 0 m S b d e c a y

) , 9 6 2 ( o f 6

5 F e a n

d

6 5 C o

d e c a y )

a n

d 1 2 2 3 k e

V

( o f 6 5 F e a n

d 9 8 Y

d e c a y

) . T h e 1 3 0 m S b i o n s a n

d 9 8 Y O 2

m o

l e c u

l e s w e r e a

b l e t o r e a c

h t h e d

e t e c t i o n

t a p e

i n a

d o

u b l y - c

h a r g e

d f o r m

( s e e t e x t f o r

d e

t a i l s ) .




A decay scheme for 65Co was proposed already in earlier β -decaywork [22]. Prompt β -γ -γ coincidences (see Table II) confirmed that the

310- and 963-keV transitions are in cascade. Prompt β -γ events coin-cident with delayed 63-keV γ rays in a 1-150 µs time window after theβ event confirmed that the 1210-keV transition feeds an isomeric statewith a 63-keV excitation energy. Out of the total 63-keV decays, 22 % of the activity is missed due to the limited time window of 1 to 150 µs fora 69 µs half-life [46] and 75 % due to internal electron conversion. Thehalf-life effect is taken into account for its γ intensity, as shown in the de-duced 65Co decay scheme of Fig. 2. The relative intensity of the 63-keVtransition, as shown in Table II, also includes the correction for electronconversion, which is necessary to extract the β branching towards the63-keV level in 65Ni. No coincidence relationships were observed for the

lines of 1273 and 1141 keV, confirming their placement as ground-statetransitions [22]. From comparing the off-resonant subtracted β activitywith the total γ activity a strong ground state feeding of 91.7(8) % wasdeduced, which is consistent with Ref. [22].

Table III: Transitions in 65Ni from 65Fe β decay (data set I) are indicated bytheir energy E (keV), the corresponding off-resonant subtracted peak countrate Aγ , transition intensity I rel relative to the 882.5-keV transition (100 %)

and the ratio of relative transition intensities I rel(II )I rel(I )

from data set II and I.

E (keV) Aγ (cts/h) I rel (%) Irel(II )Irel(I)

63.4 (4) 0.50 (12) 10 (3) 6 (2)310.4 (1) 4.1 (5) 10.9 (14) 8 (2)

963.4 (2) 1.9 (5) 12 (3) 7 (2)

1141.1 (2) 1.4 (4) 12 (2) 8 (2)

1210.6 (2) 1.0 (5) 8 (2) 5 (2)

1273.2 (3) 1.0 (4) 8 (2) 6 (2)

All observed γ transitions following 65Co β decay exhibit the samegrowing-in and decay behavior. A half-life of 1.00(15) s was deduced forthe 65Co ground state from a single-exponential fit of the time-dependentsummed intensity of these β -gated γ lines during the beam-off period.This value is slightly smaller, but certainly not significantly differentfrom the previously determined half-life values of 1.14(3) s [22] and1.25(5) s [47]. The decay behavior of β and γ rays was fitted in theformer work, whereas only single β rays were fitted in the latter.



122 Paper III

37Ni65

28

38Co65

27

=5.956(13) MeVβ

Q

-β

0)-

(7/2 1.00(15) s

(%)βI

92(1)<1.5

<0.6

3.2(4)

5.1(9)

log ft

4.4(1)>6.1

>6.4

5.4(1)

5.1(1)

2.52 h

sµ69(3)0

63.4(4)

310.4(1)

1141.1(2)

1273.5(2)

-5/2

-1/2

-3/2

)-

,9/2-

(7/2

)-

(5/2

4 2 ( 9 )

1 2 7 3 .

2 ( 3 )

3 9 ( 9 )

1 2 1 0 .

6 ( 2 )

7 9 ( 1 3 )

9 6 3 .

4 ( 2 )

1 0 0

1 1 4 1 .

1 ( 2 )

8 2 ( 1 1

)

3 1 0 . 4

( 1 )

1 6 ( 5 )

6 3 .

4 ( 4 )

Figure 2: The 65Co decay scheme into 65Ni. Spin and parities without bracketsare taken from [48], while those within brackets are deduced from the presentβ -decay study.

The deduced 65Co decay scheme of Fig. 2 does not contain the pre-viously assigned 340-, 384- and 882-keV transitions [22]. The 340- and882-keV γ rays follow the β decay of 65Fe, see section III B, while theexpected 384-keV peak integral in the β -γ spectrum would be 17(2) asdeduced from the γ intensities given in Ref. [22] and the 310-keV peakintegral. No 384-keV peak is observed in the spectrum, but this is still

consistent within 2σ with Ref. [22], due to the background conditions.The structure of 65Ni has also been studied in (t pol, d) transfer reac-

tion experiments [48] from which spin and parities have been deduced forvarious levels. The 5/2− ground state is strongly fed by direct Gamow-




Teller β decay, which is consistent with an expected (7/2−) ground stateof 65Co. The 1141-keV level, for which spin and parity quantum num-

bers were not yet assigned, is strongly fed. Based on a (7/2−

)65

Coground state and a lack of γ deexcitation to the low-spin states, a spinand parity of (7/2−) or (9/2−) can be expected. Also, the state at1274 keV gets significant β feeding (log f t = 5.1(1)), and a subsequentstrong γ decay is observed to the 5/2− ground state, the 1/2− state at63 keV and the 3/2− state at 310 keV. The observed γ decay to the63-keV, 1/2− state rules out (7/2−) and (9/2−) assignments and leaves(5/2−) as the only possibility. This is, however, in disagreement withthe previously assigned spin and parity of 1/2− in Ref. [48].

Missing γ -ray activity from higher lying states feeding the 1274-keVlevel seems unlikely due to the relatively small β -endpoint energy of

5.956(13) MeV. Furthermore, the 1/2−

assignment is not consistentwith 64Ni(n, γ ) studies. This reaction populates a 1/2+ level in 65Niat 6098 keV [49], which decays predominantly by high-energy E 1 tran-sitions to 1/2− and 3/2− levels. The (n, γ ) work clearly establishes four1/2− and 3/2− states at low energy (at 64, 310, 692 and 1418 keV).None of these levels are fed directly in the 65Co β decay. Moreover,the 6098-keV level does not populate directly the 5/2− ground state northe 1141- and 1274-keV states, which indicates that the latter two stateshave spin J = 5/2 or greater. In the event that a 1/2− assignment to the1274-keV level would have been correct, the strong β feeding would haveto originate from a low-spin, β -decaying isomer in 65Co. Penning-trap

mass measurements, however, could not identify a β -decaying isomer in65Co [50].

B. Level structure in 65Co

1. β -decay study of 65Fe at LISOL

Peaks enhanced in the data with the lasers tuned to the iron reso-nance and absent in the data with the lasers on the cobalt resonance, canbe unambiguously assigned to the 65Fe β decay feeding excited statesin 65Co. Hence, the data provide clear evidence that the intense linesat 340 and 883 keV, previously assigned to the 65Co decay [22], occurin fact in the 65Fe β decay. At 838 and 1223 keV, the contaminant ac-tivity from the doubly-charged 130mSb ions and 98YO2 molecular ionsform a doublet with the iron lines. The relative γ intensities of the



124 Paper III

Energy (keV)0 200 400 600 800 1000 1200

C o u n t s / 1

k e V

0

2

4

6

8

10

12

14

16

18

20

22

1 2 8 k e V

2 1 3 k e V

340 keV

7 3 6 k e V

9 6 1 k e V

1 0 7 6 k e V

1 1 1 4 k e V

Figure 3: The γ -ray spectrum of prompt coincidence events with β -gated, 883-keV events.

iron lines were obtained by subtraction of the off-resonant contribution,

which could be deduced from data set II. The iron line at 961 keV alsoforms a doublet with the 963-keV transition from 65Co decay. Hence,the contribution of the cobalt line is obtained from the 310-keV peakintegral and the relative γ intensities of the 310- and 963-keV γ rays,as deduced in the 65Co decay, see Table II. It was checked that the γ intensities of both the 1211-keV and the 1273-keV transitions relativeto the 310-keV line in data sets I and II are in agreement.

Two independent level schemes can be constructed using the transi-tions and their coincidence relations given in Table IV. Starting with themost intense line in Table IV, the 883-keV transition, a level at 883 keVis deduced. Fig. 3 shows the γ spectrum of prompt coincidence events

with β -gated, 883-keV events. It reveals a strong coincidence with 340-keV γ rays. In combination with the 1223-keV cross-over transition, the1223-keV level could be established as shown on the left hand side inFig. 4. The coincident events at 128 and 213 keV match perfectly the




Table IV: Transitions in 65Co from 65Fe β decay (data set I) are indicated bytheir energy E (keV), the corresponding off resonant subtracted peak count rate

Aγ and transition intensity I rel relative to the 882.5-keV transition (100 %).Multiply I rel by 0.20 (6) to get absolute intensities. The γ -ray energies of coincident events are listed in the last column with the number of observedβ -γ -γ coincidences between brackets.

E (keV) Aγ (cts/h) I rel (%) Coincident γ -events

127.6 (3) 1.7 (6) 3.4 (12) 213(8), 736(5), 883(5), 961(2)

212.5 (2) 5.2 (6) 11.1 (13) 128(7), 736(3), 883(17), 1089(7)

340.07 (6) 16.5 (7) 47 (2) 736(27), 774(6), 883(53), 961(8)

413.0 (10) - 2.6 (12) 1000(4)

736.1 (10) 4.3 (4) 22 (2) 340(28), 883(8), 1223(7)

774.0 (10) - 6 (4) 340(5), 883(2), 1223(1)

836.6 (2) 2.6 (5) 14 (3) 1642(4)864.0 (10) - 1.8 (10) 213(6), 883(1)

882.50 (9) 17.0 (6) 100 128(7), 213(20), 340(53), 736(6),

961(9), 1076(5), 1114(12)

960.5 (2) 1.4 (5) 9 (3) 310(6), 340(10), 883(8)

999.7 (3) 2.7 (4) 18 (2) 413(4), 1480(4)

1076.2 (3) 1.2 (3) 8.3 (18) 883(6)

1088.7 (6) 0.6 (2) 3.9 (13) 213(6), 883(2)

1113.5 (3) 2.1 (3) 15 (2) 883(12)

1222.7 (2) 3.1 (4) 23 (3) 736(7), 774(1), 961(1)

1412.5 (2) 2.6 (3) 22 (3) 1480(7)

1441.1 (4) 0.9 (3) 8 (2) -

1479.5 (2) 5.3 (4) 47 (3) 1000(5), 1413(7)

1625.5 (4) 0.7 (2) 7 (2) -

1641.9 (3) 2.4 (3) 23 (3) 837(5)

1996.6 (4) 3.9 (3) 44 (4) -

2443.3 (4) 2.4 (2) 31 (3) -

2557.5 (3) 2.3 (2) 31 (4) -

2896.0 (4) 0.9 (2) 14 (3) -

energy difference of 340 keV. Due to its higher intensity, the 213-keV

transition is placed below the 128-keV one and on top of the 883-keVγ ray, establishing the 1095-keV level. The 1959-keV state could beestablished on the basis of the observed coincidences with 1076- and736-keV events, which differ by 340 keV. The 1076-keV transition is



126 Paper III

thus placed on top of the 883-keV level and the 736-keV γ line on topof the 1223-keV state. The 864-keV transition towards the 1095-keV

level was only observed from coincidences with 213-keV events (and one883-keV event), see Table IV. The coincidence relationships between1114- and 883-keV events and a non-coincident cross-over 1997-keV lineprovide evidence for a 1996-keV state. The 774-keV transition towardsthe 1223-keV level is only observed from coincidences with 340-, 883-and 1223-keV events, see Table IV. Based on the 961-keV coincidenceswith 340- and 883-keV events and coincidences between the 1089- and213-keV events, a level at 2183-keV could be established, from whichthe 961- and the 1089-keV transitions feed the 1223-keV and 1095-keVstates, respectively. The 961-keV coincidences with 310-keV γ rays aredue to the 963-keV 65Ni component in this doublet. Based on all the

arguments given above, the β -decay scheme is constructed as given onthe left in Fig. 4.

The β -decay scheme shown on the right of Fig. 4 is constructed fol-lowing the same principles. The strongest transitions in this level schemeare the 1480- and 1642-keV transitions feeding the ground state. The2479-keV level could be established from the 1480- and 1642-keV co-incidence relations with 1000- and 837-keV γ rays, respectively. The2892-keV state could be established on the basis of coincidences be-tween 1413- and 1480-keV events and observed 1000-keV coincidenceswith 413-keV events. The γ -ray transitions at 1441, 1626, 2443, 2558and 2896 keV, which do not show any γ coincidences, are placed as

ground-state transitions in this level structure based on spin and parityassignment considerations. These are discussed further below in thissection.

By systematically shifting the relative excitation energy of both 65Feβ -decay paths, it was checked that the non-coincident lines at 1441, 1626,2443, 2558 and 2896 keV do not fit energy differences between states of the two structures simultaneously. As a result, two independent 65Feβ -decay paths without mutual coincident transitions have been deducedfrom data set I pointing to the presence of two β -decaying states in65Fe. This is consistent with the recent discovery in Penning-trap massmeasurements [50] of a long-lived isomer (T1/2 > 150 ms) at a 402-

keV excitation energy in65

Fe, presumably of high spin (9/2+

), whilethe ground state has low spin (1/2−) [51]. Our gas cell is fast enoughto allow detection of nuclei in the 100-ms range. Two other excitedlevels are known at a lower energy in 65Fe; i.e., at 364 and 397 keV,




3 8

C o

6 5

2 7

3 9

F

e

6 5 m 2

6

3 9

F e

6 5

2 6

= 8 . 2

9 ( 2 4 ) M

e V

β

Q 0

) -

( 1 / 2

0 . 8

1 ( 5 ) s

4 0 2

) +

( 9 / 2

1 . 1

2 ( 1 5 ) s

3 8

C o

6 5

2 7

( % )

β I

( % )

β I

< 2 3

1 2 ( 3 )

< 3

1 8 ( 5 )

5 ( 2 )

5 ( 3 )

4 . 2

( 1 5 )

7 ( 3 )

2 0 ( 3 )

4 0 ( 6 )

1 0 ( 2 )

1 8 ( 5 )

1 6 ( 4 )

1 8 ( 5 )

1 4 ( 4 )

8 ( 3 )

l o g

f t

l o g

f t

>

5 . 7

5 . 5

9 ( 1 3 )

> 6

. 2

5 . 3

( 2 )

6 . 1

( 2 )

6 . 0

( 3 )

6 . 1

( 2 )

5 . 8

( 2 )

5 . 0

6 ( 1 1 )

4 . 7

4 ( 1 1 )

5 . 2

9 ( 1 4 )

5 . 2

( 2 )

5 . 2

( 2 )

5 . 1 4 (

1 6 )

5 . 1

( 2 )

5 . 4

( 2 )

) -

( 7 / 2

) -

( 7 / 2

) -

( 3 / 2

) -

( 1 / 2

) -

( 3 / 2

) -

, 7 / 2

-

( 5 / 2

) -

( 9 / 2

) -

, 7 / 2

-

( 5 / 2

) -

( 1 1 / 2

) -

, 3 / 2

-

( 1 / 2

) -

( 3 / 2

) -

, 3 / 2

-

( 1 / 2

) -

( 1 1 / 2

0

0

8 8 2

. 5

1 0 9 5

. 0

1 2 2 2

. 6

1 4 4 1

. 1

1 4 7 9

. 5

1 6 2 5

. 5

1 6 4 1

. 9

1 9 5 8

. 7

1 9 9 6

. 2

2 1 8 3

. 1

2 4 4 3

. 3

2 4 7 9

. 3

2 5 5 7

. 5

2 8 9 2

. 1

2 8 9 6

. 0

1 4 ( 3 ) 2 8 9 6 . 0 ( 4 )

2 2 ( 3 ) 1 4 1 2 . 5 ( 2 ) 2 . 6 ( 1 2 ) 4 1 3 . 0 ( 1 0 )

3 1 ( 4 ) 2 5 5 7 . 5 ( 3 )

1 1 ( 3 ) 8 3 6 . 6 ( 2 ) 1 7 . 7 ( 2 4 ) 9 9 9 . 7 ( 3 )

3 1 ( 3 ) 2 4 4 3 . 3 ( 4 )

2 3 ( 3 ) 1 6 4 1 . 9 ( 3 )

7 ( 2 ) 1 6 2 5 . 5 ( 4 )

4 7 ( 3 ) 1 4 7 9 . 5 ( 2 )

3 . 9 ( 1 3 ) 1 0 8 8 . 7 ( 6 ) 9 . 4 ( 2 9 ) 9 6 0 . 5 ( 2 )

4 5 ( 4 ) 1 9 9 6 . 6 ( 4 ) 1 4 . 7 ( 2 3 ) 1 1 1 3 . 5 ( 3 )

6 ( 4 ) 7 7 4 . 0 ( 1 0 )

8 . 3 ( 1 8 ) 1 0 7 6 . 2 ( 3 ) 1 . 8 ( 1 0 ) 8 6 4 ( 1 )

2 2 ( 2 ) 7 3 6 . 1 ( 1 )

8 ( 2 ) 1 4 4 1 . 1 ( 4 )

2 3 ( 3 ) 1 2 2 2 . 7 ( 2 ) 4 7 . 5 ( 2 0 ) 3 4 0 . 0 7 ( 6 ) 3 . 2 ( 1 1 ) 1 2 7 . 6 ( 3 )

1 1 . 3 ( 1 3 ) 2 1 2 . 5 ( 2 )

1 0 0 8 8 2 . 5 0 ( 9 )

Figure 4: The two 65Fe decay schemes, see text for a detailed discussion.

respectively [52]. In the event that the 402-keV isomer does (partially)decay internally, a γ ray has to be observed at 363 or 402 keV in thesingles γ spectrum, ignoring low-energy transitions. These transitions



128 Paper III

t (ms)

2500 3000 3500 4000 4500

C o u n t s / 1 0

0 m s

10

210

Figure 5: Summed decay behavior with corresponding fit of the γ lines at340, 736, 883 and 1997 keV, representative of the β decay of the 65Fe groundstate. The line represents a single exponential fit resulting in a half-life valueof 0.81(5) s.

t (ms)2500 3000 3500 4000 4500

C o u n t s / 3 0 0 m s

10

210

Figure 6: Summed decay behavior with corresponding fit of the γ lines at1000, 1413, 1480 and 1642 keV, representative of the β decay of the 65mFeisomer. The line represents a single exponential fit resulting in a half-life valueof 1.12(15) s.




have not been observed in our 65Fe decay study. A proof of the presenceof two β -decaying states in 65Fe would be the observation of γ rays

with different half-lives. The decay behavior of γ rays belonging tothe two different level schemes of Fig. 4 has been fitted by a singleexponential function, shown in Figs. 5 and 6, resulting in half-life valuesof 1.12(15) s and 0.81(5) s, respectively. Previously determined half-lifevalues of 0.45(15) s [53] and 1.3(3) s [17] were significantly different andRefs. [17, 50] already suggested the presence of a β -decaying isomer in65Fe to explain the discrepancy. However, the deduced half-life valuesare both longer than the value in Ref. [53] and, therefore, cannot beexplained on this basis.

The relative energy position of the two level structures could not bederived from the experimental data. For this reason, it is a priori unclear

whether both branches decay into a common ground state of 65

Co or if one of the branches decays into an isomeric state. In the latter case,the isomer has to reside at a relatively low excitation energy of ∼ 50keV or less, since the Penning-trap mass measurements of Ref. [50] didnot resolve an isomeric state in 65Co. The relative 65Ni γ intensities indata set I (lasers on iron) are found to be similar to those of data set II(lasers on cobalt). This is illustrated by the ratio of relative transition

intensities I rel(II )I rel(I )

from both data sets, see Table III. Because more than

90% of the β feeding goes directly to the 5/2− ground state, it has alsobeen checked that the absolute γ intensity of the 310-keV transitionbelonging to the 65Co decay is the same (within the uncertainties) in

the direct 65Co decay (data set II) and via the 65Fe decay (data set I).The fact that these ratios and the absolute γ intensity of the 310-keVtransition are similar further supports the assumption of the presence of only one β -decaying state in 65Co.

An intermediate conclusion here is that there is evidence for two ex-citation structures in 65Co without any interconnecting transitions, fedby two β -decaying states in 65Fe considerably differing in spin. Whetherthese level schemes are built on the same state and which one belongsto the decay of the high-spin (respectively low-spin) state needs furtherconsideration. For the clarity of further discussion, we will attributethe left structure of Fig. 4 to the decay of the low-spin and the right

structure to the high-spin state. This will be discussed in paragraphIIIB3.



130 Paper III

Figure 7:65

Co level scheme deduced from the64

Ni+238

U deep-inelastic reactionby gating on any two coincident γ rays observed in the β decay of 65Fe. Levelsdrawn with thick lines were observed in the analysis of the PPP cube, thoserepresented with thin lines were identified by placing double gates in the DDDcube. A star marks the states that were seen in both PPP and DDD cubes.All states seen in the DDD cube correspond to levels established in the β -decaydata.

2. Deep-inelastic reaction at ANL

The β -decay data alone are insufficient to claim the (non-)existence of a β -decaying isomer in 65Co with absolute certainty. Crucial informationon the 65Co level structure was extracted, however, from a deep-inelasticreaction study. In the present work, only the analysis of triple coinci-dence data (cubes) revealed useful results. As this type of reactionsleads to the production of a wide range of projectile- and target-likefragments, the resulting complexity of the γ spectra can be resolved byusing coincidence techniques. However, in the case of weakly-producednuclei such as 65Co, the analysis of γ -γ coincidence events did not providespectra sufficiently clean to allow for the identification of new transitionsand higher-order coincidences proved essential. Therefore, the successof the present analysis relied entirely on the high selectivity that couldbe achieved by analyzing triple gates in the coincidence cubes.

Excited levels in 65Co were established by gating on any two coin-cident γ rays observed in the β -decay work reported in the previoussection. The Radware [54] software package was used in the analysis.




200 300 400 500 600 700 800Energy [keV]

0

100

200

300

400

C o u n t s / k e V

300 600 900 1200 1500 1800Energy [keV]

0

200

400

600

800

C o u n t s / k e V

200 400 600 800 1000Energy [keV]

2

4

6

8

10

12

14

C o u n t s / k e V

300 600 900 1200Energy [keV]

0

10

20

30

40

C o u n t s / k e V

gate 1479-1000 keV

prompt cube

gate 243-190 keV

prompt cube

delayed cube

sum gates 1479-1000 & 1642-837 keV

delayed cube

gate 883-340 keV

1 9 0

2 4 3 3

5 9

4 4 7

3 5 9

8 3 7

1 0 0 0

1 4 7 9

1 6 4 2

7 3 6

9 6 1

7 7 4

4 1 3

Figure 8: Example of spectra from coincidence gates on transitions in 65Coin prompt (a and b) and delayed cubes (c and d). Transitions in 65Co areidentified by their energies.

The study of triple coincidence data revealed the partial level scheme

presented in Fig. 7. Examples of triple-coincidence spectra are found inFig. 8. As seen in the spectra of Figs. 8c and 8d, the delayed triple-coincidence spectra contain much less statistics when compared to theprompt coincidence data given in the upper part of the same figure(8a and 8b). This is due to the fact that the observed delayed transi-tions result from the β decay of 65Fe, which is only weakly producedin 64Ni+238U deep-inelastic reactions. The investigation of the delayedcube is expected to confirm levels in 65Co reported in the previous sec-tion. On the other hand, the direct population of excited states can bestudied by analyzing the prompt cube. In this case, the reaction mecha-nism favors the population of fairly high-spin yrast and near-yrast states,

which might differ from those populated in β decay.Indeed, the analysis of the delayed cube confirmed most of the levelsobserved in the β -decay work of Fig. 4. As already mentioned above,due to their high selectivity, only triple coincidences were used in the



132 Paper III

present study. Therefore, only cascades of three or more coincident γ rays observed in the β -decay work could be confirmed by the investiga-

tion of the deep-inelastic data set. As a consequence, the γ rays of 1076,1114, 1223, and 1997 keV proposed to arise from the decay of the levelspopulated by the (1/2−) ground state of 65Fe, see Fig. 4, and those of 1412, 1441, 1625, 2443, 2557 and 2896 keV believed to deexcite statespopulated in the decay of the (9/2+) isomer could not be investigated.The levels proposed in the β -decay work and confirmed by the analysisof the DDD cube are drawn with thin lines or marked with a star in thelevel scheme of Fig. 7.

The prompt population of the levels in the left part of Fig. 7 wasstudied by analyzing the PPP cube. No combination of gates set ontransitions depopulating levels proposed (in the previous section) to re-

ceive feeding from the low-spin isomer in65

Fe provided useful informa-tion. This indicates a very weak cross-section for direct population in adeep-inelastic reaction and suggests low-spin values for these levels.

The prompt double-gates, set on the 1000-1479 keV and 837-1642 keVcascades corresponding to the two different decay paths of the 2479-keVstate, provided clear evidence for the presence of four low-energy coin-cident γ rays with energies of 190, 243, 359, and 447 keV, see Fig. 8a.Based on the results of the analysis of all possible combinations of dou-ble gates on the observed transitions, the new γ rays were arranged inthe level scheme of 65Co and deexcite from the levels represented withthick lines in Fig. 7. The 413-keV transition, observed in the β -decay

work, and also confirmed in the analysis of the delayed cube to be in co-incidence with the 1000-1479 keV and 837-1642 keV intense transitions(see Fig. 8c), was not observed in the PPP cube. This indicates thatthe 2892-keV state does not belong to the yrast or near-yrast sequencein 65Co. The 2669-keV level identified in the prompt data was found todeexcite predominately via the 1190-keV transition (72% branching) tothe 1479-keV level.

For this type of deep-inelastic reaction, angular correlation measure-ments are commonly used to determine the multipolarity of γ rays. How-ever, in 65Co, two of the strongest prompt transitions that could possiblybe used as gates, e.g., the 1480- and 1190-keV γ rays, form a doublet

with two intense lines in69

Ga [55], a nucleus strongly produced in thepresent reaction. This prevents reliable multipolarity assignments forthe new states identified in 65Co in the deep-inelastic data set. Also,the statistics for the other observed transitions is too low to allow for




an accurate angular-correlation analysis.

3. Spin and parity considerations and assignments

Unfortunately, the deep-inelastic data did not allow spin and parityassignments to be made on the basis of angular correlations. Thus,for the levels observed in the analysis of the delayed data and markedwith a star in Fig. 7, spin and parities assigned in the β -decay workare assumed, as will be discussed further in this paragraph. However,a comparison with the near-yrast levels of 59Co [56] and 61,63Co [16]populated in other deep-inelastic reactions, reveals a strikingly similarlow-energy structure, as can be noticed in Fig. 9. This suggests a (7/2−)ground state, and (9/2−), (11/2−) and (11/2−) levels at 1480, 1642 and2479 keV, respectively. Note, however, that the 2479-keV level is alsoobserved in the 65mFe β -decay of the (9/2+) isomer with a low log f tvalue of 5.2(2). This value is inconsistent with the proposed negativeparity. One should, nevertheless, also realize that the reported log f tvalues are essentially lower limits due to the possibility of unobserved γ -ray activity from high-energy levels. Because of the systematic similaritywith the 59−63Co level structures obtained in deep-inelastic reactions, the(11/2−) assignment to the 2479-keV level is suggested. The states on topof this 2479-keV state most likely form the (13/2−), (15/2−) sequence,similarly to 61,63Co [16] as can be seen in Fig. 9, but positive paritycannot be entirely disregarded. It is worth mentioning that 15/2 is themaximum spin value of negative parity that can be achieved within theπf −1

7/2ν ( p3/2f 5/2 p1/2)−2 configuration. The highest observed level at 3271

keV might have either J π=17/2+ or 15/2−.In the deep-inelastic data there is also no linking transition observed

between the low-spin levels (left part of Fig. 7) and the high-spin levels(right part of Fig. 7). They are placed, as in Fig. 4, on the (7/2−) groundstate of 65Co, as the only argument for a low-spin isomer in 65Co, thefeeding of the previously (1/2−) assigned 1274-keV level in 65Ni [48], hasbeen argued against in paragraph III A.

In Fig. 4, all the states fed by the (1/2−) 65Fe ground state (log f t ≤

5.6(2)), and subsequently decaying towards the (7/2−

) ground state, canbe assigned as (3/2−) levels; i.e., the states at 883, 1223 and 1996 keV.Allowed Gamow-Teller transitions and γ transitions with multipolarityless than three are assumed. The states at 1959 and 2183 keV are also



134 Paper III

Co61

-7/2 0

-9/2 1285

-11/2 1664

)-

(11/2 2338

)-

(13/2 3471

)-

(15/2 3657

(17/2) 4093

Co63

-7/2 0

-9/2 1383

-11/2 1673

)-

(11/2 2539

)-

(13/2 3034

)-

(15/2 3225

(17/2) 3581

Co65

)-

(7/2 0

)-

(9/2 1479

)-

(11/2 1642

)-

(11/2 2479

)-

(13/2 2669

)-

(15/2 3028

(15/2,17/2) 3271

Figure 9: Yrast and near-yrast levels in odd-mass 61−65Co that are systemati-cally populated in deep-inelastic reactions. The 65Co levels at 1479, 1642, and2479 keV, respectively, are also observed in the β decay of the 65Fe isomer (fullcircle). The levels of 61,63Co are taken from Ref. [16].

significantly fed in β decay from the (1/2−

) ground state, but their decaytowards the (7/2−) 65Co ground state is not observed. It is temptingto assign these states a spin and parity of 1/2−, but from Weisskopf estimates, a 3/2− assignment cannot be ruled out. The state at 1095 keV




is fed by low-spin levels and decays preferentially into the (3/2−) stateat 883 keV rather than towards the (7/2−) ground state. Hence, a

(1/2−

) assignment is tempting, but again (3/2−

) cannot be disregarded.Note also that the 1095-keV level is not fed in β decay, pointing to thefact that its structure is significantly different from the other observedlow-spin states; see also section IV B for more details.

C. 67Fe decay to 67Co

Fig. 10(a) presents the vetoed, β -gated γ spectra from data set IVwith the lasers tuned resonantly to iron in black and from data set Vwith the lasers off normalized to the laser-on time in red. Fig. 10(b)provides the vetoed, β -gated γ spectra from data set VI with the laserstuned resonantly to iron in black and from data set VII with the lasersoff normalized to the laser-on time in red. The full circles indicate linesfrom 67Fe, open squares from 67Co and open triangles from contaminantβ decay. From data set IV the 67Fe half-life was extracted with a singleexponential fit of the 189-keV time dependence during the decay period(T 1/2 = 416(29) ms) [23]. From data set VI the 67Co level scheme wasconstructed [23].

Lines present in the spectra with the lasers on and absent with thelasers off can unambiguously be identified as coming from 67Fe β decay.The isomeric behavior of a laser-enhanced line at 492 keV was alreadyevidenced and extensively discussed in Ref. [23]. The most intense tran-sitions in the 67Fe decay have energies of 189, 492, 680, 1252, 1483, 1509,2054, 2080 and 2089 keV. The strong γ line at 694 keV originates from67Co β decay [7]. The contaminant lines are originating from doubly-charged molecules. The lines at 270, 1969 and 2240 keV are from thedecay of 106Tc; the lines at 296 and 401 keV from 102Nb; and the lineat 1428 keV from 94Sr. Molecules are formed with CO, O2 and 40Ar,respectively.

The 492-keV and 680-keV levels have already been established fromcorrelations measured in the seconds time range [23]. However, theconstruction of the higher-energy structure of 67Co, given in Fig. 12,has not been discussed in detail yet. A solid basis is given by the γ spectrum of coincident 189-keV events, shown in Fig. 11. The coincident571-keV line and a 1252-keV cross-over γ ray give evidence for the stateat 1252 keV. The 1859-keV state is placed, based on the 1179-keV linein the spectrum of Fig. 12 together with the, albeit weak, 1368-keV



136 Paper III

C o u n t s / 1 k e V 1 0 0

2 0 0

3 0 0

4 0 0

5 0 0

6 0 0

1 8 9

2 9 6

5 1 1

6 8 0 6 9 4

1 2 5 2

1 4 2 8

1 5 0 9

2 0 5 4 2 0 8 0

2 0 8 9

2 1 5 3

1 . 6 s / 1 . 4 s / 3

c y c l e

1 5

×

( a )

E n e r g y

( k e V )

0

5 0 0

1 0 0 0

1

5 0 0

2 0 0 0


0

5 0 0

1 0 0 0

1 5 0 0

2 0 0 0

2 5 0 0

3 0 0 0

1 5

×

1 8 9

2 7 0 2 9 6

4 0 1

5 1 1

6 8 0 6 9 4

8 7 7

1 2 5 2

1 4 2 8

1 4 8 3 1 5 0 9

1 9 6 9

2 0 5 4 2 0 8 0

2 0 8 9

2 1 5 3

2 2 4 0

1 0 s / 0 s / 1

c y c l e

( b )

F i g u r e

1 0 : T

h e v e t o e

d ,

β - γ s p e c t r u m

w i t h t h e

l a s e r s t u n e

d t o i o n

i z e

i r o n

i n b l a c k a n

d w

i t h t h e

l a s e r s o

ff n o r m a

l i z e

d t o t h e

l a s e r - o n t i m e

i n r e

d ( o n - l i n e v e r s i o n o n

l y ) i n t

h e

1 . 4

s / 1 . 6

s / 3 c y c

l e ( t o p

) a n

d t h e

1 0 s /

0 s /

1 c y c

l e ( b o t t o m

) . T h e

l i n

e s

f r o m

6 7 F e β

d e c a y

a r e m a r k e

d w

i t h a s t a r a n

d t h o s e

f r o m

6 7 C o w

i t h a n o p e n t r i a n g

l e .

C o n t a m

i n a n t l i n e s a r e n o t m a r k e

d ,

s e e

i n

t h e t e x t f o r

f u r t h e r

i n f o r m a t i o n .




Table V: 67Co transitions from data set IV are indicated by their energyE (keV), the corresponding off resonant subtracted peak count rate Aγ cor-

rected for β efficiency and γ intensity Irel relative to the 189-keV transition(100 %). The last six lines give upper γ -intensity limits (95 % confidence limit)of important transitions. Multiply I rel by 0.847 (36) to get absolute γ intensi-ties. The γ energies of coincident events are listed in the last column with thenumber of observed β -γ -γ coincidences between brackets.

E (keV) Aγ (cts/h) Irel (%) Coincident βγ -events

188.93 (8) 186 (6) 100 571(22), 877(7), 1179(10), 1483(5),

2054(34), 2080(10), 2089(29)

491.55 (11) 99 (15) 99 (29) -

571.4 (2) 3.4 (10) 3.7 (14) 189(17), 1483(1), 1509(3)

680.4 (2) 6.6 (11) 8 (3) -

876.9 (6) 3.4 (10) 5 (2) 189(9), 1179(5), 1368(2)1178.9 (3) 1.9 (6) 3.3 (14) 189(7), 877(5)

1251.9 (4) 5.4 (19) 10 (4) 1483(6), 1509(4)

1368.0 (10) 0.5 (4) 1.1 (9)a 877(2)

1483.2 (2) 3.4 (7) 7 (2) 189(5), 571(1), 1252(6)

1508.9 (3) 3.8 (8) 8 (3) 189(1), 571(3), 1252(4)

2054.2 (2) 6.9 (9) 18 (5) 189(35)

2079.8 (5) 3.3 (9) 8 (3) 189(14)

2088.7 (2) 6.3 (9) 16 (5) 189(29)

2243.3 (2) - < 10 -

2269.0 (3) - < 3.9 -

2277.6 (2) - < 3.3 -

2734.8 (2) - < 4.5 -

2760.6 (3) - < 4.4 -

2769.2 (2) - < 0.9 -

a The relative intensity is based on the number of coincidences with β -gated 877-keVγ rays.

cross-over transition. Evidence for a 2735-keV level is delivered by the189-keV γ ray being coincident with the 2054-keV line and the presenceof the 877-keV and 1483-keV events, which are coincident with 1179-

keV and 1252-keV events, respectively. The 2761-keV state could beestablished from the 189-keV γ ray being coincident with the 2080-keVline and the 1509-keV events being coincident with 1252-keV events.The level at 2769 keV, finally, is placed on the basis of the 2089-keV



138 Paper III

Energy (keV)0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200

C o

u n t s / 1 k e V

2

4

6

8

10

12

14

16

18694 - 189

5 7 1

8 7 7

1 1 7 9

1 4 8 3

2 0 5 4

2 0 8 0

2 0 8 9

Figure 11: The γ spectrum of prompt coincidences with β -gated 189-keVevents. The structure indicated by 694 − 189 is due to Compton scatteringof the 694-keV line.

line in the spectrum of Fig. 11. The spectrum also indicates an intensepeak at 505 keV (marked with ”694−189”), which contains the 189-keVcoincident Compton events originating from the 694-keV transition.

The γ intensities indicated in Fig. 12 are relative to the 189-keVtransition (I γ = 100). The assigned transitions, count rates and relativeintensities are summarized in Table V. The data do not leave room for β feeding towards the 67Co ground state by comparing the total γ intensityof 67Co and 67Ni. The β feeding towards the excited 67Co states is basedon missing γ intensities. As can be seen in Fig. 12, the total feeding isshared 50− 50 between the state at 680 keV and the group of levels at2769, 2761 and 2735 keV. It is remarkable that the latter group of states

decays to the level at 680 keV, but not towards the ground state nor thestate at 492 keV. Therefore, Table V also provides upper limits (95%confidence limit) for the respective cross-over transitions. Compared tothe 2054-keV transition, all the cross-over transitions, except for the2243-keV γ ray, are at least 4 times weaker. The larger upper limit forthe 2243-keV transition is due to the presence of a 106Tc contaminationat 2240 keV. The transitions at 571, 877, 1179 and 1368 keV were firmlyassigned to the 67Fe β decay following the inspection of the observed β -γ -γ coincidences. The isomeric 492-keV state has been fully characterizedby correlations with β -gated 189- and 694-keV γ events.

The spins and parities of the four lowest 67Co levels are assigned

in Ref. [23]. The67

Fe ground state was initially assigned a spin andparity of J π = (5/2+) from isomeric 67mFe γ decay [57], but this wouldbe inconsistent with the strong β branch towards the (3/2−) state at680 keV. On the other hand, a (1/2−) assignment for the 67Fe ground




40Co6727

41Fe67

26=9.4(5) MeV

βQ

-β

0)-

(1/2 416(29) ms

(%)βI

<28

<2449(9)

<5

<2

24(6)

13(4)13(4)

log ft

>5.4

>5.45.0(3)

>5.8

>6.0

4.8(2)

5.0(2)5.0(2)

)-

(7/2

)-

(1/2)

-

(3/2

)-

(5/2

)-

,3/2-

(1/2

)-

(3/2)

-(3/2

)-

(1/2

329(28) ms

496(33) ms

-β

-β <20%

0

491.6680.5

1251.9

1859.1

2734.82760.62769.2

1 6 ( 5 )

2 0 8 8 .

7 8

( 3 )

2 0 7 9 .

8 8

( 3 )

1 5 0 8 .

9 1 8 ( 5 )

2 0 5 4 .

2 7 ( 2 )

1 4 8 3 .

2 5 ( 2

)

8 7 6 . 9

1 .

1 ( 9 )

1 3 6 8

3 .

3 ( 1 4 )

1 1 7 8 .

9

1 0 ( 4 )

1 2 5 1 .

9 3 .

7 ( 1 4 )

5 7 1 .

4

8 ( 3 )

6

8 0 .

4 1 0 0

1

8 8 .

9

9 9 ( 2 9 )

4 9 1 .

6

Figure 12: Partial 67Co level scheme. Multiply the relative γ intensities by0.85(4) to obtain absolute γ strengths.

state, as proposed in Ref. [50], is in agreement with the proposed level

scheme. It also explains the lack of feeding towards both the (7/2−)ground state and the 1252-keV (5/2−) level. The low log f t limit of 5.4for the β feeding of the (1/2−) isomer will be discussed in next section.The strong β decay towards the states at 2735 (log f t = 4.8(2)), 2761(log f t = 5.0(2)) and 2769 keV (log f t = 5.0(2)) gives strong supportfor spin and parity of (1/2−) or (3/2−).

The 2735- and 2761-keV levels are observed to decay to the (5/2−)state at 1252 keV with an intensity similar to that feeding the (3/2−),680-keV level, while the 2769-keV level is only observed to decay to the680-keV state and not to the 1252-keV level. From Weisskopf estimates,E2 and M1 transitions from the 2.75-MeV levels towards the 1252-

keV state are, respectively, three orders of magnitude and two times lessprobable than M1 transitions to the 680-keV level. Hence, the 2735- and2761-keV states can tentatively be assigned a (3/2−) spin and parity andthe 2769-keV level (1/2−) quantum numbers. The state at 1859 keV is



140 Paper III

observed to decay to both the (3/2−) state at 680 keV and the (1/2−)level at 492 keV and not to the 7/2− ground state. This restricts its spin

and parity to 1/2−

or 3/2−

, despite the lack of direct β feeding from the67Fe ground state.

IV. INTERPRETATION

A. Levels in 65Ni

The 65Co ground state has spin and parity (7/2−), which arises fromthe πf −17/2

proton-hole. The dominant β -decay path is the Gamow-Teller

conversion of a f 5/2-neutron into a f 7/2-proton feeding states in 65Ni,

which can be interpreted as a νf

−1

5/2 neutron-hole coupled to

66

Ni. Byfar, the strongest β strength is observed toward the 5/2− ground state,which can be interpreted rather naturally as the νf −1

5/2neutron-hole state.

The other levels that are fed in β decay reside at an excitation energyof 1141 and 1274 keV, which are tentatively assigned (7/2−, 9/2−) and(5/2−) spin and parity, respectively. The low-energy level structureof 65Ni can then be interpreted as a νf −1

5/2, νp−1

1/2or νp−1

3/2neutron-hole

coupled to the 66Ni level structure. The 1/2− state at 63 keV is the νp−11/2

neutron-hole state and the 3/2− level at 310 keV is the νp−13/2

neutron-hole state. The 1274-keV and the 1141-keV levels can be interpreted asthe coupling of the νf −1

5/2hole to the 2+ state in 66Ni, which lies at 1426

keV (see Fig. 13).

B. Levels in 65Co

As will be discussed in this paragraph, 65Co can be interpreted interms of two coexisting structures. On the one hand, states are suggestedarising from a πf −1

7/2proton hole coupled to the first excited 2+

1 and 3+1states of the 66Ni core, see Fig. 13. On the other hand, the (1/2−) stateat 1095 keV is suggested to arise from proton excitations across theZ = 28 shell closure. This assignment is based on the similarity with

the established (1/2−) proton intruder state in 67Co, which is observedin the 67Fe β decay [23]. In addition, the comparison with the 67Costructure indicates that the (3/2−) state at 1223 keV can be interpreted




as the first member of the rotational band built on top of the (1/2−)proton intruder state.

The most straightforward configuration of the suggested (1/2−

)65

Feground state [50] is πf −2

7/2νp−1

1/2. This assignment is, indeed, consistent

with the ground state of the 66Co isotone, which is proposed to be the3+ member of the πf −1

7/2νp−1

1/2configuration [8, 58]. For both isotones,

the preferred decay mode is a Gamow-Teller conversion of a f 5/2-neutroninto a f 7/2-proton [8]. Since the dominant neutron configuration is iden-tical in the two isotones, a similar β -decay pattern is expected for bothcases. In the 66Co β decay, two levels at 2672 and 3228 keV with a dom-inant νp−1

1/2νf −1

5/2configuration, coupling to a respective spin and parity

of 2+ or 3+, are strongly fed [8]. In the 65Fe β decay, strong allowedGamow-Teller decay is expected to J π = 1/2− and/or 3/2− states with

a dominant πf −17/2νp−11/2νf −15/2 configuration, which is a πf −17/2 proton-hole

coupled to the strongly fed 2+ or 3+ states of 66Ni.The strongest feeding is observed to the (3/2−) level at 1996 keV

with a log f t value of 4.74(11). This is very similar to the log f t valueof 4.2(5) of the 66Co β decay towards the 3+ state at 2670 keV [8].On this basis, the 1996-keV state in 65Co can be interpreted as arisingfrom a coupling of the πf −1

7/2proton hole with the 3+ state, and a large

percentage of the πf −17/2νp−11/2νf −15/2 configuration is assigned, as depictedin Fig. 13. One of the states at either 1959 or 2183 keV may well bethe 1/2− member of the multiplet, but, in this case, the higher log f t

values indicate that the proposed configuration is less dominant than inthe 3/2− member.The high-spin members of the πf −1

7/2νp−1

1/2νf −1

5/2multiplet are not fed

in the β decay of the (1/2−) ground state and should rather be searchedfor in the decay of the 9/2+, 65mFe isomer. The (9/2+) 65Fe isomericstate, however, has to involve the νg+1

9/2configuration and, similar to

the (1/2−) ground state, the Gamow-Teller conversion of a f 5/2-neutroninto a f 7/2-proton is expected to be the preferred decay mode. The 2479-keV state is, despite its apparent low log f t value, tentatively assigned(11/2−) and the 2669-keV level tentatively (13/2−), which would be thehighest possible spin formed by a πf −1

7/2⊗3+ coupling. There is, however,

no further evidence to support such an interpretation.The states at 1480 and 1642 keV were assigned (9/2−) and (11/2−),

respectively, from the systematics of 59,61,63Co structures revealed indeep-inelastic experiments [16, 56]. Since the configuration of the (9/2−)



142 Paper III

38Co65

27

)3/2

+1pπ7/2

-2fπ(

)-

(7/2

)-

(3/2

)-

(1/2)

-

(3/2

)-

,7/2-

(5/2)-

(9/2)-

,7/2-

(5/2)-

(11/2

)-

,3/2-

(1/2)-

(3/2)-

,3/2-

(1/2

)-

(11/2

)-

(13/2

(15/2)

(17/2)

0

883

10951223

1441148016261642

195919962183

2443247925582669

289228963028

3271

38Ni66

28

+0

⊗7/2

-1fπ

+2

⊗7/2

-1fπ

)+

(3)

5/2

-1f ν

1/2

-1p ν(⊗

7/2

-1fπ

)+

(4

0

1426

2672

3185

Figure 13: The 65Co levels interpreted as proton-hole states coupled to 66Nicoexisting with a proton intruder state at 1095 keV.

and (11/2−) states in the lighter cobalt isotopes were identified as cor-responding to a coupling of πf −17/2

with the first excited 2+1 state [59], it

is tempting to assign the same configuration to the 1480- and 1642-keVstates. The 2+1 excitation energy in 66Ni of 1425 keV and the observedweak β decay from the (9/2+) isomer to these levels is consistent withthis interpretation. Two other states, at 1441 and 1626 keV, exhibit sim-ilar excitation energies and β -decay strengths, see Fig. 4, which indicate

that these might be other members of the multiplet. A first-forbiddendecay from the (9/2+) level can only feed levels with J ≥ 5/2. Moreover,the 1441- and 1626-keV states are only observed to decay to the (7/2−)ground state. Hence, they are good candidates for the 5/2− and 7/2−




members of the multiplet. The only missing member of the multiplet,at this point, is the 3/2− level, but with the (3/2−) levels at 883 and

1223 keV, there are two possible candidates in this case as well.Both (3/2−) states are rather strongly fed by direct β decay, but

the (1/2−, 3/2−) level at 1095 keV gets almost no β feeding (log f t >6.2) and, therefore, must be associated with a fundamentally differentconfiguration. This low-energy structure is very similar to the one seenin 67Co, where the β decay is strongly hindered to a (1/2−) state at492 keV, which was interpreted as a π(1 p − 2h) intruder state [23].Analogously, the 1095-keV level is most likely a deformed (1/2−) stateinvolving proton excitations across Z = 28. As in 67Co, the intruderstate appears low in energy because of strong attractive proton-neutronresidual interactions [60], that are maximized by the weakening of the

N = 40 subshell closure.From this point of view, the first excited (3/2−) level can be inter-

preted as the πf −17/2 coupling to the 2+1 state, and the second excited

(3/2−) level as the first rotational band member of the (1/2−) protonintruder, in analogy with 67Co. Nevertheless, both states are signifi-cantly fed in 65Fe β decay with respective log f t values of 5.59(13) and5.3(2). Their similar strengths indicate significant configuration mixingfor both levels. With the 883-, 1441-, 1480-, 1626-, and 1642-keV statesinterpreted as members of the πf −1

7/2 ⊗ 2+ quintet, coexisting with the1095- and 1223-keV states interpreted as proton intruder configurations,we describe all levels below 1.7 MeV.

C. Levels in 67Co

The 67Fe ground state requires, contrary to 65Fe, excitations acrossN = 40 to account for its (1/2−) spin and parity. In fact, the groundstate of the 68Co isotone has been interpreted as associated with aπf −1

7/2νg+2

9/2νp−1

1/2configuration [8]. Hence, the ground state of 67Fe con-

sists most likely of a dominant πf −27/2

νg+29/2

νp−11/2

configuration and, as inthe A = 65 case discussed in the previous paragraph, one should expecta similar 68Co and 67Fe β -decay pattern of a νf 5/2 → πf 7/2 allowed

Gamow-Teller conversion. However, the68

Co β -decay study revealedthat there is no level in 68Ni with a dominant νg+2

9/2νf −15/2νp−11/2 configura-

tion in its wave function. In 68Ni, two levels at 4027 and 4165 keV wereinterpreted as arising from this multiplet, but with considerable mixing



144 Paper III

with the πf −17/2

πp+13/2

configuration. Therefore, the β -decay pattern of 67Fe and 68Co may not be as strikingly similar as in the case of 65Fe and

66Co.Strong feeding is observed to three levels at ∼ 2.75 MeV with low

log f t values of ∼ 5.0. This compares well with the β decay of the65Fe ground state to three levels at ∼ 2 MeV, and is indicative of theirstructure consisting of a dominant πf −1

7/2νg+2

9/2νf −1

5/2νp−1

1/2configuration.

However, the γ decay in 65Co and 67Co is substantially different. InFigs. 4 and 10 it can be noticed, for instance, that the 1996-keV level in65Co strongly decays towards the ground state, while no ground statetransitions have been observed from any of the ∼ 2.75-MeV levels in67Co. Thus, there appears to also be a significant structural changewhen going from the N = 38 nucleus, 65Co, to the N = 40 nucleus,

67Co. The low-energy states at 680 and 1252 keV have been discussedalready in previous work [23] and were interpreted as the first membersof a rotational band built on the (1/2−) proton intruder state.

V. CONCLUSIONS

The mass A = 65 β -decay chain from iron down to nickel and the 67Feβ decay have been investigated at the LISOL facility. The 65Co structurehas been studied in detail from the combined analysis of β decay andcomplementary deep-inelastic data, which were taken at ANL. A new65

Fe and a more detailed67

Fe decay scheme have been presented anddiscussed.

The β decay of 65Fe is feeding two independent level structures orig-inating from a (1/2−) ground state and a (9/2+) isomeric state. Thehalf-lives of both states have been determined as T 1/2 = 0.81(5) s andT 1/2 = 1.02(14) s, respectively. The deduced 65Co structure can be in-

terpreted as arising from the coupling of a πf −17/2 proton-hole state with

core levels of 66Ni, coexisting with a proton intruder state at 1095 keV.The subsequent β decay of 65Co is revisited in the present work.

Apart from the wrongly assigned 883- and 340-keV transitions, whichare now unambiguously placed in the 65Fe decay scheme, the 65Co decay

scheme is found to be consistent with that proposed in Ref. [22]. The twoindependent level structures observed in the 65Fe β decay are placed onone common (7/2−) ground state. As a consequence, we claim that theprevious 1/2− assignment of the 1274-keV level in 65Ni [48] is incorrect.




Instead, a (5/2−) spin and parity is suggested. The observed low-energystructure of 65Ni is interpreted as arising from νf −1

5/2, νp−1

1/2and νp−1

3/2

neutron-hole configurations coupled to the 66Ni core structure.The 65Fe and 67Fe ground states feature similar β -decay patterns.

Strong feeding is observed to three high-energy (1/2−), (3/2−) nickelcore-coupled states arising from νp−1

1/2f −15/2

and νg+29/2

p−11/2

f −15/2

neutron con-

figurations, respectively, and to a (3/2−) level suggested to arise from aproton intruder configuration, which in the case of 65Co is strongly mixedwith the 2+ core-coupled configuration. However, there is also evidencefor structural changes between 65Co and 67Co. A strong transition wasobserved in 65Co from the 1996-keV level to the spherical (7/2−) groundstate, whereas the analogous ground state transition was not observedfrom any of the ∼ 2.75-MeV levels in 67Co. The structure could not

be discussed quantitatively due to the lack of reliable large-scale shellmodel calculations. Nevertheless, it is clear that low-energy proton in-truder configurations are now observed from N = 38 onwards due to thestrong tensor interaction between the πf −17/2 proton hole and the νf 5/2and νg9/2 orbitals, demonstrating how subtle the N = 40 subshell gapis.

Acknowledgments

We gratefully thank J. Gentens and P. Van den Bergh for run-

ning the LISOL separator and we acknowledge the support by the Eu-ropean Commission within the Sixth Framework Programme throughI3-EURONS (contract no. RII3-CT-2004-506065), BriX-IUAP P6/23,FWO-Vlaanderen (Belgium), GOA/2004/03, the Foundation for Pol-ish Science (A.K.), the U.S. Department of Energy, Office of Nu-clear Physics, under Contracts DEFG02-94ER40834 and DE-AC02-06CH11357, and the Alexander von Humboldt Foundation (W.B.W.).

[1] M. Bernas et al., Phys. Lett. B 113, 279 (1982).

[2] R. Broda et al., Phys. Rev. Lett. 74, 868 (1995).[3] T. Pawlat et al., Nucl. Phys. A 574, 623 (1994).[4] R. Grzywacz et al., Phys. Rev. Lett. 81, 766 (1998).[5] S. Franchoo et al., Phys. Rev. Lett. 81, 3100 (1998).[6] W. F. Mueller et al., Phys. Rev. Lett. 83, 3613 (1999).



146 Paper III

[7] L. Weissman et al., Phys. Rev. C 59, 2004 (1999).[8] W. F. Mueller et al., Phys. Rev. C 61, 054308 (2000).[9] J. Van Roosbroeck et al., Phys. Rev. C 69, 034313 (2004).

[10] B. Zeidman and J.A. Nolen, Jr, Phys. Rev. C 18, 2122 (1978).[11] G. Georgiev et al., J. Phys. G 28, 2993 (2002).[12] O. Sorlin et al., Phys. Rev. Lett. 88, 092501 (2002).[13] N. Bree et al., Phys. Rev. C 78, 047301 (2008).[14] I. Stefanescu et al., Phys. Rev. Lett. 98, 122701 (2007).[15] I. Stefanescu et al., Phys. Rev. Lett. 100, 112502 (2008).[16] P. H. Regan, J. W. Arrison, U. J. Huttmeier, and D. P. Balamuth, Phys.

Rev. C 54, 1084 (1996).[17] O. Sorlin et al., Nucl. Phys. A 669, 351 (2000).[18] M. Sawicka et al., Eur. Phys. J. A 22, 455 (2004).[19] M. M. Rajabali et al., in Proceedings of the Fourth International Confer-

ence on Fission and Properties of Neutron-Rich Nuclei , edited by J. H.

Hamilton, A. V. Ramayya, and H. K. Carter (Sanibel Island, USA, 2007),p. 679.

[20] L. Gaudefroy, Ph.D. thesis, Universite de Paris XI Orsay (2005).[21] N. Hoteling et al., Phys. Rev. C 74, 064313 (2006).[22] U. Bosch et al., Nucl. Phys. A 477, 89 (1988).[23] D. Pauwels et al., Phys. Rev. C 78, 041307(R) (2008).[24] T. Otsuka, T. Suzuki, R. Fujimoto, H. Grawe, and Y. Akaishi, Phys. Rev.

Lett. 95, 232502 (2005).[25] E. Caurier, F. Nowacki, and A. Poves, Eur. Phys. J. A 15, 145 (2002).[26] O. Sorlin et al., Eur. Phys. J. A 16, 55 (2003).[27] N. A. Smirnova, A. De Maesschalck, A. Van Dyck, and K. Heyde, Phys.

Rev. C 69, 044306 (2004).

[28] M. Hjorth-Jensen, T.T.S. Kuo, and E. Osnes, Phys. Rep. 261, 125 (1995).[29] F. Nowacki, Ph.D. thesis, IReS, Strasbourg (1996).[30] M. Hannawald et al., Phys. Rev. Lett. 82, 1391 (1999).[31] P. Adrich et al., Phys. Rev. C 77, 054306 (2008).[32] N. Aoi et al., Nucl. Phys. A 805, 400c (2008).[33] S. Rahaman et al., Eur. Phys. J. A 34, 5 (2007).[34] G. Audi, A. H. Wapstra, and C. Thibault, Nucl. Phys. A 729, 337 (2003).[35] T. Otsuka, T. Matsuo, and D. Abe, Phys. Rev. Lett. 97, 162501 (2006).[36] J. Hakala et al., Phys. Rev. Lett. 101, 052502 (2008).[37] A. M. Oros-Peusquens and P. F. Mantica, Nucl. Phys. A 669, 81 (2000).[38] Y. Kudryavtsev et al., Nucl. Instr. Meth. Phys. Res. B 204, 336 (2003).[39] M. Facina et al., Nucl. Instr. Meth. Phys. Res. B 226, 401 (2004).[40] P. Van den Bergh et al., Nucl. Instr. Meth. Phys. Res. B 126, 194 (1997).

[41] J. Eberth et al., Prog. in Part. and Nucl. Phys. 46, 389 (2001).[42] D. Pauwels et al., Nucl. Instr. Meth. Phys. Res. B 266, 4600 (2008).[43] L. Weissman et al., Nucl. Instr. Meth. Phys. Res. A 423, 328 (1999).[44] N. Hoteling et al., Phys. Rev. C 77, 044314 (2008).




[45] I. Y. Lee, Nucl. Phys. A 520, c641 (1990).[46] URL: http://www.nndc.bnl.gov/ensdf/.[47] E. Runte et al., Nucl. Phys. A 441, 237 (1985).[48] E. R. Flynn, R. E. Brown, F. D. Correll, D. L. Hanson, and R. A. Hard-

ekopf, Phys. Rev. Lett. 42, 626 (1979).[49] S. Cochavi and W. R. Kane, Phys. Rev. C 6, 1650 (1972).[50] M. Block et al., Phys. Rev. Lett. 100, 132501 (2008).[51] M. Block et al., Phys. Rev. Lett. 101, 059901(E) (2008), erratum of

Ref. [50].[52] J. M. Daugas et al., AIP Conf. Proc. 831, 427 (2006).[53] S. Czajkowski et al., Z. Phys. A 348, 267 (1994).[54] D. Radford, Nucl. Instr. Met. Phys. Res. A 361, 297 (1995).[55] P. Bakoyeorgos, T. Paradellis, and P. A. Assimakopoulos, Phys. Rev. C

25, 2947 (1982).[56] E. K. Warburton, J. W. Olness, A. M. Nathan, J. J. Kolata, and J. B.

McGrory, Phys. Rev. C 16, 1027 (1977).[57] M. Sawicka et al., Eur. Phys. J. A 16, 51 (2003).[58] O. Ivanov, Ph.D. thesis, Katholieke Universiteit Leuven (2007).[59] K. W. C. Stewart, B. Castel, and B. P. Singh, Phys. Rev. C 4, 2131 (1971).[60] K. Heyde, P. Van Isacker, M. Waroquier, J. L. Wood, and R. A. Meyer,

Phys. Rep. 102, 291 (1983).





Paper IV: Evidence for a1/2

− β -decaying isomer in71Ni

149






Evidence for a β -decaying 1/2− isomer in 71Ni

I. Stefanescu1,2,3,4, D. Pauwels1, N. Bree1, T.E. Cocolios1, J.

Diriken1, S. Franchoo5, M. Huyse1, O. Ivanov1, Y. Kudryavtsev1,

N. Patronis1, J. Van De Walle1, P. Van Duppen1, W.B. Walters2


Celestijnenlaan 200D, B-3001 Leuven, Belgium 2Department of Chemistry and Biochemistry,

University of Maryland, College Park, Maryland 20742, USA3Physics Division, Argonne National Laboratory,

Argonne, Illinois 60439, USA4Horia-Hulubei National Institute for Physics and Nuclear Engineering,

PO-Box MG-6, Bucharest, Romania and 5IPN Orsay, F-91406 Orsay Cedex France

Abstract

We report on the investigation of the population mechanism for the 454-KeVlevel in 71Cu. This level was identified for the first time in a recent Coulombexcitation measurement with a radioactive beam of 71Cu. The selective natureof the Coulomb-excitation process as well as nuclear-structure considerationsconstrain the possible spin values for the newly observed state to I π=1/2−.A re-examination of the data set obtained in a β -decay study at the LISOL

separator revealed that this state is also populated in the decay of

71

Ni, mostprobably by direct feeding from a newly identified 1/2− β -decaying isomerhaving a T 1/2=2.34(25) s. In this paper we investigate the proposed scenarioby reanalyzing the β -γ and γ -γ coincidences obtained in the β -decay study atLISOL.

PACS numbers: 25.70.De,21.10.Ky,21.60.Cs,27.50.+e



152 Paper IV

I. INTRODUCTION

Isomeric states in nuclei around closed shells can occur due to thelarge spin difference between the valence orbitals (single-particle iso-mers) or when the maximum amount of angular momentum created ina single-particle configuration is reached (seniority isomers). Depend-ing on the transition probabilities involved, an isomeric state can decayby e.g., γ transitions to lower lying-states or β radiation to the groundor excited states of the daughter nucleus. The investigation of nuclearisomers gives important information regarding the evolution of the shellstructure in a specific mass-region.

The identification of isomeric states in the neutron-rich nuclei withZ∼28 and N∼40-50 constitutes a field of a great current interest. These

states store key information about the structural changes induced byincreasing the neutron number and especially by the filling of the uniqueparity νg9/2 orbital. An experiment employing the fragmentation of a86Kr34+ beam with an energy of 60.3 MeV/nucl. led to the identificationof thirteen new µs-isomers in the neutron-rich nuclei from Sc (Z =21)to As (Z =33) [1]. Spins and parities assignments were based on theobserved γ -decay pattern and comparisons with the systematics. Mostof the identified isomers were found to originate from the stretched νgn

9/2configurations and decay to the lower-lying states via E 2 or M 2 γ -transitions [1].

In recent years, β -decaying isomers in the neutron-rich nuclei around68

Ni have been extensively studied as well [2–6]. Such isomers, arisingfrom the large spin difference between the opposite parity orbitals νp1/2and νg9/2, are expected to be found at low excitation energies in the odd-odd and odd-N nuclei with N∼40. Among these, the odd-N Ni isotopesare of special interest since their low-energy levels are expected to arisemainly from neutron single-particle excitations whose investigation offersimportant information concerning the core properties of 68Ni.

Low-lying states in the neutron-rich 67,69,71,73Ni were identified in theβ decay of their Co isobars obtained in proton-induced fission combinedwith resonant laser ionization [2, 7] and in fragmentation reactions [1, 3,8, 9]. 1/2− and 9/2+ spins and parities were proposed for the ground-

states of 67

Ni and69

,71

,73

Ni, respectively, based on the observed β -decaypattern and shell-model calculations [2, 3, 7–10]. In 69Ni, the 1/2− stateoriginating from 2 p−1h excitations ν ( p−1

1/2g29/2) across the N=40 subshell

was found to be a long-lived isomer (T 1/2=3.5(5) s) decaying via a fast




Gamow-Teller β transition (logft = 4.3(2)) to the first excited 3/2−

state at 1298 keV in 69Cu [2, 3, 11, 12]. The observed weak branch to

the 3/2−

ground-state of 69

Cu was explained by invoking some mixingof the wave function, dominated by the πp+1

3/2νg+0

9/2component, with the

πp+13/2

νp−21/2

g+29/2

configuration proposed for the excited 3/2− level at 1298

keV [2, 3]. No feeding of the isomer to the single-particle 1/2− stateat 1096 keV in 69Cu was observed, suggesting a rather pure πp+1

1/2νg0

9/2structure for this level.

Level schemes of the neutron-rich odd-A Ni isotopes beyond 69Niare still poorly known. In all odd-A Ni isotopes with masses from 71to 77, the shell model predicts a spin and parity 9/2+ for the groundstate and a low-lying 1/2− level dominated by the νp1/2 neutron-holeconfiguration [10]. Sawicka et al. [8] reported four γ transitions in each

of the 71,73Ni isotopes observed in the β decay of the 71,73Co isobars.Due to the poor statistics, γ -γ coincidences could not be constructed.Therefore, the observed transitions were placed in a level scheme basedon shell model predictions [8].

Most of the γ rays reported by Sawicka et al. [8] were recently con-firmed by the results of a decay-spectroscopy experiment performed atNSCL, MSU [9]. In that experiment, the 71,73Co isotopes were producedin the fragmentation of a 86Kr beam with an energy of 140 MeV/nucleononto a thick 9Be target. The secondary fragments were implanted in adouble-sided silicon strip detector surrounded by the NSCL Ge detectorarray SeGA used to detect the γ rays. The good statistics obtained

in that measurement allowed for the analysis of γ -γ coincidences whichprovided the basis for the placement of the observed transitions in thedecay schemes of 71,73Co given in Fig. 4 of Ref. [9]. The two strongpeaks observed at energies 566 and 774 keV did not show any coinci-dence relationship with each other nor with any of the other transitionsobserved in the γ spectrum associated with the β decay of 71Co. Basedon a comparison with the systematics and shell-model predictions, bothtransitions were tentatively placed to feed the 1/2− level, suggested tobe a β -decaying isomer [9].

The present study was prompted by the observation of a new statelocated at 454 keV populated in a recent Coulomb excitation experiment

with postaccelerated radioactive beam of 71Cu produced at ISOLDE,CERN. The results of that measurement are presented in Ref. [13]. Thelow beam-energy (∼3 MeV/u) used in that experiment ensured that thepopulation of the excited states proceeds mainly via E 2 excitations from



154 Paper IV

Energy [keV]

300 350 400 450 500 550 600 650 700 750

C

o u n t s

50

100

150

200

250

454 keV-

3/2→)-

(1/2

534 keV-

3/2→-

5/2

Cu71

Energy [keV]900 1000 1100 1200 1300 1400 1500

C o u n t s / 4

k e V

20

40

60

80

100

120

140

1213 keV

1096 keV

-3/2→

-5/2

-3/2→

-1/2

Cu69

Figure 1: Particle-γ -ray coincidence spectra obtained after Coulomb excitationexperiment with radioactive beams of 71Cu (top) and 69Cu (bottom). Thespectra are Doppler corrected for the mass of the projectile.

the 3/2− ground-state, therefore only levels with spins 1/2−, 3/2−, 5/2−

and 7/2− were expected to be populated. The top of Figure 1 showsthe γ spectrum after Coulomb excitation obtained with the beam of 71Cu. The spectrum is Doppler corrected for the mass of the projectile.The newly observed γ ray of 454 keV and the known 5/2− → 3/2−g.s.transition of 534 keV [11, 12, 14] are clearly visible in the spectrum.

In the lighter Cu isotopes, an 1/2−

state dominated by the π2 p1/2single-particle orbital was identified at low excitation energies. Its en-ergy is very close to that of the 5/2− level found to contain a largecomponent from the π1f 5/2 orbital [15]. The Coulomb excitation exper-




Energy[keV]

200 600 1000 1400 1800

C o u

n t s

0

500

1000

1500

2000

2500

*

* **

*

**

Energy[keV]440 460 480 500 520 540

C o u n

t s

100

300

500

700

454keV

*

*

*O

*

* 5 1 1 k e V

Figure 2: Beta-gated γ spectrum for mass A=71 obtained from the data setreported in [11, 12]. The γ rays following the β decay of 71Ni are marked withan asterisk. In the inset, the region around 500 keV is enlarged, showing the454-keV line. The peak marked with a circle was assigned to the β decay of the daughter nucleus 71Cu.

iment mentioned above included also a measurement with radioactivebeam of 69Cu [13]. A portion of the Doppler-corrected particle-γ coinci-dence spectrum obtained in that run is shown at the bottom of Figure1. The two peaks present in the selected energy range were identified asthe transitions depopulating the first and second excited states in 69Cu,namely the 1/2− and 5/2− levels at 1096(6) [16] and 1213.5(1) keV [12],respectively. Population of the closely-lying 3/2− state at 1297.9(1) keVwas not observed in the aforementioned Coulomb excitation measure-ment.

As pointed above, the E 2 excitation from the 3/2− ground-state of 71Cu constrains the spin of the newly identified state to values I π ≤7/2−.A spin 7/2− would imply a pure E 2 character for the 7/2− →3/2− de-populating transition. The calculated Weisskopf estimate for the partialdecay-lifetime indicates that an E 2 transition of 454 keV will proceedin ∼2 ns, more than three orders of magnitude slower than an M 1 tran-



156 Paper IV

sition. The observation of a Doppler broadened 454-keV peak in ourCoulomb excitation spectrum suggests a half-life in the picosecond range

for the emitting level and therefore an M 1 character for the depopulat-ing γ ray. This restricts the spin of the 454 keV level to values I π ≤5/2−.In Ref. [13], spin and parity (1/2−) were assigned to the newly observedstate at 454 keV, based on the systematics of the lighter Cu isotopes andcomparison with the Coulomb excitation spectrum with beam of 69Cu.Such a spin assignment is also in agreement with the shell-model andparticle-core coupling calculations [12, 17–19]. It is worth mentioningthat in 71Cu, the second 3/2− state is still unknown. Shell-model andparticle-core calculations predict this state around 1900, 1662, and 1100keV, respectively [12, 17, 19].

It is also worthwhile to mention that isomeric 1/2− states originating

from 2 p− 1h excitations across Z =40 have been observed in the valencepartner of 71Ni, 9343Tc50 [21]. In fact, the 1/2− isomer was found to be thefirst excited state in the N =50 isotones from Nb (Z =41) to Rh (Z =45)with a half-life ranging from 60.9 days to 1.96 minutes, respectively [21].In 93Tc, however, the β -decay from the 1/2− isomer (T 1/2=43.5 min)was found to compete with a M 4 transition to the 9/2+ ground-state[21].

This paper focuses on the possible decay modes of the 1/2− state in71Ni. We analyze and discuss the experimental evidence indicating thatthis state is a β -decaying isomer feeding the newly observed (1/2−) stateat 454 keV in 71Cu [13]. The data sets used in the present study were

obtained in two different β -decay experiments performed at the LISOLfacility, Louvain-la-Neuve. In the first measurement, the β -decay studyof 71Ni was used as a means to investigate the low-lying level scheme of 71Cu [11, 12]. The second experiment was dedicated to the identificationof the energy levels in 71Ni populated in the decay of the 71Co isobar.

II. EXPERIMENTAL DETAILS

The 71Ni and 71Co beams were produced in two separate measure-ments at the LISOL facility by colliding a 30-MeV proton beam withtwo thin 238U foils mounted inside a gas cell [20]. The cell was filledwith 500 mbar of Argon gas. The radioactive Ni and Co atoms were res-onantly photoionized, mass separated and implanted in a movable tapesurrounded by β and γ detectors arranged in a close geometry. Table I




Table I: Half lives of the mother nuclei, specific implantation-decay cycles, mea-suring times with and without laser radiation, beam intensities and productions

rates for 71Ni and 71Co. During experiment I, the lasers were tuned on nickel,while during experiment II they were tuned on cobalt.

Exp. Nucleus T 1/2 Cycle Laser Laser Ibeam Yieldno (s) (impl./decay) ON OFF (µA) (ions/µC)I 71Ni 2.56(3)a 6 s/10 s 35 h 09 min - 6.1 3.0(6)II 71Co 0.079(5)b 0.6 s/1 s 16 h 02 min 12 h 57 min 6.7 0.032(8)

a Ref. [12].bRef. [8].

gives a summary of the experimental conditions in both measurements.

In the first experiment,71

Ni was implanted in a Mylar tape sur-rounded by two HPGe detectors positioned in the horizontal plane andat 90◦ and 270◦ with respect to the beam axis. The relative efficiencyof the detectors reached 70% and 75%, respectively. The emitted betaparticles were recorded in a plastic ∆E scintillator located between thetwo Ge detectors, in forward direction. A detailed description of theexperimental setup can be found in [12].

In the second experiment, the β decay of 71Co was observed by meansof four plastic ∆E detectors while the emitted γ rays were recordedwith three HPGe detectors of 70%, 75% and 90% relative efficiencylocated at 90◦, 0◦ and 270◦, respectively, with respect to the beam axis.

Measurements with and without laser radiation were performed in orderto disentangle the γ rays emitted by the nuclei of interest from the non-resonant transitions.

III. EXPERIMENTAL RESULTS

A. β decay of 71Ni

The β -gated γ spectrum obtained in the experiment with 71Ni beamis presented in Fig. 2. In the inset, the region around 500 keV isenlarged, showing the transition of 454 keV. Gamma rays attributed tothe decay of 71Ni (see Ref. [12] for details) are marked with an asterisk.Open circles label the transitions arising from the 71Cu decay.

In Ref. [12], the 454-keV transition was found not to be in coincidencewith any of the γ rays attributed to 71Cu, therefore it was not further



158 Paper IV

discussed in that paper. The proposed spin value (1/2−) for the 454keV level out of the Coulomb excitation study rules out the possibility

of a direct β branch from the 9/2+

ground state of 71

Ni. Furthermore,the lack of γ -ray coincidences in the β decay study of [12] also excludesindirect feeding from the ground state of 71Ni, see further. Therefore,the alternative scenario that this state is fed by a 1/2− β -decaying isomerin 71Ni is investigated.

The time evolution of the γ intensity of the 454-keV transition isshown in Fig. 3. The data were fitted with a single exponential. Thepoor statistics forced us to take bins of 2 seconds each resulting in threeand five data points for the implantation and decay periods, respectively(see Table I). The last two seconds of the decay period were excludeddue to the very low number of counts observed in the peak. A value of

T 1/2=2.34(25) s was extracted from the fit.

Time [s]0 2 4 6 8 10 12 14

C o u n t s

10

20

30

40

50

60

70

80

454 keV

=2.3(3) s1/2T

Figure 3: Time evolution of the intensity of the 454 γ -ray fitted with a singleexponential function yielding to a half-life of T 1/2=2.3(3) s.

Figure 4 compares the γ -γ spectra gated with the 447-keV transition(top) and the 454-keV line (bottom). The 447-keV transition deexcitesthe level at 981 keV which is populated both directly in the β -decayof the 9/2+ ground-state of 71Ni and from feeding from higher-lyingstates in 71Cu [12]. As can be seen from the inset of Fig. 2, the 447-keV line is twice stronger than the peak at 454 keV. The observationof the 472- and 534-keV transitions in the spectrum coincident with the447 keV γ ray provided the basis for its placement in the level scheme




Energy [keV]

500 1000 1500 2000 2500

C o u n t s / k e V

0

10

20

30

4050

60 5 3 4

4 7 2

gate 447 keV

Energy [keV]

500 1000 1500 2000 2500

C o u n t s / k e V

0

10

2030

40

50

60

gate 454 keV

Figure 4: Background-subtracted γ -γ coincidence spectra gated on the 447 keVtransition (top) and 454 keV γ -ray (bottom).

of 71Cu as shown in Fig. 7 of Ref. [12]. In the spectrum gated with

the 454-keV γ ray shown in the bottom of Fig. 4, no clear peak canbe distinguished from the background, indicating that γ feeding fromhigher-lying states has a negligible contribution to the population of the454-keV level. The observed background is due to true coincidences withβ particles interacting with the Ge detectors. The non-observation of any coincident γ ray supports the scenario that this state is directly fedby a 1/2− isomer in 71Ni.

From the observed number of counts in the 454-keV peak and takinginto account the absolute γ -ray branching from the (1/2−) β -decayingisomer (see section III B) we extract a production rate of 0.2(1) at/µCof the 1/2− isomer in experiment I. With a ground state yield of 3.0(6)

at/µC, see Table I, this results in an isomeric ratio of 7(4)%. Within thesame experimental conditions, a lower limit of 0.74 at/µC was reportedfor the production of the (1/2−) isomer in 69Ni, which was found torepresent nearly 20% from the total production rate of 69Ni [12].



160 Paper IV

C o u n t s / k e V 5 0

1 0 0

1 5 0

o

o

o

C o 7 1

2 8 2 , o

o

o o

oo

N i 7 1

4 4 7 ,

N i 7 1 m

4 5 4 ,

N i 7 1

4 7 2 ,

C u 7 1

5 1 1

N i 7 1

5 3 4 , o

C o 7 1

5 6 6 , C u 7 1

C u 7 1

o

C u 7 1

C o 7 1

7 7 4 ,

L a s e r O N

E n e r g y [ k

e V ]

2 0

0

3 0 0

4 0 0

5 0 0

6 0 0

7 0 0

8 0 0

C o u n t s / k e V

0 5 0 1 0 0

1 5 0

L a s e r O F

F

F i g u r e 5 : B e t a - g a t e d γ

s p e c t r u m

f o r A = 7 1 w h

e n l a s e r s a r e o n ( t o p ) C o r e s o n a n c e a n d l a s e r s a r e o ff ( b o t t o m ) . T r a

n s i t i o n s

b e l o n g i n g t o

t h e d e c a y o f 7 1 C o ( s e e t e x t ) ,

7 1 N

i a n d 7 1 C u a r e m a r k e d o n t h e fi g u

r e .

C o n t a m i n a n t γ

l i n e s a r e m a r k

e d w i t h

o p e n c i r c l e s .

T h e o p e n s q u a r e s m a r k γ

l i n e s b e l o n g i n g t o t h e d e c a y o f 1 1 2 A g , w h i c h o r i g i n a t e s f r o m

1 1 2 R h i s o t o p e s i m

p l a n t e d

n e x t t o t h e t a p e d u r i n g t h e o p t i m i z a t i o n o f t h

e l a s e r - i o n s o u r c e .




B. β decay of 71Co

Figure 5 shows part of the β -gated γ -spectra observed in the mea-surement with the lasers tuned to ionize Co (top) and without laserradiation (bottom). Transitions belonging to the A=71 decay chain arelabeled on the figure. The contaminant lines, represented with opencircles, were found to be emitted by the 142La or 102Nb fission products.142La as well as 102Nb in the form of a molecule with 40Ar could reachthe detection setup in a 2+ charge state and therefore with the same A/qratio as the ions of interest. Another source of contamination found togive a non-resonant signal in the β -gated γ spectra shown in Fig. 5 was112Ag, produced in the decay of 112Rh which was implanted next to thetape during the optimization of the laser-ion source.

With the lasers tuned on the Co resonance, the transitions of 282,566 and 774 keV, assigned to the decay of 71Co in Refs. [8, 9], are clearlyvisible in Fig. 5(top).

The lasers-off spectrum (Fig. 5, bottom) shows the presence of the534-keV line from the non-resonant production of 71Ni. The upper limitsof the γ intensities of the other lines from the decay of 71Ni are consistentwith Ref. [12]. However, in the Co on resonance spectrum (Fig. 5, top),an excess of 35(11) counts in the 454-keV line was observed when usingthe intensity ratio I γ (534)/I γ (454) from Ref. [12] (see Fig. 2). Thisconfirms that the 454-keV line is populated in the decay of the newlyidentified (1/2−) isomer of 71Ni, which in turn is fed by the β -decay of 71

Co [9]. A comparison of the intensity of the 534-keV line in the top andbottom spectra of Fig. 5 indicates that in the Co on resonance spectrumthe observed intensity mainly stems from non-resonant production of 71Ni. Thus, our data do not allow to confirm the ∼10% indirect feedingof the 71Ni ground state in the 71Co decay [9]. However, using the 71Codecay scheme of Ref. [9], we can deduce the absolute 454-keV γ -rayintensity.

From the intensities of the 566-, 774-, and 454-keV lines observedin the spectrum displayed in Fig. 5, we determined an absolute γ -raybranching of 40(15)% to the 454-keV transition. In Fig. 5, the absoluteγ -ray branching is taken as the direct β branching to the 454-keV level

and the remaining intensity of 60(15)% is attributed to the direct feedingof the ground state of 71Cu. Because weaker γ transitions to both the454-keV level and ground state might have been missed, the β branchingvalues should be considered as upper limits. The value extracted for the



162 Paper IV

feeding to the excited state corresponds to a logft of 5.4(2), assumingthat the (1/2−) isomer in 71Ni is indeed located at 499 keV [9].

IV. DISCUSSION

Let us now discuss the implications of the present findings on theevolution of the nuclear structure in this mass-region. Figure 6 showsthe comparison between the β -decay chains 69Co → 69Ni → 69Cu [2, 12]and 71Co → 71Ni → 71Cu [9, 12]. Both 69,71Co isotopes are assumed tohave a 7/2− ground-state dominated by the πf −1

7/2proton-hole configura-

tion for which the major decay path is the Gamow-Teller decay of a f 5/2core neutron to fill the f 7/2 proton orbital. In 69Ni, the strong β -decaybranches from 69Co observed to the levels at 915 and 1518 keV sug-gested dominant νf −1

5/2⊗ 0+(70Ni) and νf −1

5/2⊗ 2+(70Ni) configurations,

respectively, although the latter is considerably mixed up with a νp−11/2

⊗ 2+(70Ni) component [2]. As discussed in Ref. [9], the expected strongGamow-Teller β -decay branch from the 7/2− ground-state of 71Co re-stricts the spins and parities of the excited states populated in the 71Nidaughter nucleus to 9/2−, 7/2− and 5/2−. Based on shell-model predic-tions and the observed systematics, spin and parity 5/2− were assignedto the levels at 1065 and 1273 keV in 71Ni, see Ref. [9] and Fig. 6.

In both 69,71Ni nuclei, the 5/2− states receiving the main β -feedingare assumed to decay via E 2 transitions towards the (1/2−) isomer. In71

Ni, however, shell-model predicts that the first excited level is 7/2+

[10]. The presence of such state below the (1/2−) level reduces thespin difference between the 5/2− levels populated in β -decay and the9/2+ ground-state and increases the probability for γ -decay 5/2− →7/2+ → 9/2+g.s., by-passing the (1/2−) isomer. Based on the analysis of γ -γ coincidences, the observed 813-252 keV cascade was assigned to thisspin-sequence in Ref. [9].

The β -decay of the (1/2−) isomer in 69Ni was found to populateessentially the state at 1298 keV in 69Cu, see Fig. 6. From the compar-ison of the γ -intensity feeding into the 321-keV level in 69Ni with theintensity of the 1298-keV transition in 69Cu, a β -branching of 74(9)%

was determined in Ref. [2] for the level at 1298 keV. This branchingcorresponds to a logft value of 4.3(2), see Ref. [2] and Fig. 6. Spinand parity 3/2− were assigned to the 1298-keV state, viewed as the p3/2proton coupled to the 2 p − 2h, 0+ state at 1770 keV in the 68Ni core




0 0.5 10

0.5 1

0.5

1

0

71Co

44

(7/2-) 79(5)ms

71Ni

43

(9/2+

)

(7/2+

)

(1/2-)

(5/2-)

(5/2-)

252

499

1065

1273

71Cu

42

5/2-

3/2-

(1/2-) 454

534

0

2.56(3)s

2.34(25)s

~~

~~

Qb=11.33(92)

Qb=6.87(37)

log ft %b

40(15) 5.43(21)

7 7 4

5 6 6

8 1 3

60(15) 5.37(17)

(7/2-)

(1/2-)

(5/2-)

(5/2-)

(9/2+

)

321

915

1518

1821

5.0(2)

4.7(2)

5.6(2)

0.22(2)s

69Co

42

log ft %b

2.9(4)

17.1(18)

47.9(20)

69Ni

41

69Cu

40

(3/2-)

5/2-

1/2-

3/2-

10961213

1298

log ft %b

4.3(2)

>5.8

74(9)

<3

26(9) 5.3(2)

3.5(5)s

11.2(9)s0

~~

~~

Qb=5.36(14)

Qb=9.3(4)

Figure 6: Observed β -decay chain 69Co → 69Ni → 69Cu [2, 12] and 71Co →71Ni → 71Cu as proposed in Ref. [9] and present work. Qβ values are given inMeV.

[2]. Such configuration implies very low collectivity for the 3/2−

state, inagreement with its non-observation in the Coulomb excitation spectrumshown in Fig. 1. In contrast to the 3/2− single-particle level at 1298keV in 69Cu, the state at 454 keV in 71Cu was found to exhibit large col-lectivity (B(E 2; 1/2− → 3/2−g.s.)=20.4(22) W.u. as determined in Ref.[13]). By relating the number of counts in the peaks at 1096 and 1213keV observed in the bottom spectrum of Fig. 1 with the correspondingB(E 2) values reported in Ref. [13], an upper limit of 1.4 W.u. can beextracted for the B(E 2) value for the 1298-keV transition. Thus, thedecay of (1/2−) isomer in 69,71Ni populates states with very differentcharacter in the daughter nuclei.

In71

Ni, however, our evidence shows that the β -decaying isomerfeeds mainly the proposed (1/2−) state at 454 keV in 71Cu. As dis-cussed in Ref. [13], the large B(E 2) value measured for the 454 keVtransition excludes a single-particle character of πp1/2 type for the 454



164 Paper IV

keV level. The increased collectivity indicates significant deformationsetting in with increasing the number of g9/2 neutrons, as also suggested

by the results of recent Coulomb excitation experiments with radioac-tive beams of 70Ni [23]. The onset of collectivity was associated with thequenching of both Z =28 and N =40 gaps through the combined effect of the attraction and repulsion between the fp protons and g9/2 neutrons[23–25]. Thus, the observed β -decay branch from the (1/2−) isomer in71Ni to the 454-keV level in 71Cu can be explained by assuming that theodd proton occupies the K =1/2 downsloping orbit of the p3/2 orbital, onthe prolate side, while the neutron part of the wave function is, depend-ing on deformation, dominated by νp+2

1/2g+29/2

or νp−21/2

g+49/2

configurations.

This indicates that in both 69,71Ni isotopes, the β -decay of the (1/2−)isomer proceeds via a fast Gamow-Teller transition but in the case of

71Ni the spin of the final state in the daughter nucleus is changed by thedeformation. Interesting to note is that a similar deformed π1/2−[321]has been observed in 67Co, stemming from a π(1p-2h) proton excitationacross Z =28 [6].

V. CONCLUSIONS

In this paper, the results of the investigation of the decay of theproposed (1/2−) β -decaying isomer in 71Ni are presented and discussed.The key observable for this study is the newly observed level at 454

keV in71

Cu reported recently in Ref. [13] and for which the comparisonwith the systematics and model calculations predict a spin and parity of 1/2−. The experimental evidence discussed here combines the results of the Coulomb excitation measurement with radioactive beams [13] withthe results of two decay experiments aiming to the investigation of theβ -decay of 71Co and 71Ni. The analysis of the β -decay of 71Ni indicatesthat the 454-keV state observed in 71Cu is fed by the (1/2−) β -decayingisomer in 71Ni for which a half-life of T 1/2=2.34(25) s was determined inthe present work.

The large B(E 2) value measured in Ref. [13] for the 454-keV transi-tion depopulating the (1/2−) state in 71Cu indicated a deformed struc-

ture for this level. This indicates that in both69,71

Ni isotopes the mainβ -decay branch of the (1/2−) isomer goes to the level dominated bythe πp3/2ν ( p

−2

1/2g29/2) configuration in the daughter nuclei. In 71Cu, how-

ever, due to deformation, the nuclear properties of the level receiving




the main β -feeding are dictated by the K =1/2 downsloping orbit of theπp3/2 orbital.

We gratefully thank J. Gentens and P. Van den Bergh for runningthe LISOL separator. This work was supported by the European Com-mission within the Sixth Framework Programme through I3-EURONS(Contract RII3-CT-2004-506065), BriX/IUAP P6/23, FWO-Vlaanderen(Belgium), GOA 2004/03 and US Department of Energy.

[1] R. Grzywacz et al., Phys. Rev. Lett., 81, 766 (1998).[2] W. F. Mueller et al., Phys. Rev. Lett., 83, 3613 (1999).[3] J. I. Prisciandaro et al., Phys. Rev. C, 60, 054307 (1999).

[4] L. Weissman et al., Phys. Rev. C, 65, 024315 (2002).[5] J. Van Roosbroeck et al., Phys. Rev. Lett., 92, 112501 (2004).[6] D. Pauwels et al., Phys. Rev. C, 78 041307(R) (2008).[7] L. Weissman et al., Phys. Rev. C, 59, 2004 (1999).[8] M. Sawicka et al., Eur. Phys. J. A, 22, 455 (2004).[9] M.M. Rajabali et al., Proceedings of the Fourth International Conference

Fission and properties of neutron-rich nuclei , Sanibel Island, USA, p.679(2007).

[10] A. F. Lisetskiy, B. A. Brown, M. Horoi, and H. Grawe, Phys. Rev. C, 70,044314, (2004).

[11] S. Franchoo et al., Phys. Rev. Lett., 81, 3100 (1998).[12] S. Franchoo et al., Phys. Rev. C, 64, 054308 (2001).[13] I. Stefanescu et al., Phys. Rev. Lett., 100, 112502 (2008).

[14] T. Ishii et al., Phys. Rev. Lett., 81, 4100 (1998). A, 669, 81 (2000).[15] B. Zeidman and J.A. Nolen, Jr., Phys. Rev. C, 18, 2122 (1978).[16] F. Ajzenberg-Selove, R.E. Brown, E.R. Flynn, and J.W. Sunier, Phys.

Rev. C, 24, 1762 (1981).[17] N.A. Smirnova, A. De Maesschalck, A. Van Dyck, and K. Heyde, Phys.

Rev. C, 69, 044306, (2004).[18] H. Grawe et al., Proceedings of the Workshop on The Beta Decay, from

Weak Interaction to Nuclear Structure, Strasbourg, p. 211 (1999).[19] A.M. Oros-Peusquens and P.F. Mantica, Nucl. Phys. A, 669, 81 (2000).[20] Y. Kudryavtsev et. al Nucl. Instrum. Methods Phys. Res. B 114, 350

(1996).[21] National Nuclear Data Center, Brookhaven.

[22] M. Bernas et al., Z. Phys. A, 336, 41 (1990).[23] O. Perru et al., Phys. Rev. Lett., 96, 232501 (2006).[24] I. Stefanescu et al., Phys. Rev. Lett., 98, 122701 (2007).[25] T. Otsuka, T. Suzuki, R. Fujimoto, H. Grawe, Y. Akaishi, Phys. Rev.

Lett., 95, 232502 (2005).





Appendix A

Correlations

In paper I, the developed correlation technique is discussed. However,due to its restricted number of pages, only the most important resultsare reported. In section 3 of the paper the main ideas are discussed of how the correlations are constructed from the experimental data, whilesection 4 summarizes the mathematical derivation of the two conditionsthat are required to reliably interpret correlations. Both issues will bediscussed in greater detail in the sections A.1 and A.2 of this appendix,respectively. Monte-Carlo simulations have been performed to parame-terize the second condition, which is the topic of section A.3. In section5 of the paper, the first experimental results of the correlation technique

are presented. More details about the experimental conditions are givenin section A.4 of this appendix.

A.1 Construction of correlations: technical in-formation

Section 3 of paper I summarizes the three steps of the correlation tech-nique. First, the correlated histograms are built. Second, the randomlycorrelated events, which are contained in the correlated histograms, areestimated. Third, the histograms containing the estimated randomly

correlated events are subtracted from the correlated histograms. How-ever, no technical details are presented of the construction of these his-tograms, which is schematically illustrated in Fig. A.1.

In the first step, all the trigger events that are present in the data are

167



168 Correlations

~

~

tcyc0

t +timp d ec

C y c l e

#

Ncyc

i+1

i

i-1

2

1

ttr

DtDt2 tD pr

~

~

tcyc0

t +timp d ec

C y c

l e #

Ncyc

i+1

i

i-1

2

1

a)Correlatedevents

b)Estimationrandomlycorrelatedevents

ttr

DtDt

tcyc

Allcyclesttr

Nhi Nhi

t + t/Ntr hiD

Figure A.1: Construction of histograms containing all correlatedevents (A) and histograms containing the estimated randomly corre-lated events (B) for a trigger event at cycle time ttr in cycle numberi.



Construction 169

scanned. In Fig. A.1, the situation is depicted for a valid trigger event at

time ttr in the ith implantation-decay cycle. Each cycle is timp+tdec longwith timp the time of the beam on period and tdec the time of the beamoff period. Before and after each valid trigger event, N hi correlated his-tograms are built in equal time slices of ∆t/N hi long, within a correlationtime window ∆t of typically four times the correlation half-life of the in-termediate state, but outside the prompt trigger event window (typically∆t pr = 0.5 µs). This is illustrated in part (a), where N hi = 10 corre-lated histograms are built before and N hi = 10 after the trigger event.The correlated histograms contain the number of correlated events as afunction of energy. It is important to note that not all trigger eventsare valid. Imagine that the trigger event occurs at a cycle time ttr with

ttr > timp + tdec−∆t−∆t pr. Then, the first correlated histograms com-ing after the trigger event are filled, while the last histograms are notfilled. This causes systematic effects, which are avoided in the currentapplication of the correlation technique. Therefore, a restriction is puton the trigger events. If correlations are built after the trigger event, ttrhas to satisfy ttr ≤ timp+tdec−∆t−∆t pr. If correlations are built beforethe trigger event, ttr has to satisfy ttr ≥ ∆t + ∆t pr. Fig. A.2 shows anillustrative distribution of trigger events taken from a data set with a10s/0s/1 implantation-decay cycle and where the correlation time win-dow is chosen ∆t = 2 s. In the case of correlations coming after, triggerevents with ttr > 10s + 0s

−2s

−0.5 µs are rejected, while in the case

of correlations coming before, trigger events with ttr < 2s + 0.5 µs arerejected.

The second step is crucial in this correlation technique aimed forapplication on weakly produced exotic nuclei through the ISOL scheme,a method where no implantation trigger is available. At low-energy ISOLsystems, the acceleration voltage (typically 60 kV) is not high enoughto give an unambiguous implantation signal. Moreover, the events thathave to be correlated with each other are events like single β rays, singleγ rays, and β -gated γ rays and are less characteristic as other charged-particle signals like alphas, β -delayed nucleons, and direct nucleons. Asa consequence, the accurate knowledge of random correlations becomesmandatory.

Because all implantation-decay cycles are equivalent, the randomcorrelations in the corresponding correlated histograms can be estimated



170 Correlations

(s)cyct0 1 2 3 4 5 6 7 8 9 10

C o u n t s / 5 m s

0

2

4

6

8

10

1214

16

t=2 s)∆(a) Valid trigger events for correlations coming after (

(s)cyct0 1 2 3 4 5 6 7 8 9 10

C o u n t s / 5 m s

0

2

4

6

8

10

12

14

16

t=2 s)∆(b) Valid trigger events for correlated events coming before (

Figure A.2: Example of valid trigger events for correlations in a cor-relation time window of ∆t = 2 s. The data are taken in a 10s/0s/1implantation-decay cycle. The trigger distribution at the top is in-tended for correlations coming after the trigger events, while the dis-tribution at the bottom is intended for correlations coming before thetrigger events.

by the events in the other cycles. For the trigger event that occurs atcycle time tcyc = ttr in cycle i, see part (a) of Fig. A.1, this correspondsto all the events with cycle time ttr −∆t ≤ tcyc ≤ ttr + ∆t in all cycles,but not in cycle i, see part (b) of Fig. A.1. Because the program hasto run for each trigger event through the whole data set, this proceduredemands, however, an excessive computer processing time. To decreasethe computing time drastically, a different approach had to be used,which is an approximation of this one.

The distribution of the correlation event type (single γ , single β or β -gated γ ) for the full statistics of all cycles is gathered in one histogram

and is split into discrete time intervals, which are small with respectto the half-lives that govern the implantation-decay behavior. Of eachtime interval, the energy spectrum is built and stored with the timeinformation tcyc of the start of the time interval. For a trigger event



Construction 171

occurring at cycle time tcyc = ttr, the first histogram containing the

estimated random correlations after the trigger event is constructed bysumming the stored spectra of the correlation event type, of which theircycle times range in ttr < tcyc < ttr + ∆t/N hi. This is illustrated at thebottom of Fig. A.1, where the subdivisions are indicated of the differentcycle time windows within the time window ∆t/N hi of the first histogramcontaining the estimated random correlations. Because the resultinghistogram contains the statistics of N cyc cycles, one has to normalizeto it. More general, the cycle times of the 2N hi histograms range inttr + z ·∆t/N hi < tcyc < ttr + (z + 1) ·∆t/N hi with z = 0, 1,...,N hi − 1if random correlations are estimated after the trigger event and z =

−1,

−2,...,

−N hi if random correlations are estimated before the trigger

event. From the trigger distribution that is constructed in the first step,the number of trigger events per time interval is exactly known and,instead of scanning N tr times through the whole data set (with N tr

the number of trigger events), one has to scan only once through thetrigger distribution. This approximation, however, is associated witha systematic error of 1/N cyc and many implantation-decay cycles arerequired in order that this error becomes negligible (see section A.2 formore details). In the example of Fig. A.2, a discrete time interval of 5 ms is chosen.

In the final third step, the histograms containing the estimated ran-domly correlated events are subtracted from the correlated histograms.

The result is a set of histograms as a function of |tc−ttr| where tc−ttr =(z + 1

2) ·∆t/N hi is the correlation time, each containing the experimen-tally deduced estimation of the true correlations. Possibly the correla-tions have a specific energy condition that has to be applied to integratethe number of correlations as a function of |tc− ttr|. Different situationscan then occur:

• There is no correlation between the chosen trigger and correlatedevents. As a consequence, the correlated integrals fluctuate aroundzero.

• The chosen trigger and correlated events are correlated by oneintermediate state with half-life T 1/2. As a consequence, the cor-related integrals have a single exponential decay distribution witha decay constant λ = ln(2)/T 1/2.



172 Correlations

• The chosen trigger and correlated events are correlated by more

than one intermediate state with respective half-lives T 11/2, T 21/2,...As a consequence, the correlated integrals have a growing-in anddecay behavior, which corresponds to the half-lives T n1/2.

The first case is trivial. In the second case, the half-life of the interme-diate state can be determined by fitting the distribution with a singleexponential decay curve. Determining its half-life through the correla-tions is crucial, as the intermediate state’s growing-in and decay activityin the implantation-decay cycle has at least a mother-daughter distribu-tion involving less accurate half-life determinations. Furthermore, thebranching I b of the intermediate state into the correlated channel can be

deduced from the number of true trigger events N

tr

true (for a definition,see next section), the integral A of the decay curve determined for times0 ≤ |tc− ttr| ≤ ∞ and the detection efficiency εc of the correlated event:

I b =A/εcN trtrue

. (A.1)

The third case is typically used as a cross-check for the half-lives andbranching ratios of the intermediate states determined from correlationsinvolving only one of them.

A.2 LimitationsBelow, the situation is discussed for the correlation time window ∆tthat is opened by the γ 1-trigger event as shown in Fig. A.3. Correlationswith the γ 3-transition are investigated. First, the definitions of the threedifferent types of correlation and trigger events as formulated in paperI are repeated for clarity.

• The true correlation event (indicated as ”True” in the figure) isthe detection within this correlation time window of γ 3. All othercorrelation events are random correlations.

• The first type of random correlations, indicated as ”R1” and ”R2”in the figure, is the detection within the correlation time windowof γ 3, resp. γ 3 coming from another decaying nucleus of the sametype fed through the preceding γ 1, resp. γ 2 (γ, γ 1, ...have the



Limitations 173

bg1 g1’

g3 g3’

g2’’

g3’’

g1’’’ g1’’’’

E1

E2

E3

E0

T1/2

True R1 R2 Escape

E4

Escape

g4’’’

Figure A.3: An example of five hypothetical consecutive γ -ray decaycascades is shown. An isomeric state at energy E 3 de-excites with ahalf-life T 1/2. In the text, the situation is discussed for the correlationtime window that is opened by γ 1.

same energy value). In the ”R2” case, it is more generally requiredthat the randomly correlated event is an event of the same typeas a truly correlated event, but belonging to a decay cascade thatdoes not contain the transition of the type of the trigger event.

• The second type of a random correlation, labeled in the text bythe subscript ”bg”, but not shown in figure A.3, is the detectionwithin the correlation time window of a background event insidethe correlation energy window.

• A true trigger event is a trigger event that is followed by the inves-tigated correlated event, irrespective of the fact that the correlatedevent gets detected or not. In figure A.3 only γ 1 and γ 1 are truetrigger events.

• The first type of a faulty trigger event is the detection of transi-tions, like γ 1 and γ 1 in the figure, which are not followed by theinvestigated correlation event. One can indicate this as an escapeout of the (γ 1 − γ 3) correlation scheme.

• The second type of a faulty trigger event (not shown in figure A.3)is a background event inside the trigger photo-peak energy window.



174 Correlations

The total number of true correlations N ctrue can be expressed by the

equation

N ctrue = N trtrueI bεc

1− e−λ∆t

(A.2)

where N trtrue is the number of true trigger events, I b is the branching

ratio, εc the detector efficiency for the correlation events, λ = ln(2)T 1/2

the

decay constant of the intermediate state and ∆t the correlation timewindow.

The total number of correlations N cexp as deduced from the experi-mental procedure is the sum of all the random correlations and all thetrue correlations occurring within the N tr correlation time windows and

can be expressed by the equation

N cexp = N tr ·AcR∆t + N trtrue · I bεc

1− e−λ∆t

(A.3)

where N tr is the total number of triggers and AcR is the total count

rate of all random correlated events1. The correlated events can besubdivided into three categories, see definitions above, of which the lattertwo categories correspond to the random correlations.

To incorporate these distinctions the latter equation A.3 may thenbe rewritten as

N cexp = N tr · AcR1 + AcR2 + Acbg

∆t + N trtrue · I bεc

1− e−λ∆t

(A.4)

where AcR1 and Ac

R2 is the count rate of randomly correlated events of type ”R1” and ”R2”, respectively, and Ac

bg of background events.The random correlations of type ”R1” are directly related to the

trigger events by

AcR1 =

Atrtrue

εtrI bεc

1− e−λ∆t

(A.5)

where Atrtrue is the count rate of the true trigger events and εtr the trigger

detection efficiency.1More complete would be writing (N cR − 1)/∆tmeas i.o. Ac

R in order to take intoaccount the true correlation that is neglected here, with N cR the counts of all randomcorrelated events and ∆tmeas the total measuring time.



Limitations 175

Substituting equation A.5 in equation A.4 with ∆t chosen large

enough with respect to T 1/2 (e.g., ∆t = 4T 1/2) gives to a good ap-proximation

N cexp = N tr ·

Atrtrue

εtrI bεc + Ac

R2 + Acbg

∆t + N trtrue · I bεc (A.6)

The total number of experimentally deduced random correlationsN rexp is determined from the statistics contained in the N tr correlationtime windows, which each time contain the statistics integrated over allthe implantation-decay cycles normalized by the total number N cyc of implantation-decay cycles. This is expressed by the equation

N rexp =

N cyci=1

N tr · Atr

trueεtr I bεc + AcR2 + Acbg

∆ti

N cyc

+N trtrue · I bεc

1− e−λ∆t

N cyc

(A.7)

but is not exactly the same as the true random correlations, due to thecontribution of the second term. As a consequence, the experimentallyestimated true correlations N csub = N cexp−N rexp contain a systematic er-ror with respect to the true correlations (see equation A.2) correspondingto

N csub = N cexp −N rexp

= N trtrue ·

I bεc − I bεcN cyc

= N trtrueI bεc ·

1− 1

N cyc

= N ctrue ·

1− 1

N cyc

(A.8)

The first condition is therefore based on the requirement that

N cyc 1. (A.9)

Second, the experimentally estimated true correlations will only beaccurate enough if they are not dominated by the random correlations.



176 Correlations

This can be rephrased by saying that the statistical uncertainty δN csub of

experimentally estimated true correlations has to be small enough withrespect to the statistical uncertainty δN ctrue of the true correlations,which is formulated

δN csub < α · δN ctrue. (A.10)

with α a factor that has to be deduced from simulations based on theMonte-Carlo method, see section A.3.

The statistical error of N csub is

δN csub =

(δN cexp)2 + (δN rexp)2. (A.11)

The first term under the square root is deduced from equation A.3 andwith ∆t chosen large enough with respect to T 1/2 it is given by theequation

(δN cexp)2 = N tr ·AcR∆t + N trtrue · I bεc. (A.12)

Analogously, the second term is deduced from equation A.7, in which thesummation over all implantation-decay cycles is replaced by multiplyingwith N cyc:

(δN rexp)2 =N tr ·N cyc ·Ac

R∆t + N trtrue · I bεcN 2cyc

. (A.13)

Since N cyc has to be a large number from the first condition, thismeans that

(δN cexp)2 (δN rexp)2 (A.14)

and to a very good approximation one can write

δN csub = δN cexp. (A.15)

Working out condition A.10 and using equations A.15, A.12 and A.2gives

δN csub = δN cexp < α · δN ctrue

N tr

·AcR∆t + N

trtrue · I bεc < α

2

·N trtrueI bεc

Atrtrueεtr

I bεc + AcR2 + Ac

bg < α2−1∆t · N trtrueN tr · I bεc

AcR2 + Ac

bg <α2−1∆t · N trtrueN tr −

Atrtrueεtr

· I bεc. (A.16)



Monte-Carlo simulations 177

As discussed in section A.3, it is shown from simulations that

α <√

5 (A.17)

is a safe limit for performing reliable half-life fits.

The first two terms at the left-hand side of the inequality are relatedto the purity of the beam and the background conditions for the corre-

lated events, while the ratioN trtrueN tr in the first term at the right-hand side

of the inequality is related to the purity of the beam and the background

conditions for the trigger events. The ratioAtrtrueεtr

in the second term atthe right-hand side of the inequality will make the correlation techniqueobsolete when the beam intensity is too high. As mentioned above, a

typical choice of the correlation time window ∆t is ∆t = 4 · T 1/2. Thismeans that equation A.16 can be rewritten as

AcR2 + Ac

bg <

α2 − 1

4 · T 1/2· N trtrue

N tr− Atr

true

εtr

· I bεc. (A.18)

In perfect conditions, i.e.; AcR2 = Ac

bg = 0 Hz and all trigger events are

true trigger events (N tr = N trtrue), equation A.18 reduces to

Atrtrue

εtr<

α2 − 1

4 · T 1/2with α2 = 5, (A.19)

putting a limitation on the beam intensity, which is inversely related tothe half-life value.

A.3 Monte-Carlo simulations

To deduce a reliable value for α, Monte-Carlo simulations have beenperformed. Randomizers assign to each trigger event an implantation-decay number, a time stamp inside the implantation-decay cycle and acertain detection efficiency. The trigger events are distributed uniformlyor according to a single exponential growing-in (and subsequent decay)

time structure. Each time a trigger event occurs, a correlated event isgenerated that occurs after the trigger event with an exponential timedistribution e−λt, where λ is the decay constant. It is also possible togenerate unrelated events that are independent of the trigger events.



178 Correlations

Following the experimental procedure outlined in section A.1, the

decay behavior of correlated events is constructed as a function of thetime difference tc − ttr between the trigger and the correlated event.The importance of random correlations depends on the decay constantand the rate of trigger and unrelated events, see equation A.18. Thisis illustrated in Fig. A.4, where the left and right columns correspondto α2 = 3.8 and α2 = 9 conditions, respectively, where α2 is calculatedfrom

α2 =

AcR2 + Ac

bg

I bεc+

Atrtrue

εtr

· N tr

N trtrue· 4T 1/2 + 1. (A.20)

In the simulations, the Acbg value is always kept zero, since changing

the value of AcR2 has the same effect. The input decay constant of the

presented results always corresponds to a half-life value of T 1/2 = 480 msand the number of implantation-decay cycles was fixed to 800, which ismuch larger than 1. The histograms at the top contain the numberof simulated events within the correlation time window as a function of tc−ttr. The middle histograms contain the estimated number of randomcorrelations as a function of tc − ttr and are subtracted from the topspectra resulting in the bottom spectra. It is clear that the subtractionis necessary to reproduce a decay behavior, which is consistent withT 1/2 = 480 ms. If, however, the random correlations are dominant asin the right column, the decay fit cannot reliably reproduce the half-life

value.The most important outcome of the simulations is the determination

of a critical value for α. Fig. A.5 shows the fitted half-life values of sixseries of 18 independent simulation runs. Each series corresponds to re-spective conditions of α2 = 1, 1.7, 3.8, 5.2, 6.5, and 9. The trigger eventsare distributed uniformly in the implantation-decay cycle. It has beenverified that growing-in (and decay) distributions generate the same re-sults if the count rates in equation A.18 are taken as the maximumcount rates during the implantation-decay cycle (typically at cycle timetcyc = timp). The input half-life value of T 1/2 = 480 ms is indicated bythe dashed line in the histograms. From the spread in the fitted half-life

values, the reduced-χ2 value χ2/17 is deduced for each series. For lowα2 values, see the top row, there is a small spread of the fitted half-lifevalues, which corresponds to a reduced χ2 close to 1. In the middle row,the results are shown for α2 = 3.8 and 5.2. A larger spread is observed,



Monte-Carlo simulations 179

(ms)tr-tct0 500 1000 1500 2000

C o u n t s / 2 0

0 m s

0

2000

4000

6000

8000

=3.8, exp. deduced corr.

2α

(a)

(ms)tr-tct0 500 1000 1500 2000

C o u n t s / 2 0

0 m s

0

2000

4000

6000

8000

=9, exp. deduced corr.

2α

(a)

(ms)tr

-tc

t0 500 1000 1500 2000

C o u n t

s / 2 0 0 m s

0

2000

4000

6000

8000

=3.8, exp. deduced random corr.2α(b)

(ms)tr

-tc

t0 500 1000 1500 2000

C o u n t

s / 2 0 0 m s

0

1000

2000

3000

4000

5000

6000

7000

8000

=9, exp. deduced random corr.2α(b)

(ms)tr

-tc

t0 500 1000 1500 2000

C o

u n t s / 2 0 0 m s

0

500

1000

1500

2000

2500

3000

=3.8, exp. deduced true corr.2α(c)

=485(9) ms1/2Fitted T

(ms)tr

-tc

t0 500 1000 1500 2000

C o

u n t s / 2 0 0 m s

0

1000

2000

3000

=9, exp. deduced true corr.2α(c)

=428(8) ms1/2Fitted T

Figure A.4: The simulated decay behavior of correlated events,which is constructed following the experimental procedure. The leftand right column present the results of a simulation with α2 = 3.8

and 9 conditions, respectively. The three rows correspond to the threedifferent steps for constructing the experimentally deduced true cor-relations: experimentally deduced correlations (top row), experimen-tally estimated random correlations (middle row), and the random-subtracted correlations (bottom row).



180 Correlations

Run number5 10 15

( m s )

1 / 2

T

400

450

500

550

=12α(a) /17=1.412

χ

Run number5 10 15

( m s )

1 / 2

T

400

450

500

550

=1.72α(b) /17=1.362

χ

Run number0 5 10 15

( m

s )

1 / 2

T

400

450

500

550=3.8

2

α(c) /17=4.17

2

χ

Run number0 5 10 15

( m

s )

1 / 2

T

400

450

500

550=5.2

2

α(d) /17=5.24

2

χ

Run number0 5 10 15

( m s )

1 / 2

T

400

450

500

550

=6.52α(e) /17=13.082

χ

Run number0 5 10 15

( m s )

1 / 2

T

400

450

500

550

=92α(f) /17=18.852

χ

Figure A.5: The fitted half-life values of six series of 18 independentsimulation runs indicated with the resulting reduced-χ2 value. Each

series corresponds to respective conditions of α2

= 1, 1.7, 3.8, 5.2, 6.5,and 9, which is depicted in the respective panels (a), (b),..., (f). Theinput half-life value of T 1/2 = 480 ms is indicated by the dashed line.



Experimental conditions at LISOL 181

2α

1 2 3 4 5 6 7 8 9 10

2 χ

R e d u c e d

0

2

4

6

8

10

12

14

16

18

20

( m

s )

1 / 2

T

0

100

200

300

400

500

600

700

800

900

1000

Figure A.6: Plot of the reduced-χ2

value as a function of α2

. Thedotted line interconnecting the points is indicated to guide the eye.The average half-life values are marked by open circles as a functionof α2, where the line corresponds to a half-life value of 480 ms.

which is reflected in the enhanced χ2 values of 4.17 and 5.24, respec-tively. The spread looks, however, still reasonable, certainly comparedto the results for α2 = 6.5 and α2 = 9 conditions shown in the bottomrow. A more comprehensive overview is given in Fig. A.6, where the χ2

values are plotted as a function of α2. The χ2 value slowly rises up to5.2 < α2 < 6.5. Beyond α2 = 5.2, a steep rise is observed up to α2

7

followed by a plateau at χ2 = 19. On this basis, it can be concluded thatα2 = 5 is a critical value, beyond which half-life values determined fromfitting the correlated decay behavior becomes unreliable. This behavior,however, is not understood. Nevertheless, the average half-life valuesdetermined in the simulations stay close to the input half-life value of T 1/2 = 480 ms.

A.4 Experimental conditions at LISOL

By using the free-running digital electronics, all required ingredients

for building correlations are available at the LISOL facility to satisfythe two conditions: data-acquisition in many implantation-decay cycles,low background conditions for both the trigger and correlated events,and weak but high-purity beams. The correlation technique has been



182 Correlations

applied for the first time on data taken in a 10s/0s/1 implantation-decay

cycle with the mass separator tuned to A/Q = 67 and with the laserstuned to ionize iron isotopes. By correlating the 492-keV γ events withβ -gated 189- and 694-keV events, a long-lived isomeric state at 492 keVcould be established and characterized in 67Co.

As discussed in Ref. [5], during the micro beam on periods of 100 ms(see also chapter 3), an overwhelming amount of neutron-induced γ -activity is observed. The neutrons originate from proton-induced reac-tions on the gas cell windows, the uranium target, and the beam dump.During the micro beam off periods, the prompt neutron-induced eventsdecay in the first 15 ms, after which the γ -activity is more than a factorof 10 lower than during the micro beam on periods. The validity of

correlating events with single γ 492-keV events critically depends on itsbackground rate. The effect is also present in single β events [5], albeitless drastic, where it should be also taken into account. It is negligiblefor β -gated γ events [5] and is not of a concern there.

The situation of the single 492-keV events is depicted in Fig. A.7,where three single γ spectra are plotted with different conditions. Inthe top panel, no condition is put on the implantation-decay time of the single γ events. The spectrum is dominated by neutron-induced γ events and the 492-keV peak is barely visible on top of the background.In the middle panel, single γ events are rejected that occurred during

a micro beam on period and during the first 15 ms of the micro beamoff period. The 511-keV peak and the γ background are reduced bya factor of 21 and 15, respectively, while the 492-keV integral is onlyreduced by a factor of 2.5, which is consistent with the measuring timeratio 200ms

85ms . Consequently, the 492-keV peak is now clearly visible. Inaddition, advantage can be taken from the granularity of the MINIBALLclusters. Since the 492-keV transitions are not coincident with any otherevent, the spectrum is further cleaned by allowing only multiplicity M =1 events. This means that a γ event was registered by one core signal,while none of the other 5 core signals nor one of the 3 β detectors firedwithin a time window of ±500 ns. The resulting spectrum is shown in

the bottom panel of the figure. No counts are lost in the 492-keV peak,while the background is further reduced by 29%.

The different parameters determining the correlation conditions arepresented in Tables A.1, A.2, and A.3. Each Table corresponds to the




E (keV)400 450 500 550 600 650 700


0

10

20

30

40

50

60

70

80

90

1003

10×

spectrum, no conditionsγ (a) Single

4 9 2

E (keV)400 450 500 550 600 650 700


0

2000

4000

6000

8000

10000

12000 spectrum, 15-100 ms micro offγ (b) Single

4 9 2

E (keV)400 450 500 550 600 650 700

C o u n t s / 1

k e V

0

2000

4000

6000

8000

10000

12000spectrum, 15-100 ms micro off, M=1γ (c) Single

4 9 2

Figure A.7: Single γ spectra zoomed in the 492-keV energy regionwith three different conditions: no conditions (a), only γ events duringthe last 85 ms of a micro off beam period are allowed (b), and inaddition only multiplicity M = 1 events are allowed (c).



184 Correlations

three micro beam conditions on the single γ events: no condition, only

events during the last 85 ms of the micro off beam period, and in additiononly multiplicity M = 1 events, respectively. In the last column, theresulting α2 value is shown, which is calculated from equation A.20.Because the β -detector signals only serve as trigger signals and containno energy information, no distinction can be made between ”R2” typeand background type random β correlations. Therefore, all the randomcorrelation activity is specified under the ”Ac

R2” column.

Without any conditions on the single γ events, the α2 value rangesfrom 12 to 46 for the different combinations of triggers and correlations,see table A.1. Hence, it is clear that the background conditions have tobe improved to apply the correlation technique successfully. In a first

step, this is done by rejecting the single γ events occurring during themicro beam on period and during the first 15 ms of the micro beamoff period. As is shown in table A.2, the α2 values drop drastically.In case 492-keV events are the trigger events, the drop is caused bythe reduction in the N tr/N trtrue ratio. In case 492-keV events are thecorrelation events, the drop is caused by the reduction in the Ac

bg count

rate. Despite the drastic improvement, the α2 values are still slightlyabove the critical value of 5 in case of the mutual correlations of 492-keVand β -189-keV events. In case of single β particles correlated with 492-keV events, the value of 13 is still far away from the critical value. Whenapplying the additional condition of allowing only multiplicity M = 1

events, the α2 values are further reduced, as can be seen from tableA.3. The values of α2 stay below 5, except for the correlated β events.The single γ background around the 492-keV peak is only reduced by29%, but eventually it turns out to be crucial to determine the half-lifeof the 492-keV isomer by a half-life fit on the decay behavior of the492-keV events correlated with β -189-keV events. As can be seen in theTables, it is the high count rate of Ac

R2 that dominates the high α2 valuefor the correlated β events. In fact, it is difficult to meet the desiredrequirements for single-β correlations. The β detectors used at LISOLhave a summed background count rate of about 0.5 Hz. This meansthat Ac

R2

≥0.5 Hz and for the typical half-lives of T 1/2 = 0.5 s in the

A = 67 decay chain, equation A.18 becomes

1s−1 +Atrtrue

εtr< 2s−1 · N tr

N trtrue(A.21)




with a branching ratio of I b = 1 and a β -detection efficiency of εc = 0.5.

This illustrates that the trigger conditions become very strict in casecorrelations with single β events are investigated. Moreover, Ac

R2 istypically higher, which also accounts for the β ’s originating from othersources in the decay chain and from contaminants.

Table A.1: The α2 values in the 67Fe run with the 10s/0s/1implantation-decay cycle. Single γ events are not constrained by anycondition. The first and second column contains the selected trig-ger and correlated event, respectively. The notation of, e.g., β -189indicates β -gated 189-keV events.

Trig. Corr. Ac

R2 Ac

bg T 1/2 N tr

true N tr

Atr

true εtr εc α2

(s−1) (s−1) (s) (s−1)β -189 492 0.035 1.641 0.496 4036 5360 0.026 0.098 0.105 44

492 β -189 0.0 0.009 0.496 5308 157436 0.031 0.105 0.098 24β -694 492 0.0 1.641 0.329 4413 6353 0.028 0.042 0.105 32

492 β -694 0.009 0.002 0.329 10622 105030 0.063 0.105 0.042 12492 β 1.432 0.0 0.329 10622 105030 0.063 0.105 0.50 46

Table A.2: The α2 values in the 67Fe run with the 10s/0s/1implantation-decay cycle. Single γ events are only allowed if theyoccurred during the last 85 ms of a micro beam off period. The first

and second column contains the trigger and correlated event, respec-tively. The notation of, e.g., β -189 indicates β -gated 189-keV events.

Trig. Corr. AcR2 Ac

bg T 1/2 N trtrue N tr Atrtrue εtr εc α2

(s−1) (s−1) (s) (s−1)β -189 492 0.035 0.113 0.496 4036 5360 0.026 0.098 0.105 5.4

492 β -189 0.0 0.009 0.496 2063 12791 0.031 0.105 0.098 5.8β -694 492 0.0 0.113 0.329 4413 6353 0.028 0.042 0.105 4.3

492 β -694 0.009 0.002 0.329 4128 11095 0.063 0.105 0.042 4.0492 β 1.432 0.0 0.329 4128 11095 0.063 0.105 0.50 13.2

As schematically illustrated in Fig. A.8, the application of a micro

beam condition has consequences for the case that both trigger and cor-related events are single γ or β events. If all correlated (case (a)) or alltrigger events (case (b)) are allowed, which is representative for β -gatedγ events, the Monte-Carlo simulations indicate no problems. In these



186 Correlations

Trig.

Corr.

a)

A c t i v i t y

A c t i v i t y tcyc

A c t i v i t y

tcyc tcyc

A c t i v i t y

tcyc

Dtrej

DtallTrig.

Corr.

b)

tc tr -tDt/Nhi

tc tr -tDt/Nhi

Trig.

Corr.

c)

A c t i v i t y

tcyc

A c t i v i t y

tcyc

d)

tc tr -tD D Dt / N = t + thi all rej

Dtall

tcyc

12 3

12 3

3

21

4

5

123

1

2

3

4

5

XX

X

XX

X

22 2Total 5 t r i g g e r t i m e s

3correlationtimes Overlap

Figure A.8: Schematic representation of different trigger and cor-

relation combinations: a micro beam condition is required for thetrigger events (a), the correlated events (b), and both trigger andcorrelated events (c). Events are allowed during ∆tall and rejectedduring ∆trej . In situations (a) and (b), the time width ∆t/N hi israndomly chosen, while in situation (c), the time width of a corre-lated histogram is as long as one micro cycle (∆ tall + ∆trej). Thearrows in between the trigger and correlation distributions representsome specific cases where the beginning and the length of an arrowcorrespond to the cycle time tcyc of the trigger and the time widthof a correlated histogram, respectively. The thick lines in the arrowsindicate the overlap with the allowed cycle times during which eventscan fill the correlated histogram. The arrows at the bottom represent

the correlated histograms as a function of tc − ttr where the thicklines represent the overall distribution of allowed events. Panel (d)illustrates in three discrete steps the time overlap of correlation timewindows opened by 5 triggers at equidistant cycle times with the al-lowed cycle times assuming situation (b). In the table at the righthand side, crosses mark the overlapping positions.




Table A.3: The α2 values in the 67Fe run with the 10s/0s/1implantation-decay cycle. Single γ events are only allowed if theyhave M = 1 and if they occurred during the last 85 ms of a microbeam off period. The first and second column contains the trigger andcorrelated event, respectively. The notation of, e.g., β -189 indicatesβ -gated 189-keV events.

Trig. Corr. AcR2 Ac


(s−1) (s−1) (s) (s−1)β -189 492 0.035 0.081 0.496 4036 5360 0.026 0.098 0.105 4.6

492 β -189 0.0 0.009 0.496 2063 9708 0.031 0.105 0.098 4.7β -694 492 0.0 0.081 0.329 4413 6353 0.028 0.042 0.105 3.7

492 β -694 0.009 0.002 0.329 4128 9093 0.063 0.105 0.042 3.5492 β 1.432 0.0 0.329 4128 9093 0.063 0.105 0.50 11.0

cases, all correlation times tc − ttr have the same overlap time with theallowed correlation regions and no systematic effects arise. This is illus-trated in the figure by the arrows in between the trigger and correlationdistributions, which represent some specific situations of the filling of acorrelated histogram. The beginning of each arrow corresponds to thetrigger time, the length corresponds to the time width of the correlatedhistogram and the thick line indicates the overlap with the allowed re-gion. In case (a), the trigger events are restricted by a micro beam

condition, but all cycle times of the correlated events are allowed. Itis evident that all correlation times tc − ttr have the same overlap. Incase (b), all cycle times of trigger events are allowed, but the correlatedevents are restricted by a micro beam condition. Because there is norestriction on the trigger time, all correlation times tc− ttr will have thesame overall overlap. This is illustrated in panel (d) of the figure, wherein three discrete steps the time overlap is shown of the correlation timewindows opened by 5 triggers at equidistant cycle times with the allowedcorrelation regions. In the table at the right hand side, crosses mark theoverlapping positions. Adding up the overlapping positions results ina uniform overlap distribution. It is worth mentioning that the time

width of the correlated histogram and the allowed region can be chosenindependently from the micro cycle. When both trigger and correlatedevents have to satisfy a micro structure as in case (c), however, system-atic effects arise, which cannot be circumvented. From the example in



188 Correlations

panel (d), it is clear that if only the first two (and not the last three)

trigger times are allowed, representing the situation in Fig. A.8(c), thereis no uniform time overlap. Moreover, requiring additional conditions,like ∆tall = ∆trej and ∆t/N hi = ∆tall + ∆trej , is not sufficient to avoidthis systematic effect. Therefore, if one wants to correlate two singleevents, one is restricted to the macro beam off period where no microbeam conditions are necessary.

Table A.4: The α2 values in the 67Co run with the 2s/2s/3implantation-decay cycle. Single γ events are only allowed if theyhave M = 1 and if they occurred during the last 85 ms of a microbeam off period. The first and second column contains the trigger

and correlated event, respectively. The notation of β -694 indicatesβ -gated 694-keV events.

Trig. Corr. AcR2 Ac


(s−1) (s−1) (s) (s−1)β -694 492 0.0 0.071 0.329 1624 4684 0.039 0.042 0.105 7.1

492 β -694 0.032 0.002 0.329 2437 6084 0.094 0.105 0.042 6.6492 β 1.385 0.0 0.329 2437 6084 0.094 0.105 0.50 13.1

Apart from the data taken in a 10s/0s/1 implantation-decay cycleand with the lasers tuned to ionize iron isotopes, also another data setwas acquired: a 2s/2s/3 implantation-decay cycle with the lasers tunedto ionize cobalt isotopes. The correlation conditions of the 67Co runare listed in Table A.3. The high α2 values larger than 5 indicate thatno reliable half-life fits can be performed on correlated events. This ismainly caused by the large direct 67Co ground state production, whichis reflected in the AR2 value for the β -gated 694-keV γ events correlatedwith 492-keV γ events and the N tr/N trtrue ratio for the 492-keV γ eventscorrelated with β -gated 694-keV γ events. The resonant laser ionizationscheme is not able to separate the isomer and the ground state hinderingthe production of pure isomeric beams in this specific situation. Alsothe low selectivity of β signals is a problem, as can be noticed from theAR2 value for β events correlated with β -gated 694-keV γ events.



Nederlandstaligesamenvatting

Inleiding

De structuur begrijpen van een atoomkern is een uitdaging die kernfysicial sinds de ontdekking van de atoomkern in 1911 bezig houdt. De be-langrijkste motivatie van dit specifieke onderzoek is het begrijpen vande krachten die aan het werk zijn in atoomkernen en hoe de atoomkernwordt opgebouwd op basis van zijn bouwstenen, de protonen en neutro-nen. De uitdaging zit hierin dat enerzijds de nucleon-nucleon interactieniet voldoende begrepen is en anderzijds het typisch aantal nucleonen ineen kern dikwijls te groot is voor een ab-initio behandeling, maar ook te

weinig voor statistische benaderingen zoals bvb. toegepast wordt in devaste-stoffysica. Om die reden wordt gebruik gemaakt van kernmodellenom de kernstructuur te begrijpen. Sinds een aantal jaren ligt de nadrukin het experimentele kernfysisch onderzoek op kernen met ongewoneproton- tot neutronverhoudingen (zogenaamde ”exotische” kernen). Uitdit onderzoek blijkt dat de huidige modellen er dikwijls niet in slagenom de eigenschappen van deze kernen te voorspellen. Het is daaromvan groot belang dat deze exotische kernen bestudeerd worden om dekernmodellen verder te verfijnen en zodoende een beter begrip te krijgenvan de sterke en zwakke interactie.

De kernen in de buurt van de Z = 28 gesloten schil en N = 40

gesloten subschil genieten grote aandacht in het huidige onderzoek. Hetschillenmodel voorspelt een uitgesproken schilsluiting bij Z = 28, zieFig. 1.1, die bevestigd wordt door uitgevoerde massametingen. Er wordtook een vrij grote energiesprong voorspeld tussen de 2 p1/2 en 1g9/2 neu-

189



190 Samenvatting

tronorbitalen bij N = 40, maar minder uitgesproken dan bij Z = 28.

Daarom spreekt men in dit geval van een subschil.Het nikkel isotoop 68Ni ligt op de kruising van de Z = 28 en N = 40

(sub)schilsluitingen. De eerste aangeslagen toestand in 68Ni is een 0+

toestand [15] en, zoals is weergegeven in Fig. 2.1(a), is de eerst aange-slagen 2+ toestand beduidend hoger in 68Ni dan in de naburige nikkelisotopen met even massa [16]. Deze kenmerken zijn typisch voor dubbel-magische kernen, waardoor in eerste instantie werd gesuggereerd datN = 40 een goede schilsluiting is. In meer recente studies van 68Niwerd echter aangetoond dat de N = 40 subschilsluiting eerder fragielis. Massametingen duiden aan dat er wat energie-overwegingen betreftgeen uitgesproken schilsluiting is bij N = 40, zie Fig. 2.1(c). Nochtans

is de B(E 2 : 0+1 → 2+1 ) overgangswaarschijnlijkheid klein (Fig. 2.1(b)),maar wel verschillend van nul. Zoals besproken in Ref. [22], is dit eenaanwijzing van sterke paringsverstrooiing over de N = 40 sluiting.

Deze tegenstellingen worden verklaard op basis van het verschil inpariteit tussen de νpf schil en het νg9/2 orbitaal. De energiesprong vande νpf schil naar het νg9/2 orbitaal op zich is niet bijzonder groot, maarbelangrijke pariteitsbehoudende excitaties, zoals bvb. quadrupoolexci-taties, zijn niet toegelaten. Hierdoor ligt de 2+1 toestand op een groteexcitatie-energie, terwijl in het geval van een volledig inerte Z = 28sluiting een B(E 2) waarde van nul wordt verwacht. De gemeten B(E 2)

waarde, die verschillend is van nul, duidt echter aan dat een beduidendaantal neutronen het νg9/2 orbitaal bezet die een romppolarizatie in-duceren via de protonen. De νg9/2 neutronbezetting wordt toegewezenaan sterke paringsverstrooiing en is consistent met het feit dat twee-neutronseparatie-energieen van de nikkelisotopen geen duidelijke piekvormen bij N = 40.

Dankzij het pariteitsverschil over de eerder kleine N = 40 sub-schilsluiting, heeft experimenteel onderzoek uitgewezen dat 68Ni een sta-biliserende invloed uitoefent op de naburige kernen 67,69Ni en 68−70Cu.Voorbij N = 40, wanneer het νg9/2 orbitaal gevuld wordt, heeft menechter geobserveerd dat er in de Z ≥ 28 kernen een toegenomen collec-

tiviteit optreedt. Dit is het gevolg van de sterke interactie tussen neu-tronen in het νg9/2 orbitaal en protonen in de πf 7/2 en πf 5/2 orbitalen.Meer νg9/2 neutronen zorgen ervoor dat het πf 7/2 orbitaal stijgt, terwijlhet πf 5/2 orbitaal daalt in energie, waardoor de Z = 28 schilsluiting



Samenvatting 191

verkleint. Beneden Z = 28 spelen in principe dezelfde interacties een

bepalende rol. Meer specifiek zijn het de interacties tussen protonen inhet πf 7/2 orbitaal en neutronen in de νf 5/2 en νg9/2 orbitalen die destructuur bepalen beneden Z = 28 en rond N = 40. Door protonenweg te nemen uit het πf 7/2 orbitaal stijgt het νf 5/2 en daalt het νg9/2orbitaal in energie, waardoor de reeds kleine N = 40 subschilsluitingin 68Ni nog verkleint. Het effect van een stijgend νf 5/2 orbitaal wordtwaargenomen in de Z ≤ 28 kernen en er zijn sterke aanwijzingen datde grondtoestand van 64Cr (Z = 24, N = 40) vervormd is en dat devervorming reeds inzet bij kleine excitatie-energieen in 66Fe (Z = 26,N = 40).

Dit werk concentreert zich op het β verval van 65,67Fe naar toe-

standen van de 65,67Co isotopen (N = 38 en 40) die zich bevinden tussende sferische nikkelkernen en de ijzerkernen die een gebied van vervorminginzetten beneden Z = 28. De structuur van cobaltkernen bij kleineexcitatie-energieen met oneven massa was tot voor kort gekend tot enmet N = 36 (63Co). Ze vertonen allemaal een structuur van een πf 7/2protongat gekoppeld aan hun naburige nikkelkern. De β vervalschema’svan de 65,67Fe isotopen die bekomen worden in dit werk leveren eeneffectieve bijdrage aan de kennis van de hierboven beschreven effectieveproton-neutron interacties.

Experimentele opstelling65,67Fe, 65,67Co en 71Co isotopen werden geproduceerd aan de LISOL(Leuven Isotope Separator On-Line) faciliteit in het Centre de Recherchedu Cyclotron (CRC) te Louvain-La-Neuve, Belgie. Een protonenbun-del met een energie van 30 MeV wordt gestuurd op een 238U trefschijf en induceert een fissiereactie waarbij een groot deel van de neutronrij-ke kernen wordt geproduceerd. De trefschijf bevindt zich in een gas-cel die gevuld is met een argon buffergas. De fissieproducten vliegenuit de trefschijf, worden gestopt in het buffergas en worden met degasstroom meegevoerd naar de eindopening van de gascel. Vlak voor

de opening worden de fissieproducten bestraald door twee laserbundelsdie de isotopen van het gewenste element resonant ioniseren. De ionen,die de gascel verlaten, worden in een sextupole ionengeleider getrans-porteerd naar de hoge vacuumomgeving waar de ionen versneld worden



192 Samenvatting

naar een energie van 40 keV. Vervolgens worden de ionen na massase-

paratie geımplanteerd in een beweegbare band die omgeven wordt doordrie dunne plastic ∆E β detectoren en twee MINIBALL γ detectorclus-ters. De detectorsignalen worden uitgelezen door digitale electronica viaXIA-DGF4C modules, die aan elke gebeurtenis een energieen absolutetijdsafdruk toekennen.

Resultaten

Om de 65,67Co structuur te bepalen werden verschillende metingen uit-gevoerd op de respectievelijke massa’s. Er werden data opgenomen met

de lasers uit en de lasers ingesteld op het ionisatieschema van zowel ijzerals cobalt. Door deze data met elkaar te vergelijken, kan men γ lijnendie volgen op het 65,67Fe en 65,67Co β verval identificeren. Met behulpvan β -γ -γ coıncidenties werden hun vervalschema’s opgesteld. In ditthesiswerk werden ook 71Co en 71Ni vervaldata, die enkele jaren geledenwerden opgenomen aan LISOL, opnieuw geanalyseerd.

In het verval van zowel 67Fe als 67Co wordt een isomere overgang op492 keV waargenomen in het enkelvoudige γ spectrum, maar niet in hetβ -γ spectrum. Vanwege de afwezigheid van coıncidente γ overgangen,kan de 492-keV overgang niet eenduidig geplaatst worden in de A = 67vervalketen. Om de 492-keV lijn in langere tijdsvensters te correleren

met β , γ , and β -coıncidente γ gebeurtenissen, werd een nieuwe correla-tietechniek ontwikkeld, bedoeld voor toepassingen aan ISOL faciliteiten.

De correlaties worden gebouwd in drie stappen.

• In de eerste stap worden de trigger gebeurtenissen gescand. Degecorreleerde histogrammen worden in een correlatietijdsvenstervoor en na elke trigger gebouwd in gelijke tijdsstukken. Het cor-relatietijdsvenster is typisch 4 keer de correlatie halfwaarde tijden ligt buiten het prompt tijdsvenster van de trigger gebeurtenis.Dit resulteert in een set van histogrammen die niet alleen de echtecorrelaties bevatten, maar ook veel willekeurige correlaties.

• De willekeurige correlaties worden benaderd in de tweede stap.Elke trigger gebeurtenis vindt plaats op een welbepaald ogenblikin de implantatie-verval cyclus. De willekeurige correlaties van



Samenvatting 193

de trigger kunnen dan benaderd worden door te kijken in de cor-

responderende tijdsvensters van de andere implantatie-verval cy-cli. Om de verwerkingstijd van de computer te versnellen wordenechter alle cycli in rekening gehouden, inclusief de cyclus van detrigger gebeurtenis zelf.

• In de derde en laatste stap worden de histogrammen van stap 2afgetrokken van de histogrammen van stap 1. Het resultaat is eenset van histogrammen die de echte correlaties benaderen in functievan het tijdsverschil met de trigger.

Met behulp van deze correlatietechniek kan men isomere overgang-

en eenduidig plaatsen in een vervalketen en kan men hun halfwaardetijden en vertakkingsverhoudingen in de gecorreleerde kanalen bepalen.Er zijn echter beperkingen verbonden aan de techniek. Aan de handvan statistische principes en Monte-carlo simulaties werden twee voor-waarden afgeleid waaraan moet worden voldaan voor een betrouwbareinterpretatie van de bekomen correlatieresultaten. De eerste voorwaardeis dat er een groot aantal implantatie-verval cycli moet zijn, zodat desystematische fout, die in stap 2 gemaakt wordt, verwaarloosbaar wordt.Ten tweede moet de geleverde ionenbundel enerzijds zwak en anderzijdszuiver genoeg zijn en moet de achtergrond laag zijn. Dankzij de Monte-Carlo simulaties kan de tweede voorwaarde gekwantificeerd worden.

Er werd nagegaan dat in de67

Fe vervaldata β -coincidente γ corre-laties met de isomere 492-keV overgang aan de twee vereiste voorwaar-den voldoen, als enkel de 492-keV gebeurtenissen in rekening wordengenomen met multicipliteit M = 1 en die zich bovendien voordoen tij-dens periodes wanneer de protonenbundel afstaat. Met een gebeurtenismet multicipliteit M = 1 wordt hier bedoeld dat er binnen het prompttijdsvenster geen ander signaal is geregistreerd in de plastic detectorenen de Ge kristallen van de MINIBALL clusters. Gebruik makend vandeze voorwaarden op de 492-keV gebeurtenissen, kan er eenduidig een492-keV isomeer geplaatst worden in 67Co. Uit de correlaties wordt eenhalfwaarde tijd van 483(56) ms bekomen voor de isomeer. Deze waarde

is consistent met de waarde van 503(42) ms bekomen uit het 492-keVverval in de 67Co data. Uit het gewogen gemiddelde van beide waar-den wordt een halfwaarde tijd van 496(33) ms bepaald. Op basis vandeze halfwaarde tijd en de (7/2−) grondtoestand, wordt de isomeer een



194 Samenvatting

spin en pariteit van (1/2−) toegekend. De correlaties in de 67Fe data

geven ook aan dat de isomeer niet vervalt via β emissie (bovengrensvan 20%), maar enkel via γ emissie. De 67Co grondtoestand heeft eenbekomen halfwaarde tijd van 329(28) ms, die nieuw is ten opzichte vande literatuurwaarde [44].

De isomeer werd geınterpreteerd als een π(1p-2h) indringconfiguratiemet een prolate vervorming, waarbij een protondeeltje uit het πf 7/2orbitaal over de Z = 28 sluiting wordt geexciteerd in het πp3/2 orbitaal.De prolate vervorming is zo sterk dat het proton het K = 1/2 πp3/2Nilsson orbitaal bezet, zie Fig. 1.2. De toestanden met een excitatie-energie van 680 en 1252 keV zijn goede kandidaten voor de 3/2− en5/2− leden van de rotatieband gebouwd op de (1/2−) indringtoestand.

De 65Co structuur werd bestudeerd in een gecombineerde analyse vanhet 65Fe en 65Co β verval (LISOL) en complementaire data bekomen indiep-inelastische kernreacties aan Argonne National Laboratory (USA).In het 65Fe β verval worden twee onafhankelijke niveaustructuren waar-genomen zonder transities die de twee structuren met elkaar verbinden.De structuren corresponderen met het verval van de (1/2−) grondtoe-stand en de (9/2+) isomeer van 65Fe, die recent in een Penningval mas-sameting is waargenomen [95]. Met de diep-inelastische data worden detwee β vervalschema’s van 65Fe, zoals uit de LISOL data is afgeleid,bevestigd en kan aangetoond worden welke structuur eerder bestaatuit toestanden met grote spinwaarden. Omdat niets wijst op een iso-mere toestand in 65Co, ook niet in het β verval van 65Co zelf, wor-den de twee 65Co structuren op een gemeenschappelijke grondtoestandgeplaatst. Aangezien de 65Co toestanden gevoed worden door de 65Feniveaus met zowel een lage als een hoge spin, kan men een vrij completespectroscopie verwachten voor de toestanden op lage energie.

Zoals in 67Co, wordt ook in 65Co een (1/2−) toestand met dezelfdeπ(1p-2h) indringconfiguratie gesuggereerd. De toestand ligt op 1095keV en de (3/2−) toestand op 1223 keV kan beschouwd worden als heteerste lid van de rotatieband gebouwd op de indringtoestand. Er isechter een sterke opmenging met de (3/2−) toestand op 883 keV, die

geınterpreteerd wordt als een lid van het multiplet van het πf −1

7/2 pro-tongat gekoppeld aan de 2+1 toestand van 66Ni. De andere leden van ditmultiplet zijn toegewezen aan de niveaus op 1441, 1480, 1626 en 1642keV.



Samenvatting 195

De β -vervaldata van 71Co en 71Ni werden terug geanalyseerd naar

aanleiding van de recente waarneming van het (1/2−

) niveau in 71Cuop 454 keV in een Coulomb excitatie experiment [38]. De grote B(E 2 :3/2− → 1/2−) waarde van 20.4(22) W.u. toont aan dat de (1/2−) toe-stand sterk collectief is. Een γ lijn op 454 keV was al in een vroegereβ vervalstudie van 71Ni waargenomen, maar werd niet geplaatst in hetvervalschema [60]. Omdat er geen coıncidente γ lijnen geobserveerd wor-den, kan het niveau niet indirect gevoed worden door de grondtoestandvan 71Ni. De nieuw uitgevoerde analyse toont aan dat de γ intensiteitvan de 454 keV overgang in het verval van 71Ni toeneemt, wanneer debron van 71Ni afkomstig is van het β verval van 71Co. In combinatie metde 71Co vervalstudie van Ref. [121], geeft dit aan dat de (1 /2−) toestand

op 499 keV vervalt door β emissie.De (1/2−) toestand op 454 keV kan beschouwd worden als een toe-

stand met een configuratie die analoog is aan die van de (1/2−) protonindringtoestanden van 65,67Co. De toestand in 71Cu wordt geınterpre-teerd als de bevolking van het oneven protondeeltje in het K = 1/2πp3/2 orbitaal, maar met een vervorming die kleiner is dan die van decobalt indringtoestanden.

Bespreking

Indringtoestanden in Co

De cobaltisotopen met oneven massa (A ≤ 63) worden gekenmerktdoor een structuur waarbij het πf −1

7/2protongat koppelt met de 2+ of

4+ toestanden van hun nikkelburen. Terwijl in de nikkelisotopen nogeen stabiliserend effect van de N = 40 subschilsluiting optreedt, tonende 65,67Co structuren het tegenovergestelde effect aan. De toestandengekoppeld aan de naburige nikkelkernen volgen de energietrend van diens2+ en 4+ toestanden, maar er komt ook een (1/2−) proton indringtoe-stand sterk omlaag in excitatie-energie in 65Co en 67Co. In 67Co inhet bijzonder ontstaat er een groot energieverschil tussen de indring-

toestand (492 keV) en de eerst aangeslagen nikkel-gekoppelde toestand(1859 keV). Dit voorkomt sterke opmenging van beide configuraties zoalsin de lichtere cobalt isotopen. De (1/2−) indringtoestand zet zich reedsin in 65Co op een excitatie-energie van 1095 keV. Het feit dat de pro-



196 Samenvatting

ton indringtoestanden van de cobalt isotopen naar een minimum gaan

aan N = 40 betekent dat er naast paringscorrelaties ook sterke proton-neutron residuele interacties aanwezig moeten zijn. Dit impliceert deaanwezigheid van veel valentieneutronen of, met andere woorden, eeneerder open N = 40 schil. In 68Ni was reeds aangetoond dat er eensterke paringsverstrooiing is over de N = 40 gap. Door een proton uitde nikkelisotopen te nemen, zorgen proton-neutron interacties dat deN = 40 subschilsluiting verkleint en dat de paringsverstrooiing dus toe-neemt. Het is echter verrassend dat slechts een protondeeltje voldoendeis om het stabiliserend effect van de N = 40 subschilsluiting zo sterk teverzwakken. Dit toont aan dat N = 40 een subtiele sluiting is.

Indringtoestanden in Ni

De π(2p-2h) 0+ proton indringtoestand in 68Ni is benaderd door deexcitatie-energieen van de π(1p-2h) indringtoestand in 67Co (492 keV)en de π(2p-1h) indringtoestand in 69Cu (1711 keV) op te tellen. Hetresultaat van 2203 keV maakt van de (0+3 ) toestand op 2511 keV eengeschikte kandidaat. De 0+2 toestand op 1770 keV wordt beschouwd alsde ν (2p-2h) neutron indringtoestand in 68Ni. Ondanks de onverstoordeenergiesprong over Z = 28 en N = 40, bevinden de indringtoestandenzich op relatief lage excitatie-energieen door de winst in bindingsenergievan paringcorrelaties en proton-neutron residuele interacties [123]. De

excitatie-energie van de indringtoestanden is gekend en de energiesprongen paringsenergie kunnen experimenteel bepaald worden door gemeteneen- en twee-deeltjes separatie-energieen. Hieruit kan de proton-neutronresiduele interactie-energie berekend worden van de indringtoestandenin 68Ni. Bovendien worden de indringtoestanden van 68Ni aan de handvan deze resultaten vergeleken met die van 90Zr (Z = 40 en N = 50).

De resultaten bevestigen dat in 68Ni de neutronparingsenergie (4705(14) keV) groot is in vergelijking met de N = 40 energiesprong (3050(100) keV). De winst in proton-neutron residuele interacties van deν (2p-2h) configuratie is verwaarloosbaar, wat consistent is met een goedeZ = 28 schilsluiting. De π(2p-2h) configuratie daarentegen ondervindt

een grote winst van 3.5(10) MeV in proton-neutron residuele interactie-energie. Dit duidt de beschikbaarheid van veel valentieneutronen aan.Hun aanwezigheid wordt verklaard door de sterke paringsverstrooiingover de N = 40 subschilsluiting.



Samenvatting 197

In 90Zr is de excitatie-energie van de π(2p-2h) toestand (1761 keV)

opmerkelijk gelijkaardig aan die van de ν (2p-2h) toestand in 68Ni (1770keV). Dit wordt echter veroorzaakt door zowel een kleinere Z = 40energiesprong als een kleinere paringsenergie, in vergelijking met de si-tuatie in 68Ni. Analoog aan de ν (2p-2h) toestand in 68Ni, is de verwaar-loosbare winst in proton-neutron residuele interactie-energie. In 90Zrduidt dit op een goede N = 50 sluiting. De ν (2p-2h) toestand in 90Zrechter gedraagt zich volledig anders dan de π(2p-2h) toestand in 68Ni.De proton-neutron residuele interactie-energie bedraagt slechts 670(20)keV of minder wat er op wijst dat er slechts weinig valentieprotonenbeschikbaar zijn. Dit betekent dat Z = 40 zich als een betere sub-schilsluiting gedraagt dan N = 40. Het verschil wordt verklaard aan de

hand van de beduidend sterkere paringsverstrooiing aan N = 40 in 68Nidan aan Z = 40 in 90Zr.

Een inversie-eiland voorbij N=40?

Bij Z = 28 zal zich voorbij N = 40 een interessante competitie tussentwee fenomenen afspelen. Aan de ene kant neemt het aantal valentieneu-tronen af wat protonexcitaties over Z = 28 zal bemoeilijken, maar aande andere kant zorgt de toenemende neutronbezetting van het νg9/2 or-bitaal voor een verkleining van de Z = 28 sprong wat protonexcitatiesvergemakkelijkt. Zowel in zink (Z = 30), koper (Z = 29) en nikkel

(Z = 28) werd reeds een toename in collectiviteit geobserveerd voorbijN = 40. Meer specifiek volgt uit dit thesiswerk tevens dat het 71Cuniveau op 454 keV een collectieve configuratie heeft analoog aan die vande indringtoestanden in 65,67Co. De kleine excitatie-energie van de pro-ton indringtoestand in 67Co doet vermoeden dat er voorbij N = 40 eenonontgonnen ”Inversie-eiland” bestaat in de Z ≤ 27 kernen, waarbij deproton indringtoestand de grondtoestand wordt.

Besluit en toekomstperspectieven

In dit thesiswerk wordt dankzij de ontwikkeling en toepassing van eennieuwe correlatietechniek aangetoond dat het stabiliserende effect vande N = 40 subschilsluiting in 68Ni subtiel is en dat de verwijdering vanslechts een protondeeltje het stabiliserende effect reeds sterk verzwakt.



198 Samenvatting

De energiesprong aan Z = 40 daarentegen gedraagt zich als een robuust-

ere subschilsluiting nabij de N = 50 isotonen. Dit fenomeen wordtverklaard door de winst in paringsenergie, die dominant is over N =40 en minder belangrijk over Z = 40, en de daarmee gepaard gaandeparingsverstrooiing. Met de resultaten van het geleverde onderzoek iser een nieuwe open vraag ontstaan. Bestaat er een ”Inversie-eiland” inde cobalt en ijzer isotopen voorbij N = 40?

In het β verval van de 69,71,73Co isotopen is er alleszins geen eviden-tie gevonden voor een (1/2−) β vervallende toestand. Er zijn echter bij-komende onderzoeken nodig om te bepalen waar de indringtoestandenzich bevinden. Belangrijke bijdragen kunnen geleverd worden door β vervalstudies van de 69,71,73Fe isotopen en, gezien het mogelijke iso-

merisme in de 69,71,73Co kernen, door preciese massametingen. Er werdreeds bundeltijd toegekend aan de ISOLDE faciliteit aan het CERN inGeneve, Zwitserland, voor β vervalexperimenten van 61−70Mn. Niveausin de corresponderende ijzer isotopen zullen gevoed worden en op hunbeurt zullen de ijzer isotopen vervallen naar toestanden in cobalt. Ditlaat toe om zowel de structuur van de neutronrijke ijzer als cobalt iso-topen te bestuderen. De ontwikkelde correlatietechniek kan toegepastworden en zal een belangrijk hulpmiddel zijn in het geval dat er iso-merisme optreedt in een van de vervalketens.

De 65,67Co structuren kunnen voorlopig nog niet besproken wordenaan de hand van grootschalige schillenmodelberekeningen. Er zijn niet

alleen problemen met de grote valentieruimte die vereist is, maar ook methet gebrek aan preciese effectieve interacties. Aan de andere kant zijnde niveauschema’s die bekomen zijn in dit werk een belangrijke bron vaninformatie voor het afstellen van de effectieve interacties in dit gebied.Vooral de interacties met neutronen in het νg9/2 orbitaal lijken cruciaal.In een volgende stap kunnen deze interacties gebruikt worden voor decobalt en ijzer kernen voorbij N = 40, die in de nabije toekomst aan deISOLDE faciliteit bestudeerd zullen worden. Ook kunnen ze gebruiktworden om de geobserveerde aanzet van vervorming langs de N = 40isotonen beneden Z = 28 beter te beschrijven.



Bibliography

[1] S. C. Pieper, K. Varga, and R. B. Wiringa. Phys. Rev. C 66,044310 (2002).

[2] M. G. Mayer. Phys. Rev. 78, 16 (1950).

[3] K. L. G. Heyde. The nuclear shell model . Springer-Verlag, (1990).

[4] R. F. Casten. Nuclear Structure from a Simple Perspective. OxfordUniversity Press, (2000).

[5] O. Ivanov. Decay of 66Fe studied with a new β -γ -detection set-upat LISOL. PhD thesis, Katholieke Universiteit Leuven, (2007).

[6] M. Hjorth-Jensen, T.T.S. Kuo, and E. Osnes. Phys. Rep. 261, 125

(1995).

[7] O. Sorlin et al. Nucl. Phys. A 632, 205 (1998).

[8] G. Neyens et al. Phys. Rev. Lett. 94, 022501 (2005).

[9] T. Motobayashi et al. Phys. Lett. B 346, 9 (1995).

[10] R. Ibbotson et al. Phys. Rev. Lett. 80, 2081 (1998).

[11] B. V. Pritychenko et al. Phys. Rev. C 63, 011305(R) (2001).

[12] Y. Utsuno, T. Otsuka, T. Mizusaki, and M. Honma. Phys. Rev.

C 64, 011301(R) (2001).

[13] K. Heyde, P. Van Isacker, M. Waroquier, J. L. Wood, and R. A.Meyer. Phys. Rep. 102, 291 (1983).

199



200 Bibliography

[14] E. K. Warburton, J. A. Becker, and B. A. Brown. Phys. Rev. C

41, 1147 (1990).

[15] M. Bernas et al. Phys. Lett. B 113, 279 (1982).

[16] R. Broda et al. Phys. Rev. Lett. 74, 868 (1995).

[17] J. Van de Walle. Coulomb excitation of neutron rich Zn isotopes.PhD thesis, Katholieke Universiteit Leuven, (2006).

[18] G. Kraus et al. Phys. Rev. Lett. 73, 1773 (1994).

[19] T. Otsuka, M. Honma, and T. Mizusaki. Phys. Rev. Lett. 81, 1588

(1998).[20] URL: http://www.nndc.bnl.gov/ensdf/.

[21] C. Mazzocchi et al. Phys. Lett. B 622, 45 (2005).

[22] O. Sorlin et al. Phys. Rev. Lett. 88, 092501 (2002).

[23] O. Perru et al. Phys. Rev. Lett. 96, 232501 (2006).

[24] G. Audi, A. H. Wapstra, and C. Thibault. Nucl. Phys. A 729, 337(2003).

[25] S. Rahaman et al. Eur. Phys. J. A 34, 5 (2007).

[26] Ch. Engelmann et al. Z. Phys. A 352, 351 (1995).

[27] P. T. Hosmer et al. Phys. Rev. Lett. 94, 112501 (2005).

[28] N. Bree et al. Phys. Rev. C 78, 047301 (2008).

[29] C. Guenaut et al. Phys. Rev. C 75, 044303 (2007).

[30] H. Grawe et al. In AIP Conf. Proc. No. 561, M. Arnould et al.,editors, 287 (, Melville, NY, USA, 2001).

[31] K. Kaneko, M. Hasegawa, T. Mizusaki, and Y. Sun. Phys. Rev. C 74, 024321 (2006).

[32] K. Langanke et al. Phys. Rev. C 67, 044314 (2003).



Bibliography 201

[33] M. Girod, Ph. Dessagne, M. Bernas, M. Langevin, F. Pougheon,

and P. Roussel. Phys. Rev. C 37, 2600 (1988).

[34] R. Grzywacz et al. Phys. Rev. Lett. 81, 766 (1998).

[35] W. F. Mueller et al. Phys. Rev. C 61, 054308 (2000).

[36] H. Nann and W. Benenson. Phys. Rev. C 10, 1880 (1974).

[37] A. Passoja, R. Julin, J. Kantele, and M. Luontama. Nucl. Phys.A 363, 399 (1981).

[38] I. Stefanescu et al. Phys. Rev. Lett. 100, 112502 (2008).

[39] T. Otsuka et al. Phys. Rev. Lett. 95, 232502 (2005).

[40] E. Caurier, F. Nowacki, and A. Poves. Eur. Phys. J. A 15, 145(2002).

[41] A. M. Oros-Peusquens and P. F. Mantica. Nucl. Phys. A 669, 81(2000).

[42] E. Runte et al. Nucl. Phys. A 399, 163 (1983).

[43] G. Georgiev et al. J. Phys. G 28, 2993 (2002).

[44] L. Weissman et al. Phys. Rev. C 59, 2004 (1999).

[45] R. T. Kouzes, D. Mueller, and C. Yu. Phys. Rev. C 18, 1587(1978).

[46] J.I. Prisciandaro et al. Phys. Rev. C 60, 054307 (1999).

[47] O. Sorlin et al. Nucl. Phys. A 669, 351 (2000).

[48] U. Bosch et al. Phys. Lett. B 164, 22 (1985).

[49] W. F. Mueller et al. Phys. Rev. Lett. 83, 3613 (1999).

[50] M. Sawicka et al. Eur. Phys. J. A 22, 455 (2004).

[51] H. Sing, V. K. Tikku, B. Sethi, and S. K. Mukherjee. Nucl. Phys.A 174, 426 (1971).



202 Bibliography

[52] T. E. Ward, H. Ilhochi, and J. L. Meason. Phys. Rev. 188, 1802

(1969).

[53] D. L. Swindle, N. A. Morcos, T. E. Ward, and J. L. Meason. Nucl.Phys. A 185, 561 (1972).

[54] L. Hou et al. Phys. Rev. C 68, 054306 (2003).

[55] W. G. Cross and H. Ing. Bull. Am. Phys. Soc. 15, 755 (1970).

[56] L. Weissman et al. Phys. Rev. C 65, 024315 (2002).

[57] I. Stefanescu et al. Phys. Rev. Lett. 98, 122701 (2007).

[58] B. Zeidman and J.A. Nolen, Jr. Phys. Rev. C 18, 2122 (1978).

[59] S. Franchoo et al. Phys. Rev. Lett. 81, 3100 (1998).

[60] S. Franchoo et al. Phys. Rev. C 64, 054308 (2001).

[61] S. Franchoo. Evolution of Nuclear Structure towards 78Ni In-vestigated by the β Decay of Laser-Ionized 68−74Ni . PhD thesis,Katholieke Universiteit Leuven, (1999).

[62] K. S. Krane. Introductory Nuclear Physics. John Wiley & SonsInc., (1988).

[63] J. L. Meason and P. K. Kuroda. Phys. Rev. 138, B1390 (1965).

[64] L. M. Taff, B. K. S. Koene, and J. Van Klinken. Nucl. Phys. A164, 565 (1971).

[65] W. L. Reiter, W. H. Breunlich, and P. Hille. Nucl. Phys. A 249,166 (1975).

[66] J. D. Sherman, J. R. Flynn, O. Hansen, N. Stein, and J. W. Sunier.Phys. Lett. B 67, 275 (1977).

[67] J. Van Roosbroeck et al. Phys. Rev. Lett. 92, 112501 (2004).

[68] J. Van Roosbroeck et al. Phys. Rev. C 69, 034313 (2004).

[69] A. Baghdadi, R. Seltz, D. Magnac-Valette, G. Bonneaud, andC. Gerardin. Nucl. Phys. A 253, 20 (1975).



Bibliography 203

[70] G. Hardie, T. H. Braid, L. Schutzmeister, and J. W. Smith. Phys.

Rev. C 5, 1600 (1972).

[71] B. Rosner and C. H. Holbrow. Phys. Rev. 154, 1080 (1967).

[72] A. Marinov et al. Nucl. Phys. A 438, 429 (1985).

[73] K. Reiner et al. Nucl. Phys. A 472, 1 (1987).

[74] A. Covello and V. R. Manfredi. Phys. Lett. B 34, 584 (1971).

[75] Jose M. G. Gomez. Phys. Rev. C 6, 149 (1972).

[76] K. W. C. Stewart, B. Castel, and B. P. Singh. Phys. Rev. C 4,

2131 (1971).

[77] K. S. Burton and L. C. McYntire. Phys. Rev. C 3, 621 (1971).

[78] R. Nordhagen, B. Elbek, and B. Herskind. Nucl. Phys. A 104,353 (1967).

[79] A. G. Blair and D. D. Armstrong. Phys. Rev. 140, B1567 (1965).

[80] K. L. Coop, I. G. Graham, and E. W. Titterton. Nucl. Phys. A150, 346 (1970).

[81] A. Marinov et al. Nucl. Phys. A 431, 317 (1984).

[82] J. F. Mateja et al. Phys. Rev. C 13, 2269 (1976).

[83] J. Bron, H. W. Jongsma, and H. Verheul. Phys. Rev. C 11, 966(1975).

[84] P. H. Regan, J. W. Arrison, U. J. Huttmeier, and D. P. Balamuth.Phys. Rev. C 54, 1084 (1996).

[85] F. R. Hudson and R. N. Glover. Nucl. Phys. A 160, 482 (1971).

[86] E. Runte et al. Nucl. Phys. A 441, 237 (1985).

[87] O. Hansen, M. N. Harakeh, J. V. Maher, L. W. Put, and J. C.Vermeulen. Nucl. Phys. A 313, 95 (1979).

[88] A. G. Blair and D. D. Armstrong. Phys. Rev. 151, 930 (1966).



204 Bibliography

[89] M. Seeger et al. Nucl. Phys. A 533, 1 (1991).

[90] M. Seeger et al. Nucl. Phys. A 539, 223 (1992).

[91] U. Bosch et al. Nucl. Phys. A 477, 89 (1988).

[92] L. Gaudefroy. Spectroscopie βγ de noyaux riches en neutrons au-tour de N = 32/34 et N = 40. PhD thesis, Universite de Paris XIOrsay, (2005).

[93] T. Otsuka, T. Matsuo, and D. Abe. Phys. Rev. Lett. 97, 162501(2006).

[94] W. B. Walters. Private communication.[95] M. Block et al. Phys. Rev. Lett. 100, 132501 (2008).

[96] A. N. Deacon et al. Phys. Lett. B 622, 151 (2005).

[97] S. Lunardi et al. Phys. Rev. C 76, 034303 (2007).

[98] J. M. Daugas et al. AIP Conf. Proc. 831, 427 (2006).

[99] M. Block et al. Phys. Rev. Lett. 101, 059901(E) (2008). Erratumof Ref. [95].

[100] J. I. Prisciandaro et al. Phys. Lett. B 510, 17 (2001).

[101] R. V. F. Janssens et al. Phys. Lett. B 546, 55 (2002).

[102] D. C. Dinca et al. Phys. Rev. C 71, 041302(R) (2005).

[103] A. Burger et al. Phys. Lett. B 622, 29 (2005).

[104] S. N. Liddick et al. Phys. Rev. C 70, 064303 (2004).

[105] B. Fornal et al. Phys. Rev. C 70, 064304 (2004).

[106] M. Hannawald et al. Phys. Rev. Lett. 82, 1391 (1999).

[107] O. Sorlin et al. Eur. Phys. J. A 16, 55 (2003).

[108] N. Aoi et al. Nucl. Phys. A 805, 400c (2008).



Bibliography 205

[109] M. Honma, T. Otsuka, B. A. Brown, and T. Mizusaki. Eur. Phys.

J. A 25, s01, 499 (2005).

[110] P. Adrich et al. Phys. Rev. C 77, 054306 (2008).

[111] M. Marginean et al. Phys. Lett. B 633, 696 (2006).

[112] F. Iachello. Phys. Rev. Lett. 85, 3580 (2000).

[113] Yu. Kudryavtsev et al. Nucl. Instr. and Meth. B 204, 336 (2003).

[114] M. Facina et al. Nucl. Instr. and Meth. B 226, 401 (2004).

[115] P. Van den Bergh et al. Nucl. Instr. Meth. B 126, 194 (1997).

[116] J. Eberth et al. Prog. in Part. and Nucl. Phys. 46, 389 (2001).

[117] E. R. Flynn et al. Phys. Rev. Lett. 42, 626 (1978).

[118] S. Cochavi and W. R. Kane. Phys. Rev. C 6, 1650 (1972).

[119] E. K. Warburton, J. W. Olness, A. M. Nathan, J. J. Kolata, andJ. B. McGrory. Phys. Rev. C 16, 1027 (1977).

[120] L. Weissman et al. Nucl. Instr. and Meth. A 423, 328 (1999).

[121] M. M. Rajabali et al. In Proceedings of the Fourth International Conference on Fission and Properties of Neutron-Rich Nuclei,

J. H. Hamilton, A. V. Ramayya, and H. K. Carter, editors, 679 (,Sanibel Island, USA, 2007).

[122] R. A. Meyer, O. G. Lien, and E. A. Henry. Phys. Rev. C 25, 682(1982).

[123] K. Heyde, J. Jolie, J. Moreau, J. Ryckebusch, and M. Waroquier.Nucl. Phys. A 466, 189 (1987).

[124] J. L. Wood, K. Heyde, W. Nazarewicz, M. Huyse, and P. VanDuppen. Phys. Rep. 215, 101 (1992).

[125] K. Heyde, J. Jolie, J. Moreau, J. Ryckebusch, M. Waroquier, and

J. L. Wood. Phys. Lett. B 176, 255 (1986).

[126] T. Kibedi and R. H. Spear. At. Data Nucl. Data Tables 89, 77(2005).





Publication list

1. Decay correlations in the seconds range with laser-ionized,

mass-separated beams,

D. Pauwels, O. Ivanov, J. Buscher, T. E. Cocolios, J. Gentens, M.Huyse, A. Korgul, Yu. Kudryavtsev, R. Raabe, M. Sawicka, I.Stefanescu, J. Van de Walle, P. Van den Bergh, P. Van Duppen,Nuclear Instruments and Methods in Physics Research Section B 266 (2008) 4600

2. Shape isomerism at N = 40: Discovery of a proton in-

truder state in 67Co,D. Pauwels, O. Ivanov, N. Bree, J. Buscher, T. E. Cocolios, J.Gentens, M. Huyse, A. Korgul, Yu. Kudryavtsev, R. Raabe, M.Sawicka, I. Stefanescu, J. Van de Walle, P. Van den Bergh, P. VanDuppen, W. B. WaltersPhysical Review C 78 (2008) 041307(R)

3. Structure of 65,67Co studied through the β decay of 65,67Fe

and a deep-inelastic reaction,D. Pauwels, O. Ivanov, N. Bree, J. Buscher, T. E. Cocolios, M.Huyse, A. Korgul, Yu. Kudryavtsev, R. Raabe, M. Sawicka, I.Stefanescu, J. Van de Walle, P. Van Duppen, W. B. Walters, R.Broda, M.P. Carpenter, R.V.F. Janssens, B. Fornal, A.A. Hecht,N. Hoteling, A. Wohr, W. Krolas, T. Lauritsen, T. Pawlat, D.Seweryniak, J.R. Stone, X. Wang, J. Wrzesinski, S. ZhuSubmitted to Physical Review C

4. Evidence for a 1/2− β -decaying isomer in 71Ni,I. Stefanescu, D. Pauwels, N. Bree, T. E. Cocolios, J. Diriken, S.Franchoo, M. Huyse, O. Ivanov, Yu. Kudryavtsev, N. Patronis, J.

207



208 Publication list

Van de Walle, P. Van Duppen, W. B. Walters,


5. Characterization of the LISOL laser ion source using spon-

taneous fission of 252Cf ,Yu. Kudryavtsev, T. E. Cocolios, J. Gentens, O. Ivanov, M. Huyse,D. Pauwels, M. Sawicka, T. Sonoda, P. Van den Bergh, P. VanDuppen,Nuclear Instruments and Methods in Physics Research Section B 266 (2008) 4368

6. Interplay between single-particle and collective effects in

the odd-A Cu isotopes beyond N = 40,I. Stefanescu, G. Georgiev, D. L. Balabanski, N. Blasi, A. Blazhev,N. Bree, J. Cederkall, T. E. Cocolios, T. Davinson, J. Eberth, A.Ekstrom, D. Fedorov, V. N. Fedosseev, L. M. Fraile, S. Franchoo,K. Gladnishki, M. Huyse, O. Ivanov, V. Ivanov, J. Iwanicki, J.Jolie, T. Konstantinopoulos, Th. Kroll, R. Krucken, U. Koster,A. Lagoyannis, G. Lo Bianco, P. Maierbeck, B. A. Marsh, P. Na-piorkowski, N. Patronis, D. Pauwels, G. Rainovski, P. Reiter, K.Riisager, M. Seliverstov, G. Sletten, J. Van de Walle, P. Van Dup-pen, D. Voulot, N. Warr, F. Wenander, K. Wrzosek,Physical Review Letters 100 (2008) 112502

7. Gamow-Teller transitions in exotic pf-shell nuclei relevantto supernova explosion,Y. Fujita, B. Rubio, T. Adachi, F. Molina, A. Algora, G. P. A.Berg, P. von Brentano, J. Buscher, T. E. Cocolios, D. De Frenne,C. Fransen, H. Fujita, K. Fujita, W. Gelletly, K. Hatanaka, M.Huyse, O. Ivanov, Yu. Kudryavtsev, E. Jacobs, D. Jordan, K.Nakanishi, A. Negret, D. Pauwels, A. B. Perez-Cerdan, N. Pietralla,Z. Podolyak, L. Popescu, R. Raabe, Y. Sakemi, M. Sawicka, Y.Shimbara, Y. Shimizu, T. Shizuma, Y. Tameshige, A. Tamii, P.Van den Bergh, J. Van de Walle, P. Van Duppen, M. Yosoi, K. O.Zell,

Journal of Physics G: Nuclear and Particle Physics 35 (2008)014041

8. β -decay properties of 72Ni and 72Cu,



Publication list 209

J.-C. Thomas, H. De Witte, M. Gorska, M. Huyse, K. Kruglov,

Y. Kudryavtsev, D. Pauwels, N. V. S. V. Prasad, K. Van de Vel,P. Van Duppen, J. Van Roosbroeck, S. Franchoo, J. Cederkall,H. O. U. Fynbo, U. Georg, O. Jonsson, U. Koster, L. Weissman,W. F. Mueller, V. N. Fedosseev, V. I. Mishin, D. Fedorov, A. DeMaesschalck, N. A. Smirnova,Physical Review C 74 (2006) 054309

9. Evolution of the nuclear structure approaching 78Ni: β decay of 74−78Cu,J Van Roosbroeck H De Witte M Gorska M Huyse K Kruglov

Documents

Thesis DieterPauwels vFinal