Symplectic and cluster excitations in nuclei: : Evaluation of interaction matrix elements

Abstract

A practical method is given for the evaluation of the matrix elements of a general two-body interaction in a mixed Sp(6, R) [superset or implies] U(3)-microscopic cluster model basis. A reduction formula expresses a matrix element connecting states of excitation and in the same or in different symplectic bands in terms of matrix elements of unit SU(3) tensor operators between Sp(6, R) bandhead states. It also reduces the matrix element between a state of excitation in a Sp(6, R) band and a general binary cluster model state to a simpler matrix element of pure cluster model type, so that all matrix elements have been reduced to pure shell or cluster model form. As a test of the new methods of calculation a comparison is made between the pure [alpha]-cluster model, the pure symplectic model and a calculation using a mixed [alpha]-cluster-symplectic basis for a very simple system, the 8Be nucleus.