U(3) symmetry of the Sp(3, R) model

Abstract

The functionally independent U(3) scalars in the enveloping algebra of Sp(3, R) are given in terms of a generating function. The U(3) branching rules for the Sp(3, R) Verma modules are determined by another generating function. The U(3) scalar part of the nuclear symplectic collective model Hamiltonian is written explicitly in terms of a U(3) integrity basis. This scalar component of the Hamiltonian determines the average energy or centroid for each irreducible U(3) representation within an infinite-dimensional irreducible representation of the symplectic Lie algebra. The amplitude of the ground-state wave function for each U(3) representation space is expected to be a monotonically decreasing function of the centroid energy. A finite-dimensional truncation scheme for the nuclear shell-model excludes U(3) representation spaces with large centroid energies.