Structure-Invariant Perturbation Theory in Three-Particle Scattering

A perturbation theory for three-particle scattering is formulated which in each order of approximation leaves invariant the essential structural features of the scattering amplitudes. The correct primary and secondary singularity structure is reproduced along with unitarity (both off shell and on shell), the correct threshold behaviors, and the correct residues of the double-scattering poles in the 3-to-3 amplitude. The only integral equations to be solved are of the sort which appear in the case of finite-rank two-particle interactions. The formalism, which is related to some recent work by Noyes, depends crucially on the proof of the existence of a decomposition of the two-particle transition operators into so-called essential and residual parts. The special case when the residual part is ignored provides a practical exploitation of the separable expansions found by Fuda and Osborn.