Comparison of multiple scattering approximations in a three body problem

Abstract

An analysis of the nonrelativistic quantum mechanical problem of three particles of equal mass interacting via attractive delta function potentials in one dimension is carried out. Following the methods of McGuire and Dodd with two body potentials of equal strength, exact matrix elements for the process of elastic and rearrangement scattering are rederived and some mistakes occurring in their papers have been corrected. Then expressions are obtained for transition matrix elements for these processes in the first order using Newton, Born, Newton–Faddeev, and Lovelace–Faddeev formulation. Numerical results obtained are compared with the exact results. It is found that above breakup threshold the Newton–Faddeev scheme gives better results in comparison to other schemes for elastic as well as rearrangement scattering. Thus, this paper provides us with a comparative analysis of several multiple scattering expansions available in the literature.