An Algebraic Approach to Multichannel Scattering by Negative-Energy Weinberg States

Abstract

The single and multichannel scattering problem for elastic and inelastic collisions between two composite particles is solved by resorting to basis sets of negative-energy Sturmian functions referring to auxiliary potentials which allow an easy solution of the Sturmian eigenvalue equation. By means of these functions the original coupling potentials are approximated with finite-rank interactions. The coupled-channel equations can be then reduced to sets of algebraic linear equations which can be solved by standard matrix-inversion techniques. For illustrative purposes, our formalism is applied to the elastic neutron-alpha scattering. The results of these preliminary calculations are encouraging and show a fast convergence of the method in the whole energy region we have considered (0÷20 MeV).