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From Vibrations to Rotations as a Function of Spin
Paddy Regan
Dept. of Physics, University of Surrey,
Guildford, GU2 7XH, UK
e-mail: [email protected]
Main physics question,
Are nuclei (with Z=40-50) Rotators or Vibrators ?
* Signatures of vibrator-rotor structural evolution.
* 102Ru from WNSL-Yale
* 99-102Mo alignments/phase changes (using DICs).
* 112,114Cd medium spins from WNSL-Yale
* Odd-A cases, 101Ru
Outline
Nuclear Rotations and Vibrations
• What are the signatures (in even-even nuclei) ?– (extreme) theoretical limits
2 (4 ) 4(5) 20
( 1), 3.332 (2 ) 2(
(4 ) 2 = 2.00
3)
( 1
6
2 )N
J
EE N
EE J J
E
E
2
V
2
En
n=0
n=1
n=2
n=3
http://npl.kyy.nitech.ac.jp/~arita/vib
Signatures of (perfect) vibrators and rotors
State lifetimes, i.e., B(E2) values and selection rules (eg. n=1).
Nuclei in the Sr-Sn region show dramatic change in structure around N~60.
Sudden explosion of 2 deformation in Sr-Ru isotopes at N=60 has been explained by strong spatial overlap of Spin-Orbit Partners (SOPs) g9/2 protons and g7/2 neutrons.
(see Federman and Pittel, Phys. Rev. C20 (1979) p820)
Alignments and rotational motion in ‘vibrational’ 106Cd (Z=48, N=58),
PHR et al. Nucl. Phys. A586 (1995) p351
Can subtract off a reference (core) aligned angular momentum to see effect of quasi-particle alignments as a function of frequency.
2( 1)X
x X ref
ref X ref
I I I K
i I I
I I
ix=5h
CSM ref. Bengtsson Frauendorf and May, At. Data. Nuc. Data. Tab. 35 (1986) p15
h11/2 neutron orbital responsible for 1st crossing in even-even systems.Energy appears to correlate with transition to deformed ground states at N~60
Alignment (rotational picture at least) driven by Coriolis interaction on high-j, low- orbitals (ie. ones with large jx on collective rotation axis.
Vcor = -jx.
eg.
h11/2 [550]1/2 ‘intruder’
FS for N~57, 2~0.15->0.2
jx
50
82
[550]1/2-
1h11/2
1g9/2
[541]3/2-
Ru (Z=44) in the centre of the ‘deformed’region for N=56-58
Anharmonic vibrator for the ground state ‘band’ is the usual explanation for 100Ru and neighbours....butmid-shell (Z=40-50) natureis consistent with largest collectivity in the region.
Q.Are these nuclei deformed or vibrational ?
RuMoZr Pd Cd Sn
Experimental Details
96Zr (9Be,3n)102Ru, pace~100mb
Enriched (85%) 670g/cm2 96Zr foil on 5mg/cm2 natPb support.
Ebeam=44 MeV, lmax~25 h
YRASTBALL array at WNSL
6 clover germaniums @ 90o
5 co-axial detectors @ 50o + 126o
3 co-axial detectors @ 160o
24
24
2 :Rotor
0 : Vibrator
)2(
242
),1(2
:Rotor
,2
:Vibrator
22
22
J
J
J
n
JR
JR
J
JJER
JEJJE
EJ
nE
See PHR, Beausang, Zamfir, Casten, Zhang, Yamamoto et al., PRL in press.
If we parameterize with (E / J) vs. JCan see if rotor or vibrator by inspection
Structural change from vibrator to rotator appears to be a regular feature of this region.
Rotation stabilized by core stiffening due to population of ‘rotation-aligned’ h11/2
neutrons.
Special type of crossing, Vibrator to Rotor !!!
Q. Are backbends necessarily due to rotational alignment ?
A. NO ! Can be vibrational – rotational structure change!!
(a) gamma-gamma (b) triple coincidences
Detailed spectroscopy allowed by investigating gamma-decay sequences from high-spin states. YRASTBALL allows triple coincidences to be routinely observed. Band-like structures are clearly observed in 101Ru.
see A.D.Yamamoto et al. Phys. Rev. C66 (2002) 024302
Decay scheme for 101Ru
Band-like sequences observed on ‘intrinsic’ 11/2-, 5/2+ and 7/2+ states.
Backbending observed in positiveparity bands (1 and 2), but not innegative parity band (band 3).
Pauli blocking argumentssuggest aligning particles are therefore of h11/2 neutron nature.
Quasi-particle alignments and kinematic moments of inertia
ix=10 h11/2
band
h11/2
band
TRS calculations for 101Ru by Furong Xu (Bejing) for differentparity (and signature) configs.
2
=0.2MeV
=0.4MeV
=0.3MeV
=0.6MeV
See PHR, Yamamoto, Beausang, Zamfir, Casten, Zhang et al., AIP Conf. Proc. 656 (2002) p422
For Odd-A (Carl Wheldon’s idea)
equn. GOS-E orginal toreduces this0for note
)2()2(
)2(
24
24
2][4
2)(
i.e., ,normalised be should energies
, spin, bandhead with case rotationalfor
24
2)(
2
2
2
2
2
2
KKI
KRER
RKIRKI
KIE
KI
KE
KI
KIKIR
K
KI
I
KI
EKIR
Krotor
K
Can not use fusion-evaporation reactions to study high-spin states (and thus vibrational-rotational transitions, alignments etc.) in beta-stable and neutron-rich systems.
Use deep-inelastic reactions.
Z
N
Ebeam ~15-20% above Coulomb barrier
beam
target
(i) (ii) (iii)
max
3
1blfmax
3
1tlf
max
3/13/1
0
221
max
1
1
7
2
1
1
7
2
fragments. twoebetween th mom. ang. relative the
and , intosplit is limit, mode rolling In the
25.12
cosec1.4
where, approach,closest of distance by thegiven is
max. issection -cross DIC the whereangle The
. and 219.0
is mom. ang. peripheral max. y theclassicall-Semi
l
AA
ll
AA
l
lll
fmAAE
eZZd
d
grazing
AA
AAVERl
B
T
T
B
blftlf
TBgraz
k
TB
TBCMCM
0
10
20
30
40
50
620
677
733
790
%>Ecoul
Ltlf (roll)
v/c (tlf)
Linear(%>Ecoul)
0
10
20
30
40
50
60
620 648 677 705 733 761 790Beam Energy (MeV)
blf_ang
tlf_ang
lmax/10
Kinematics and angular mom. input calcs (assumes ‘rolling mode’) for 136Xe beam on 100Mo target.
Estimate ~ 25hbar in TLFfor ~25% above Coul. barrier. For Eb(136Xe)~750 MeV,blf~30o and tlf~50o.
100Mo +136Xe (beam) DIC calcs.
100Mo + 136Xe @ 750 MeVGAMMASPHERE + CHICO
TLFs
BLFs
elastics
-1
cos-1
by calculated then is correctionDoppler The
coscoscoscossinsinsinsin)cos(
where
)cos(r.r
by given is angleray -fragment/ the
k )cos( , j )sin()sin( ,i )cos()sin(
k, and j i, rsunit vectoCartesian For
2
2,1'
2121212112
122121
1,2
1,2
EE
rr
rzryrx
z
x
y
Isomer gating very useful in DIC experiments. Test with known case…..
Use known delayed lines in 101Mo (182 and 57 keV) to identify previously unknown h11/2 band (+ 34 keV E1 decay).
112Cd
Vib.
rotor
(h11/2)2 alignment in A~130 region appears tohave analogous behaviourto (h11/2)2 alignment in A~100 region.
Conclusion?
In many cases, ‘rotational alignment’ is actually acrossing between a quasi-vibrational groundstate configuration and a deformed rotational sequencecaused by stiffening of potential by population of high-j, equatorial (h11/2) orbitals
Summary and Future Look• 101,102Ru (and neighbours) look like -soft, anharmonic vib. nuclei at
low-spins (eg. E(4+)/E(2+)~2.3)..... BUT also have apparent rotational-like behaviour eg. band-crossing,
alignments etc. • Paradoxically, Coriolis (rotational) effects are largest in nuclei which
have SMALL deformations (ie. require large energies/frequencies to rotate). ‘Vibrational’ A=100 may be the best tests of nuclear Coriolis effects.
• Vibrational – Rotational ‘phase’ change around spin 10? Smooth evolution with crossing of anharmonic vibrational states and rotation-aligned configurations.
• Plot of E/J verses J gives model independent crossing.
many thanks to......• Arata Yamamoto (Surrey/Yale student).
• 101-102Ru Expt. Con Beausang (+ Yalies)
• 100Mo+136Xe CHICO, Rochester (Chin-Yen Wu et al.,), Manc. (John Smith et al,) + LBNL
• 7Li+110Pd, Scott Langdown (+Yalies + Paisley)
• Vibrator-Rotator (E-GOS) plots, Con B., Rick Casten, Victor Zamfir, Jing-Ye Zhang et al.,
• Odd-A, Carl Wheldon (now at GSI)
NUSTAR’05International Conference on
NUclear STructure, Astrophysics and Reactions
The University of Surrey, Guildford, UK
9-12 January 2005