Shell Model Tests of the Interacting Boson Model Description of Nuclear Collective Motion

Abstract

The IBM assumes that collective behavior arises from the coupling, through the neutron-proton interaction, of the separate low-lying states systems of valence protons and neutrons defined with respect to a major shell closure. The eigenstates of the proton (neutron) systems are assumed to be constructed purely from combining two-particle “bosons” with L = 0 and L = 2 to form many-particle states. The model is capable of handling nuclear systems which are far beyond the domain of applicability of any reasonably complete shell-model calculation. It is the purpose of this report to present the results of a large shell-model calculation of pseudo-nucleus which displays striking collective behavior suggestive of rotational phenomena. In these calculations, a specific and physically reasonable single-particle structure is given to the wave functions, and an explicit two-body residual interaction is used. An analysis of the shell model wave functions of the eigenstates of the resulting K = 0 rotational bands offers strong support to a primary assumption of the IBM; i.e., wave functions which describe collective behavior can be constructed from many-particle states of valence nucleons which are constructed only from J=0 and J=2 two-particle states.