  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 angular-momentum-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 beta-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.
