Born Approximation in a Three-Body Scattering Problem

Abstract

A one-dimensional three-body scattering problem is constructed and solved exactly. The scattering amplitudes of the exact solution are compared with those obtained by the application of the Born approximation to the problem. The latter procedure is formulated in two distinct ways, using a symmetric or asymmetric perturbation term. The results indicate that the method using symmetric perturbation is superior to that employing asymmetric perturbation, although it is more difficult mathematically. An approximation method is developed which yields results as accurate as those obtained from the symmetric perturbation and which is on the same mathematical plane of difficulty as the asymmetric perturbation scheme. Moreover, the procedure is applicable to actual physical problems and is particularly useful for the calculation of exchange scattering.