Self-Consistent Shell-Model Calculations

Abstract

In the preceding chapters we have discussed the necessary methods to study the nuclear structure of nuclei throughout the nuclear mass table, excluding strongly deformed nuclei (Bohr, Mottelson 1975) which are outside the scope of the present presentation. We have discussed the short-range (pairing) properties of atomic nuclei as illustrated most nicely near closed-shell nuclei. We have applied the concept of pairing to nuclei with many valence nucleons outside a single-closed shell nucleus, or even to nuclei with a number of valence protons and neutrons outside doubly-closed shell nuclei (Chap. 7). Also, at closed shells, particle-hole excitations show up as elementary modes of excitation and have been studied in a TDA and RPA approximation (Chap. 6). In the study of the latter chapter, extensive use was made of the methods of second quantization, developed in Chap. 5. In most applications, we started from an average field that was determined in a phenomenological way [harmonic oscillator one-body potential (Chap. 3)] and a residual nucleon-nucleon interaction was used (effective matrix elements, schematic interaction or realistic interaction) which was not self-consistently determined with the one-body potential.