Collective nuclear potential within the microscopic Sp(6,R) model

Abstract

An algorithm for projecting a microscopic nuclear Hamiltonian with a central interaction onto the enveloping algebra of the Sp(6,R) group is presented in parallel with the development of a practical procedure for constructing the corresponding part of the Sp(6,R)⊇SO(3) integrity basis. The latter is shown to consist of the invariants of the monopole–quadrupole tensor and its polynomial analogs, coupling the collective and vortex spin degrees of freedom. The algorithm uses vector coherent-state techniques and is displayed on the basis of a generic Sp(6,R) irreducible representation. The collective Hamiltonian is also shown to be expandable in terms of the enveloping algebra of the (A−1)-dimensional rotational group, where A is the total number of nucleons.