A fully algebraic solution for multichannel scattering of neutrons from nuclei

In this report I give the prescription by which an algebraic solution can be found for multichannel scattering of neutrons from nuclei. The theory, developed by the Padova group, is built upon the work of Rawitscher and Delic. The approach is predicated upon finite rank representations of realistic interaction potentials and the properties of scattering matrices for separable Schrodinger interactions. The Padova approach starts with a solvable auxiliary Sturmian function (Weinberg state) problem from which a first generation set of Sturmians are defined. That basis set is formed by choosing a solvable problem at a fixed negative energy, and thereby those Sturmians can be specified in closed analytic form. Second generation Sturmians built upon the interaction potential matrices for a multichannel scattering problem of interest then can be found as linear combinations of the first generation set. The expansion coefficients result from a matrix diagonalization process. The scheme enables an expansion (usually truncated to finite rank for convenience) of the interaction potential in terms of those second generation Sturmians and in the form of a sum of separable interactions. The analytic properties of the scattering matrix from a separable Schroedinger potential gives the means by which a full algebraic solution of the multichannel scattering problem can be realized. (author)