Iterative solutions to the nuclear reaction problem

Abstract

An iterative technique is probably the most efficient and practical way to solve the large sets of integro-differential equations resulting from a CRC analysis of the nuclear reaction problem. In this paper we present the theoretical and practical convergence properties of a new and different type of iterative technique, namely the method of moments. In order to show the power of this method we present a comparison with three other well known iterative methods: the Sasakawa method, the Austern-Sasakawa method, and the method of successive approximation. The dependence of the practical convergence on coupling strength and angular momentum is discussed for the case of inelastic scattering. The method of moments emerges as clearly superior according to both the theoretical and practical convergence criteria. Non-local potentials are shown to introduce very little additional computational difficulty when the iterative technique is used within the framework of the plane-wave expansion method. The method of moments was the only technique capable of guaranteeing convergence when non-local interactions were involved. One merely requires a Hilbert-Schmidt kernel in a finite region of space to guarantee convergence at a rate faster than that of any geometric progression.