Microscopic theory of the nuclear collective model

Abstract

This articles reviews the development of a microscopic theory of nuclear collective structure as a submodel of the nuclear-shell model. It starts by showing how the so-called geometrical (Bohr-Mottelson-Frankfurt) collective model must be augmented by the addition of vortex spin degrees of freedom to make it compatible with the shell model. A unified symplectic model emerges that can be applied both with phenomenological and microscopic interactions. Examples are given of both kinds of calculation. It is shown how the full shell model space can be expressed in an Sp(3R) contains/implies U(3) basis in which form it naturally factors into collective and intrinsic subspaces. In this way, the collective content of a shell model state becomes immediately apparent. Thus a shell model interpretation is given of collective states, including the low-lying rotational bands, the so-called beta and gamma vibrations and the giant monopole and quadrupole resonances.