Test of the coupled-equations many-body scattering formalism on a soluble three-body model

Several versions of the coupled-equations many-body scattering formalism of Baer, Kouri, Levin, and Tobocman were tested on the generalized Hulbert-Hirschfelder three-body scattering model. In this model two s-wave particles interact with an infinite mass scattering center via square well potential forces and with each other via a square well nonlocal force active only in the vicinity of the scattering center. The model exhibits elastic and inelastic scattering, knockout reactions, and knockout with excitation reactions. A convergent level expansion for the collision matrix is provided by wave function matching at the interaction boundaries. This result is compared with N-level solutions of the Baer-Kouri and Kouri-Levin versions of the coupled-equations formalism. Kouri-Levin works well for all cases tested while Baer-Kouri works well only for a particular class of cases. When the two particles are treated as indistinguishable fermions, tests may be made of the antisymmetrized forms of the coupled-equations formalism. These proved to be satisfactory. Finally the single cluster approximation to the antisymmetrized Kouri-Levin coupled-equations formalism was tested along with the resonating group method, and both were found to work very poorly for this model.[NUCLEAR REACTIONS Coupled-equations many-body formalism of Baer, Kouri, Levin, and Tobocman is tested on a soluble three-body model.]