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 !