Few channel models of nuclear reactions: Proton and deuteron elastic scattering expansions

In this paper, an asymmetric, antisymmetrized optical potential formalism is used to derive the low-order terms in multiple-scattering-type expansions for nonrelativistic proton-nucleus and deuteron-nucleus elastic scattering. In particular, the extended Faddeev theory of N-particle collisions is used to obtain the properly symmetrized, two-particle and three-particle contributions in these two cases, where it has been assumed that all potentials are pair interactions. The main purpose underlying the research reported herein has been to prove that standard results can be obtained from an asymmetric formalism. For the two-particle contributions, the usual t/sup A/rho-type expression is obtained, where t/sup A/ is an antisymmetrized, two-particle transition operator. At this level of approximation, the results for the (d,d) case are the same as for the usual folding model. The three-particle contributions in the nucleon-nucleus case are identical to those of Picklesimer and Thaler, thus further demonstrating that standard results are contained in the asymmetric approach. The antisymmetrized, three-particle contributions to the (d,d) optical potential do not seem to have been previously derived; they are the obvious analog of the nucleon-nucleus results, and are physically reasonable in form. However, at this level of approximation, the (d,d) description is no longer found to be that of a folding model