Monte Carlo shell model for atomic nuclei

The development, present status and future perspectives of the Monte Carlo shell model axe discussed. The development and limitation of the convention al shell model calculations axe shown, and stochastic approaches axe introd uced. As one of such approaches, the Quantum Monte Carlo Diagonalization (Q MCD) method has been proposed. The formulation of the QMCD method is presen ted 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 fo r a wide, probably basically unlimited, variety of nuclei. The MCSM has two major characteristic features: the feasibility of including many single-pa rticle orbits and the capability of handling many valence nucleons. We pres ent some applications for which these features played essential roles. Such applications include the structure of exotic nuclei around the neutron num ber 20, a unified description of spherical to superdeformed states in nucle i around Ni-56, a new effective interaction for pf-shell nuclei and their u nified description, and microscopic studies on the spherical-deformed shape phase transition and on the gamma -unstable deformation.