CLUSTER EXPANSIONS OF THE 3-BODY PROBLEM

This paper derives cluster expansions for the three-body scattering problem. We determine, by computation, the utility of the exact and approximate descriptions that emerge from the cluster approach. In general, cluster expansions can give simple approximate solutions to the scattering process that are accurate whenever clusters dominate the underlying physical states of the system. The approach to the problem taken here is to employ the Karlsson-Zeiger integral equations to provide a theoretical framework that is natural for a cluster expansion. Eventually one can restate the scattering problem in terms of effective intercluster potentials. We construct integral equations whose solutions are the effective potentials. The cluster expansion for this problem leads to successively more exact effective potentials. For systems composed of either three bosons or fermions and interacting through separable potentials we compare exact three-body solutions in the bound state and elastic scattering sectors with those obtained by the cluster-expansion techniques. NUCLEAR REACTIONS Three-body problem. Cluster representations. Approximation schemes. © 1979 The American Physical Society.