Collective bands in the shell-model and some thoughts on the interacting boson model

Abstract

The observation of a rotational band implies the existence of a deformation and the large measured quadrupole moments in rotational nuclei show that a substantial fraction of all nucleons contribute to the deformation. Nevertheless rotational features can emerge in a shell-model when the valence nucleons take advantage of their degeneracy to move collectively. In the first part of this article ~e consider rotations which develop in this way in light nuclei. Of course a deformed arrangement of the valence nucleons will tend to polarise the core and to produce a deformed single-particle field in place of the spherical shell-model field. This would be the starting point of the conventional collective model but, with a deformed field, there are additional variables describing the deformation and orientation of the field and they are needed to produce states with good angular momentum using some device such as projection or cranking. The difficulties associated with these collective variables are absent in the shell-model approach but the computation in a shell-model calculation becomes prohibitive except for light nuclei. To some extent, the neglect of deformation of the closed shell core can be corrected by allowing effective charges for the valence nucleons It is particularly instructive to look at the way in which rotations emerge from the shell model because of the current interest in the interacting boson model. In this model also rotations emerge from the coupling of particles (bosons rather than nucleons) without the explicit use of collective variables and the same mathematical techniques have been used.