Relationship of Quadrupole–Quadrupole Interactions to SU(3) Invariance and Rotational Bands for a Four-Nucleon System

Abstract

The nature of the quadrupole–quadrupole interaction in a simple harmonic oscillation model is analyzed in some detail, with particular reference to group symmetries, SU(3) invariance, and the existence of rotational or quasi-rotational bands. Basis states having good space symmetry and SU(3) and R(3) quantum numbers are constructed using the methods of Moshinsky and collaborators. The multi-shell calculations are limited for reasons of tractability to the 4-nucleon system. The results show that the SU(3) model is highly idealized and that the appearance of SU(3) symmetry and rotational bands is strongly influenced by major shell mixing, changes in the radial dependence of the force, and even to some extent by inclusion of self-energy terms in the quadrupole–quadrupole interaction.