Rigorous Solution of Three-Body Scattering Processes in the Distorted-Wave Formalism

Abstract

General methods are developed for obtaining convergent solutions to the exact nonrelativistic three-body scattering amplitudes within the framework of the distorted-wave representation. A simplification of the Faddeev-Lovelace coupled integral equations is obtained when the mass of one particle is either much larger or much smaller than the other two. When this mass restriction applies, it is shown that each amplitude is determined by a single, tractable integral equation. The kernel of a typical equation is well-behaved and depends only on calculable, two-body operators. The inhomogeneous term consists of two parts, one of which is the usual distorted-wave Born term and the other, a term involving excitation of a set of two-body intermediate states. Applications are made to a variety of nuclear scattering processes, and the implications for the distorted-wave Born model discussed.