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Shape evolution of highly deformed 75 Kr and projected shell model description

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 )

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Shape evolution of highly deformed 75 Kr and projected shell model description

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  1. Shape evolution of highly deformed 75Kr and projected shell model description Yang Yingchun Shanghai Jiao Tong University Shanghai, August 24, 2009

  2. 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)

  3. Outline • Motivation • Experimental data • Projected shell model calculation • Results and discussion • Conclusion

  4. 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 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

  5. 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

  6. 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 • b-decay rates H. Schatz, et al., Phys. Rep. 294 (1998) 167

  7. Energies levels of 68Se and 72Kr Bouchez et al, PRL (2003) Sun, Wiescher, Aprahamian, Fisker Nucl. Phys. A758 (2005) 765

  8. 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

  9. 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

  10. 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.

  11. Exp values of Qt and B(E2)

  12. 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 e.

  13. Basic structure for PSM • PSM wavefunction: with the projector: • The eigenvalue equation: with matrix elements: • The Hamiltonian is diagonalized in the projected basis

  14. Hamiltonian and single particle space • Hamiltonian • Interaction strengths • c is related to deformation e 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

  15. Configuration spaces • Even-even nuclei: • Odd-odd nuclei: • Odd-neutron nuclei: • Odd-proton nuclei:

  16. 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 Experimental MoI compared with PSM

  17. Quadrupole moments Qt The calculation formula used for Qt Comparision of the measured quadrupole moments Qt with the prediction of PSM calculation

  18. 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

  19. 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 e=+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.

  20. Thank you !

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