Shell-model method for Gamow-Teller transitions in heavy deformed odd-mass nuclei

Abstract

A shell-model method for calculating Gamow-Teller (GT) transition rates in heavy deformed odd-mass nuclei is presented. The method is developed within the framework of the projected shell model. To implement the computation requirement when many multi-quasiparticle configurations are included in the basis, a numerical advancement based on the Pfaffian formula is introduced. With this new many-body technique, it becomes feasible to perform state-by-state calculations for the GT nuclear matrix elements of $\ensuremath{\beta}$-decay and electron-capture processes, including those at high excitation energies in heavy nuclei which are usually deformed. The first results, ${\ensuremath{\beta}}^{\ensuremath{-}}$ decays of the well-deformed $A=153$ neutron-rich nuclei, are shown as the example. The known $log(ft)$ data corresponding to the $B({\mathrm{GT}}^{\ensuremath{-}}$) decay rates of the ground state of $^{153}\mathrm{Nd}$ to the low-lying states of $^{153}\mathrm{Pm}$ are well described. It is further shown that the $B$(GT) distributions can have a strong dependence on the detailed microscopic structure of relevant states of both the parent and daughter nuclei.