Outline Lecture 2 · Outline Lecture 2 • Isotope Shiftt: Determination of Nuclear Charge Radii • Example 1: Mg Isotopes ... 20 28 50 8 20 28 50 Z 82 N Be Mg Halo nuclei Island

Outline Lecture 2

• Isotope Shiftt: Determination of Nuclear Charge Radii

• Example 1: Mg Isotopes

• Example 2: Halo Nuclei: Charge Radii of Be Isotopes and a

Test of NR-QED Calculations

Collinear-Anticollinear Approach

• Example 3: The Calcium Isotopes

Bunched Beams

State-Selective Charge Exchange

• Hyperfine Structure and Nuclear Deformation

• Example 4: The Cd Isotopes

Reminder: Mass and Field Shift

Isotope Shifts of Mg Isotopes

Isotope A=

Charge Radii of Mg Isotopes

Other „Regions of Inversion“

A. Brown, Physics 3, 104 (2010)

https://physics.aps.org/articles/v3/104

The Beryllium Isotopic Chain

Stable Nucleus

208Pb

11Li

Neutron Halo

I. Tanihata, Progr. Part. Nucl. Phys 35, 505 (1995)

6He 8He

11Li

11Be12Be

14Be

4He

fm2.10

30

R

ARR

Theory: Mass Shift in Be+

Atomic Theory:

Photomultiplier

ion beamEkin~60 keV

collinear

laser beam

fixed frequency

+

anticollinear

laser beam

fixed frequency

Doppler-tuning 10c

10a

„CONVENTIONAL SETUP“

Acceleration /

Deceleration

2

0

222

0ca 1

= (U,m), = (U,m),

DU/U 10-4

dIS (9Be,11Be) = 18 MHz

10c

NEW APPROACH

Completely

independent

of U !

Experiment: Frequency-Comb Based

Collinear-Anticollinear Laser Spectroscopy

Laser System for Collinear-Anticollinear

Measurements

A. Krieger et al., Appl. Phys. B 123, 15 (2017)

Laser System for Collinear-Anticollinear

Measurements


Spectra of 10,11Be in D1 Transition

10Be

11Be

10Be

11Be

http://www.gsi.de/

Ion-Photon Coincidence


Experimental D1 and D2 Transition Frequencies

Be Be


pure p²

pure

(sd)²

75% admixture

of (sd)²-levels

2s1/2

1s1/2

1p1/2

1d5/2

1p3/2

1d3/2

2

4

2

62

4

12BeN=8

Extracting Nuclear Charge Radii

Rc-n 8 fm

Experimental D1 and D2 Transition Frequencies


Isotope-dependent Fine-Structure Splitting

W. Nörtershäuser, PRL 115, 033002 (2015)


Fine Structure Splitting from Even Isotopes


Take Home

• For light Nuclei the Field Shift is a small contribution to the isotope

shift.

• It can be separated only if highly precise atomic structure calculations

(now possible up to 5 electrons) and highly accurate isotope shifts are

available

• Charge Radii in this region are strongly affected by nuclear clustering

• The charge radius of 12Be clearly shows the disappearance of the N=8

shell closure

• Accurate measurements of fine-structure splittings of few-electron

systems provide a test of Quantum Electrodynamics QED

Detection Techniques in Collinear Laser

Spectroscopy

Prinzip des Akkumulieren und Kühlens

z

End p

late

pote

nti

al Accumulate

Release

Reacceleration

potentialPMT

10µs gatee.g. 100ms accumulation

=10µs gate width

Background

suppression~104

URF

Laser beamPMT

Accumulation for

e.g. 100 ms

E.M

ané

et a

l, E

ur.

Ph

ys. J. A

42, 5

03

(2

00

9)

F. Herfurth, NIMA 469, 254 (2001)

A. Nieminen, Phys. Rev. Lett. 88, 094801 (2002)

Bunched Beam Detection

~104 background

suppression

Photon Detection with Time Tagging

-500 -450 -400 -350 -300 -250 -2000

10

20

30

40

20,5

21,0

21,5

22,0

22,5

tim

e [

µs]

0

1

2

3

4

5

counts

voltage [V]

43Ca

+

Measurement of Calcium Isotopes using

Bunched Beam Detection

R.F. Garcia Ruiz et al., Nature Physics 12 (2016) 594

Spectra of 49,51,52Ca+


Extracted Charge Radii


Large charge radius of 52Ca:

No signature for shell closure

at N=32

Towards 54Ca

Goal: cross N=32 and reach N=34

For both N values there is experimental evidence for new shell closures

Challenge: Production Rate of about 1 ion/sec

Technique: State selective charge exchange

Garcia-Ruiz et al., J.Phys. G 44, 044003 (2017)

40Ca+ + Na 40Ca + Na+

(beam) (gas) (beam) (gas)

Charge Exchange Cross Section


Ratio of charge exchange cross

sections for 3d and 4s levels in

Ca+

Off-Resonance: Ion stays in 4s level

Resonance: Ion is transferred to 3d level

ce(3

d)

/

ce(4

s)

Towards 54Ca


1g

2d

3s

1h

1g9/2

1g7/22d5/2

2d3/23s1/21h11/2

1h9/2

50

5864

687082

92

50

82

Spherical Shell Model

2

28

20

28

50

8

20

28

50

82Z

N

Be

Mg

Halo nuclei

Island of inversion

Monopole migration

Ca

99Cd

130Cd

Nuclear Chart

Cd

11/2- -Isomers

F. Buchinger et al., Nucl.Phys. A 462, 305 (1987)

Fourth Harmonic Generation of 215 nm

Hyperfine Structure

Spin

Hyperfine Structure

~ Alow

~ Alow

~Aup

SpinMagnetic Moment, I

site nuclear at fieldmagnetic )0(

,)0(

e

eI

H

JI

HA

~Aup

Quadrupole moment Qs

site nuclear at

gradient fieldelectric )0(

),0(

zz

zzs

V

VeQB

Hyperfine Structure

SpinMagnetic Moment, I

site nuclear at fieldmagnetic )0(

,)0(

e

eI

H

JI

HA

~ μ(129mCd)

~ μ(111mCd)

Qs

Elektrical Hyperfine Structure

Isotope Shift

Hyperfine Structure

Isotope Shift

Hyperfine Structure

Shift of Hyperfine State Einfluss des

Quadrupolmomentes auf Niveauenergien

Nucleus

Electron Orbital

Analyzing Hyperfine Structure

Peak Positions:

choose I, Nonlinear Least Squares Fitting Au, Al, Bu, Bl, 0, 2red

Isomers (t1/2 > ms)

are easily identified

lowlowlowlowupupupup0 BABA

2

)1()1()1(

2),,(lowup,

JJIIFFCFJI

JIJI

JJIICCFJI

)12)(12(2

)1()1()1(),,( 4

3

up,low

m

low

m

low

m

low

m

low

m

up

m

up

m

up

m

up

m

IS BABAm m

ISISIsomer d Isomer-Spin: I m Isomer-Shift:

MHz

Extraction of Nuclear Moments

nucleus of site at fieldmagnetic )0(

)0(

e

eI

H

JI

HA

Determination of nuclear moments requires hyperfine fields !

Relatively large theoretical uncertainties

nucleus the of site the

at gradient fieldelectric )0(

),0(

zz

zz

V

eQVB

f

fI

AA

Re

Re

f

fB

BQQ

Re

Re

Alternatives:

Reference nuclei (stable Isotopes) with accurately known moments

Simple Structure in Complex Nuclei

1g

2d

3s

1h

1g9/2

1g7/22d5/2

2d3/23s1/21h11/2

1h9/2

50

5864

687082

92

50

82

Capacity of 1h11/2 niveau:

12 neutrons

→ 6 quad. moments

But: 10 quad. moments

Neutron pairs shared

between the neighboring

levels.

Capacity of 1h11/2 niveau:

12 neutrons

→ 6 quad. moments

But: 10 quad. moments

Neutron pairs shared

between the neighboring

levels.

D.T. Yordanov et al, PRL 110 (2013) 192501

Take Home

• Bunched beam spectroscopy increased the sensitivity by about a

factor of 100

• Isomeric states are easily discovered by laser spectroscopy

• The electric hyperfine structure reveals the nuclear deformation

• The quadrupole moment and its sign can be extracted from the

spectra

Documents

Outline Lecture 2 · Outline Lecture 2 • Isotope Shiftt: Determination of Nuclear Charge Radii • Example 1: Mg Isotopes ... 20 28 50 8 20 28 50 Z 82 N Be Mg Halo nuclei Island