We implemented a variation after projection (VAP) algorithm based on a triaxially deformed Hartree-Fock-Bogoliubov vacuum state. This is the first projected mean field study that includes all the quantum numbers (except parity), i.e., spin (J), isospin (T ) and mass number (A). Systematic VAP calculations with JT A-projection have been performed for the even-even sd-shell nuclei with the USDB Hamiltonian. All the VAP ground state energies are within 500 keV above the exact shell model values. Our VAP calculations show that the spin projection has two important effects: (1) the spin projection is crucial in achieving good approximation of the full shell model calculation.(2) the intrinsic shapes of the VAP wavefunctions with spin projection are always triaxial, while the Hartree-Fock-Bogoliubov methods likely provide axial intrinsic shapes. Finally, our analysis suggests that one may not be possible to associate an intrinsic shape to an exact shell model wave function.
The reflection asymmetric shell model has been established by means of the variational procedure and the projection method to describe the high spin states of octupole deformed nuclei. The Q•Q forces of quadrupole, octupole, and hexadecapole as well as the monopole and quadrupole pairings are included in the Hamiltonian. The shell model space is spanned by a selected set of the simultaneous angular momentum-and parityprojected BCS multiquasiparticle states which are intrinsically deformed. The general features of rotational octupole bands in even-even nuclei can be interpreted and reproduced by the present model, and the calculated results for the Ra isotopes are in good agreement with the experimental data.
A method for calculation of Gamow-Teller transition rates is developed by using the concept of the Projected Shell Model (PSM). The shell model basis is constructed by superimposing angularmomentum-projected multi-quasiparticle configurations, and nuclear wave functions are obtained by digonalizing the two-body interactions in these projected states. Calculation of transition matrix elements in the PSM framework is discussed in detail, and the effects caused by the Gamow-Teller residual forces and by configuration-mixing are studied. With this method, it may become possible to perform a state-by-state calculation for β-decay and electron-capture rates in heavy, deformed nuclei at finite temperatures. Our first example indicates that, while experimentally known Gamow-Teller transition rates from the ground state of the parent nucleus are reproduced, stronger transitions from some low-lying excited states are predicted to occur, which may considerably enhance the total decay rates once these nuclei are exposed to hot stellar environments.
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