Theory of non-relativistic three-particle scattering

Abstract

A new method, using asymptotically stationary states, is developed to calculate the S-matrix for the scattering of a non-relativistic particle by the bound state of two other particles. For the scattering with breakup of this bound state, we obtain a simplified form of the Faddeev integral equations.

It is then shown that all scattering processes without breakup of the bound state can be simply connected to the process where possible excitation or deexcitation of the bound state but no particle exchange occurs. The scattering amplitude for these processes satisfies a two-particle Lippmann-Schwinger equation with a compact kernel. It is in a form where all quantities have a clear physical meaning, so that it is well suited as a starting point for the application of approximation methods.