Cluster expansions of the three-body problem

Journal Article · Sat Sep 01 00:00:00 EDT 1979 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.20.869· OSTI ID:6089484

Eyre, D; Osborn, T A

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.

• Research Organization: Cyclotron Laboratory, Department of Physics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
• OSTI ID: 6089484
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 20:3; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOUND STATE
CLUSTER EXPANSION
ELASTIC SCATTERING
ENERGY
EQUATIONS
FUNCTIONS
GREEN FUNCTION
HAMILTONIANS
INTEGRAL EQUATIONS
KINETIC ENERGY
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
PROPAGATOR
QUANTUM OPERATORS
SCATTERING
THREE-BODY PROBLEM