Monte Carlo shell model for atomic nuclei

Abstract

The development, present status and future perspectives of the Monte Carlo shell model are discussed. The development and limitation of the conventional shell model calculations are shown, and stochastic approaches are introduced. As one of such approaches, the Quantum Monte Carlo Diagonalization (QMCD) method has been proposed. The formulation of the QMCD method is presented with an illustrative example. While the QMCD method is a general method for solving the quantum many-body interacting systems, its application to the nuclear shell model is referred to as the Monte Carlo Shell Model (MCSM). A test of the MCSM is presented, confirming the feasibility of the MCSM. The MCSM represents a breakthrough in shell model calculations: the level structure of low-lying states can be studied with realistic interactions for a wide, probably basically unlimited, variety of nuclei. The MCSM has two major characteristic features: the feasibility of including many single-particle orbits and the capability of handling many valence nucleons. We present some applications for which these features played essential roles. Such applications include the structure of exotic nuclei around the neutron number 20, a unified description of spherical to superdeformed states in nuclei around 56Ni, a new effective interaction for pf-shell nuclei and their unified description, and microscopic studies on the spherical-deformed shape phase transition and on the γ-unstable deformation.