Subtraction techniques in three-particle scattering

Abstract

A general description of subtraction techniques in scattering theory is given. Applications with the objective of achieving reduced integral equations with nonsingular kernels are applied to both the Faddeev and the Alt, Grassberger, and Sandhas forms of the three-particle equations with and without three-body forces. In the Faddeev case a method similar to one recently proposed by Karlsson is found which is analogous to well-known procedures in the two-particle case. This analogy is shown to be fairly weak when three-particle forces are included. In the absence of two-particle bound states phase-space type integral equations are found which permit the generation of approximate 3-to-3 amplitudes which satisfy unitarity and possess the correct representations of the double-scattering poles as well as the proper connectedness structure. A generalization of the so-called structure invariant perturbation theory to include three-body forces is established using the Alt, Grassberger, and Sandhas equations.NUCLEAR REACTIONS Scattering theory, three-particle scattering, unitary approximations.