Shell Model based deformation analysis of light Cadmium isotopes T. Schmidt 1, A. Blazhev 1, K....
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Transcript of Shell Model based deformation analysis of light Cadmium isotopes T. Schmidt 1, A. Blazhev 1, K....
Shell Model based deformation analysis of light Cadmium isotopes
T. Schmidt1, A. Blazhev1, K. Heyde2, J. Jolie1
1Institut für Kernphysik , Universität zu Köln, Germany2Department of Physics and Astronomy , Ghent University,
Belgium
Brix Workshop, Spring 2015, Liège, Belgium
Outline• Introduction to shell model calculations• Comparison of band structures in theory and
experiment (106Cd, 108Cd)• Introduction to the method of Kumar and Cline
(extraction of β- and γ-values)• Illustration of deformation in 98Cd• Deformation analysis of 100Cd to 108Cd as a function of
neutron number and spin
SM-Calculations with ANTOINE
• Monopole corrected, effective interaction
• Ref.: N. Boelaert et al. PRC 75, 014316
Þ Protons: Z = 38 – 50Þ Neutrons: N = 50 – 82
Illustration: Boelaert et al. PRC75, 014316, 2007
2,23 MeV
N = 50
Z = 50
Band structures
Band structures 106CdDefined by the B(E2)-strength in ground- and side-band
106Cd, Theory
B(E2) in W.u.
106Cd, Experiment
Data: NNDC & J.Wood (private communication)
Band 1
Band 2
Band structures 106Cd
Data: NNDC & J.Wood (private communication)
106Cd, Theory
B(E2) in W.u. B(E2) in W.u.
106Cd, Experiment
Band 1
Band 2
Defined by the B(E2)-strength in ground- and side-band
Only B(E2)-transitions are considered Data: NNDC
Band 1Band 2
108Cd, Theory 108Cd, Experiment
B(E2) in W.u. B(E2) in W.u.
Band 3
Band structures 108Cd
Deformation analysis
Deformation analysis• Motivation: extraction of - and -values• Use method of K.Kumar and D.Cline
• Main tool for analysis: rotational invariants• Invariants are model independent. Valid in
laboratory and inertial frame of nucleus
Invariants
Msr×…×Mws
Building Invariants: Couple n single-particle-transition-operators to angular momentum 0:
Invariants
Msr×…×Mws
Building Invariants: Couple n single-particle-transition-operators to angular momentum 0:
Kumar-Cline-method• K. Kumar: • D. Cline:
Kumar-Cline-method• K. Kumar: • D. Cline:
Kumar-Cline-method• K. Kumar: • D. Cline:
• Kumar: uses model independent reference ellipsoid
• Cline: connects P(2) to deformation of ideal vibrator of Bohr & Mottelson
98Cd 100Cd 102Cd 104Cd 106Cd 108Cd
theory
theory
theory
experient • Protons give constant contribution
• Neutron number mainly influences collectivity
Indication of collectivity; B(E2; 21+ 01
+)
Deformation with rising N
• β is rising with N, as aspected.
• Summed up to i=20• moving towards triaxiality
state 01+
Deformation in 98Cd (semi-classical)
Illustration: K. Heyde, Springer, 1990
Deformation in 98Cd (semi-classical)
Illustration: K. Heyde, Springer, 1990
Deformation in 98Cd (semi-classical)
Illustration: K. Heyde, Springer, 1990
Deformation in 98Cd• Observed problem with
Kumar-method for 2 particle configuration in max. aligned spin
• Comparison between quadrupole moments (SM-spectroscopic, calc from spectroscopic and Kumar-method) show deviation in value and sign for 81
+
Deformation following bands• Band 1 shows short
increase in deformation from spin 0+ to 2+ (Cd104 increase to 4+). Afterwards decreases with spin.
• Band 2 shows similar behavior as band 1. Increase till some lower spin (2+ or 4+ ) then decreases.
• Cd 108: starts to be influenced by h11/2
Cd 100
Cd 104
Cd 102
Cd 106
Cd 108
108Cd-deformation & h11/2 occupation
• Correlation with deformation of band 2 an occupation of h11/2
• Further analysis necessary
state
state
Band 1 Band 2
Summary and Conclusions• SM-Calculations give good reproduction for
low energy states and still acceptable up to 8+.• Deformation of 0+
1,2 show expected increase in deformation towards the middle of the shell Also increase in γ.
• Band 1 & 2 show decrease in deformation at high spin after a short increase.
• 108Cd starts to be occupied by h11/2 influencing the deformation.
Thank you for your attention
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Comparison with ideal vibrator• Cd108.• Deviations in
energy levels from ideal vibrator.
• Deviation in transition rates from ideal vibrator.
• Forbidden transitions exist.
B(E2) in W.u.Daten: NNDC