Shell model for heavy nuclei and its application in nuclear astrophysics

Performing shell model calculations for heavy nuclei is a long-standing problem in nuclear physics. The shell model truncation in the configuration space is an unavoidable step. The Projected Shell Model (PSM) truncates the space under the guidance of the deformed mean-field solutions. This implies that the PSM uses a novel and efficient way to bridge the two conventional methods: the deformed mean-field approximations, which are widely applied to heavy nuclei but able to describe the physics only in the intrinsic frame, and the spherical shell model diagonalization method, which is most fundamental but feasible only for small systems. We discuss the basic philosophy in construction of the PSM (or generally PSM-like) approach. Several examples from the PSM calculations are presented. Astrophysical applications are emphasized.