Generalized Separable Potential Theory and Bateman's Method on the Scattering Problem

Abstract

By an expansion technique based on a model, the formalism of one-rank separable term plus non-separable term for the 2-body partial wave amplitude by Kowalski and Noyes is extended to the formalism of N-rank separable terms plus a non-separable term. By using our model, ordinary Bateman's method for the integral equation is extended to treatment of the scattering problems having singular kernels. For the problem of the unphysical pole singularity of the Kowalski and Noyes theory, it is found that the singularity also appears in the ordinary Bateman's form. From our method, however, in the energy plane, the unphysical pole changes its position and finally disappears in accordance with the increase in the rank number N with the appropriate choice of N-parameters. Consequently, it is expected that our method is useful to be applied to the few-body problems with the 2-body local and/or realistic potentials.