Projected shell model for nuclear structure and weak interaction rates

The knowledge on stellar weak interaction processes is one of the most important ingredients for resolving astrophysical questions. Study of these rates is essentially a nuclear structure problem, in which the actual decay rates are determined by the microscopic inside of nuclear many-body systems. For many astrophysically-interested questions, information on detailed nuclear level structure at low excitations is important. It has been suggested that the nuclear shell model, i.e. a full diagonalization of an effective Hamiltonian in a chosen model space, is the most preferable method for calculations of these rates. However, performing a shell-model calculation for heavy nuclei is itself a long-standing problem in nuclear physics. This is particularly true for deformed mass regions where the conventional shell-model method cannot be applied. The Projected Shell Model (PSM) treats the problem in a different way. The PSM starts with a deformed single-particle basis instead of the spherical one. The many-body configurations are constructed by superimposing the angular-momentum-projected multi-quasiparticle states, and nuclear wave functions are obtained by digonalizing the two-body interactions in these projected states. Thus, it follows exactly the shell model philosophy and is a multi-major-shell shell model defined in the deformed basis. A method for calculation of Gamow-Teller transition rates is developed in the framework of the PSM. 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. A preliminary 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. Possible applications of this method are discussed.