Norm kernels and the closeness relation for Pauli-allowed basis functions

Abstract

The norm kernel of the generator-coordinate method is shown to be a symmetric kernel of an integral equation with eigenfunctions defined in the Fock--Bargmann space and forming a complete set of orthonormalized states (classified with the use of SU(3) symmetry indices) satisfying the Pauli exclusion principle. This interpretation allows to develop a method which, even in the presence of the SU(3) degeneracy, provides for a consistent way to introduce additional quantum numbers for the classification of the basis states. In order to set the asymptotic boundary conditions for the expansion coefficients of a wave function in the SU(3) basis, a complementary basis of functions with partial angular momenta as good quantum numbers is needed. Norm kernels of the binary systems 6He+p, 6He+n, 6He+4He, and 8He+4He are considered in detail.