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 its eigenfunctions defined in the Fock-Bargmann space and forming a complete set of orthonormalized states (classified with the use of the SU(3) symmetry indices) satisfying the Pauli exclusion principle. This interpretation has allowed us 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.