Shape evolution of highly deformed 75 Kr 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

Motivation 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 72 Kr ground state has oblate shape, but 74 Kr and 76 Kr have prolate shape R. Palit et al., Nucl. Phys. A 686 (2001) 141 Recently, high spin states of the 75 Kr 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 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 68 Se and 72 Kr Bouchez et al, PRL (2003) Sun, Wiescher, Aprahamian, Fisker Nucl. 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 75 Kr 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 75 Kr

Q t 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 Q t 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.

Exp values of Q t 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 75 kr 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

Hamiltonian and single particle space Hamiltonian Interaction strengths  is related to deformation  by G M is determined by observed even-odd mass difference G Q is assumed to be proportional to G M 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

Configuration spaces Even-even nuclei: Odd-odd nuclei: Odd-neutron nuclei: Odd-proton nuclei:

Results and discussion Moment of inertia as a function of spin for the positive and negative parity bands in 75 Kr. MOI is defined as : Irregularities around spin 25/2 due to alignment of g 9/2 proton in both positive and negative parity band Experimental MoI compared with PSM

Quadrupole moments Q t The calculation formula used for Q t Comparision of the measured quadrupole moments Q t 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 Q t values of 75 Kr high-spin states. Good agreement has been obtained if shape is taken to be prolate, with deformation parameter  = 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 g 9/2 rotation alignment.

Thank you !