ABSTRACT
Shell-model calculations escalate in complications with increasing number of particles outside the closed shell, because of the complexity of the angular-momentum algebra and the increasing dimension of the matrices. This chapter outlines how the excited states of a nucleus can be calculated in a very simple-minded shell-model picture, and compares the results with experimental observations. Formalism for generating a self-consistent potential that treats the pairing part of the two-nucleon potential on an equal footing with the other field-producing parts of the interaction has been developed; this is called the Hartree-Fock-Bogolubov (HFB) formalism. The inclusion of the multiple particle-hole state constitutes higher-order corrections to the Hartree-Fock (HF) ground state. The HF and HFB calculations were done with all 22 nucleons, using a slightly modified version of the effective interaction of J. P. Elliot et al. Density distribution, and the equilibrium density of nuclei – in particular, of closed-shell spherical nuclei, for which the calculations are simpler.
