Spurious solutions in few-body equations. II. Numerical investigations

Abstract

A recent analytic study of spurious solutions in few-body equations by Adhikari and Gl\"ockle is here complemented by numerical investigations. As proposed by Adhikari and Gl\"ockle we study numerically the spurious solutions in the three-body Weinberg type equations and draw some general conclusions about the existence of spurious solutions in three-body equations with the Weinberg kernel and in other few-body formulations. In particular we conclude that for most of the potentials we encounter in problems of nuclear physics the three-body Weinberg type equation will not have a spurious solution which may interfere with the bound state or scattering calculation. Hence if proven convenient the three-body Weinberg type equation can be used in practical calculations. The same conclusion is true for the three-body channel coupling array scheme of Kouri, Levin, and Tobocman. In the case of the set of six coupled four-body equations proposed by Rosenberg et al. and the set of the Bencze-Redish-Sloan equations a careful study of the possible spurious solutions is needed before using these equations in practical calculations.NUCLEAR REACTIONS Scattering theory, numerical investigations of spurious solutions, Weinberg type equations, formulations of Kouri, Levin and Tobocman; and of Bencze, Redish and Sloan.