The Nuclear Shell Model

Abstract

The shell-model approach played a fundamental role in our early understanding of atoms and nuclei; in nuclear physics in particular, it has provided us with our best understanding of the sd shell nuclei. To this day, it remains a fundamental approach in nuclear, atomic, and nonrelativistic quark physics, and it is considered a fundamental theoretical starting point in the derivation of most models applying to larger nuclei. As a numerical scheme, it has achieved considerable successes in both nuclear and atomic physics; however, it remains a notoriously difficult approach to implement when the number of particles and/or the number of shells or their specifying quantum numbers become large. In nuclear physics, it becomes difficult to apply for nuclei beyond the sd shell. For these nuclei we may well require a rethinking of the shell-model philosophy in which the collective subspace will be the aim of the calculations. The FDUO code, which we will describe below, is representative of this new trend in shell-model studies. It is designed to study nuclear collective behavior in a pair-truncated fermion space and yet it is implemented in a full shell-model-style algorithm. Furthermore it has already been successfully applied to medium and heavy nuclei to fit data. An added virtue for the purpose of this chapter is that the FDUO code is relatively short compared with the usual shell-model codes.