Abstract
This paper investigates the ability of a cluster expansion to construct accurate approximate solutions for the three-body problem where the pairwise interactions are nonseparable potentials. Our approach is to employ the Karlsson-Zeiger integral equation formalism and the decoupling scheme of Boll\'e and Kuzmichev to construct an effective intercluster potential for the three-body problem. This effective potential takes into account all virtual excitations of the three-body breakup channel. It is found that a simplifying approximation to the effective potential, utilizing only the first few terms of a cluster expansion, yields accurate numerical solutions in the bound state and low energy elastic scattering sectors. In this paper we give numerical results for a system composed of three bosons interacting via the $S$-wave projection of a Yukawa potential.NUCLEAR REACTIONS Three-body problem. Cluster expansion, local interactions.
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