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) ⊃ U(3)-microscopic cluster model basis. A reduction formula expresses a matrix element connecting states of excitation N h ̷ ω and N′ h ̷ ω 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 N h ̷ ω 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 α-cluster model, the pure symplectic model and a calculation using a mixed α-cluster-symplectic basis for a very simple system, the 8Be nucleus.
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