Configuration Interaction Approach to Atomic Nuclei: The Shell Model

Abstract

The atomic nucleus comprises protons and neutrons, with complex quantum many-body structure, arising from these two kinds of constituents and also from complicated forces binding them (nuclear forces). Nevertheless, atomic nuclei exhibit simple and beautiful features, unexpected from the complexities. The gap between the complexity and the simplicity/beauty can be filled by the shell model, the nuclear physics terminology of configuration Interaction (CI) approach. This article presents basic ideas and formulations of the shell model, up to recent developments. The computational aspect is quite crucial for the shell model, because the Schrödinger equation has to be solved with the nuclear forces and the two kinds of fermions. The traditional approach based on direct diagonalization of Hamiltonian matrix has been used since the 1950s with technical improvements. Besides this approach, a different CI methodology, Monte Carlo shell model (MCSM), was proposed in the 1990s and has been developed. These methodologies are explained in a pedagogical way. Ni and Cu isotopes are discussed as examples of various appearances of low-lying deformed states coexisting with spherical ground states. The T-plot analysis is explained as a unique way to unveil nuclear shapes contained in the MCSM wave functions. The original version of the shell model was conceived by Mayer and Jensen. Recent studies show definite departures from this picture: the evolution of the shell structure, or the shell evolution, in exotic nuclei. The shell evolution is briefly sketched, with a certain emphasis on the prominent role of the tensor force. The shell evolution is extended from a single-particle-type feature to highly correlated many-body features such as the collective motion leading to surface deformation, as referred to as type II shell evolution. Thus, this article overviews the basic and contemporary facets of the nuclear shell model in simple terms.