shape evolution of highly deformed 75 kr and projected shell model description
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Shape evolution of highly deformed 75Kr and projected shell model description
Yang Yingchun
Shanghai Jiao Tong University
Shanghai, August 24, 2009
Collaborators
Y. Sun (Shanghai)
T. Trivedi, D. Negi, R. Palit, Z.Naik, J.A. Sheikh, A.Dhal, S.Kumar, R. Kumar, R.P. Singh, S. Muralithar, A.K. Jain, H.C. Jain, S.C. Pancholi, R. K. Bhowmik, I. Mehotra (for INGA collaboration)
Outline
Motivation Experimental data Projected shell model calculation Results and discussion Conclusion
MotivationMotivation
N~Z nuclei in mass 70 – 80 region show different shapes at varying angular momentum
Y. Sun, Eur. Phys. J. A 20 (2004) 133
They have important influence on the results of the astrophysical rp process
H. Schatz, et al., Phys. Rep. 294 (1998) 167
Even-even isotope 72Kr ground state has oblate shape, but 74Kr and 76Kr have prolate shape
R. Palit et al., Nucl. Phys. A 686 (2001) 141
Recently, high spin states of the 75Kr nucleus have been populated and studied by the Indian nuclear experimentalists using Indian Nation Gamma Array (INGA)
T. Trivedi, et al., PRC submitted
Rapid proton capture (rp-process) in X-ray bursts
X-ray bursts have been suggested as possible sites for nucleosynthesis with high temperature hydrogen burning through rp-process
Capture path runs along the proton-rich region, e.g. those N~Z nuclei of mass 70 – 80
Neutron star
H. Schatz, et al., Phys. Rep. 294 (1998) 167
Important role of nuclear structure
Nuclear structure controls the clock for the stellar burning processes the total time along the reaction path entirely determine the
speed of nucleosynthesis towards heavier nuclei and the element production
What are important: nuclear masses nuclear structure (single-particle levels, nuclear shapes,
isomers, …) proton-capture rates -decay rates
H. Schatz, et al., Phys. Rep. 294 (1998) 167
Energies levels of 68Se and 72Kr
Bouchez et al,PRL (2003)
Sun, Wiescher, Aprahamian, FiskerNucl. Phys. A758 (2005) 765
Abundances in X-ray burst
It is possible that a flow towards higher mass through the isomer branch can occur (calculations using the X-ray burst model) Sun, Wiescher, Aprahamian, Fisker, Nucl. Phys. A758 (2005) 765
Without any possible isomer contribution Full flow through isomers rather than g-states
Measurement of lifetime for high spin states 75Kr
Our collaborators use Indian National Gamma Array (INGA)
Lifetimes of 16 high spin states have been measured
This is the partial level scheme
Partial level scheme of 75Kr
Qt obtained from experiment
Once lifetime have been determined, electric quadrupole transition
probability B(E2) are obtained from the values of lifetimes, and
transition quadrupole moments Qt is calculated according to the
formula
The single-particle orbits labeled by K=5/2 for positive parity band and
K=3/2 for negative band are found to be the main components of the
calculated PSM wavefunctions.
2 21620 | 2 ( 2, 2).
5tQ IK I K B E I I
Exp values of Qt and B(E2)
The projected shell model calculation
The projected shell model (PSM), which is a shell model based on deformed bases, has been used to understand the evolution of collectivity for the positive and negative parity bands of 75kr up to high spin.
One states with a deformed basis, with a deformation parameter .
Basic structure for PSM
PSM wavefunction:
with the projector:
The eigenvalue equation:
with matrix elements:
The Hamiltonian is diagonalized in the projected basis
IM K
IM Pf
DDdI
P IM K
IM K
28
12
0''
''
fENH II
'''''' I
KK
II
KK
I PNPHH
IM KP
Hamiltonian and single particle space
Hamiltonian Interaction strengths
is related to deformation by
GM is determined by observed even-odd mass difference
GQ is assumed to be proportional to GM with a ratio 0.16
Single particle space Three major shells for neutrons or protons For example, for rare-earth nuclei, N = 4, 5, 6 for neutrons
N = 3, 4, 5 for protons
PPGPPGQQHH QM 20
ppnn QQ 00
3/2
Configuration spaces
Even-even nuclei:
Odd-odd nuclei:
Odd-neutron nuclei:
Odd-proton nuclei:
,0ˆ,0ˆ,0ˆ,0ˆ I
MKIMK
IMK
IMK PPPP
,0ˆ,0ˆ,0ˆ,0ˆ I
MKIMK
IMK
IMK PPPP
,0ˆ,0ˆ,0ˆ I
MKIMK
IMK PPP
,0ˆ,0ˆ,0ˆ I
MKIMK
IMK PPP
Results and discussion Moment of inertia as a function of spin for the positive and negative
parity bands in 75Kr. MOI is defined as : Irregularities around spin 25/2 due to alignment of g9/2 proton in
both positive and negative parity band
( ) (2 1) / [ ( ) ( 2)]I I E I E I
Experimental MoI compared with PSM
Quadrupole moments Qt
2 22
1 ˆ( 2, 2) | || || | .2 1
I IB E I I QI
2 21620 | 2 ( 2, 2).
5tQ IK I K B E I I
The calculation formula used for Qt
Comparision of the measured quadrupole moments Qt with the prediction of PSM calculation
Structure study of 75Kr through band diagram
Configurations of 1- and 3-qp states for positive parity
Configurations of 1- and 3-qp states for negative parity
Conclusion
We have performed projected shell model calculations to understand the measured Qt values of 75Kr high-spin states.
Good agreement has been obtained if shape is taken to be prolate, with deformation parameter =+0.365.
The experimental quadrupole moments for both bands remain constant before the band crossing and then decrease after band crossing.
The PSM calculations reproduced the measured high-spin data and explain them through the proton g9/2 rotation alignment.
Thank you !
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