Nonresonant approximations to the optical potential

A new class of approximations to the optical potential, which includes those of the multiple-scattering variety, is investigated. These approximations are constructed so that the optical potential maintains the correct unitarity properties along with a proper treatment of nucleon identity. The special case of nucleon-nucleus scattering with complete inclusion of Pauli effects is studied in detail. The treatment is such that the optical potential receives contributions only from subsystems embedded in their own physically correct antisymmetrized subspaces. It is found that a systematic development of even the lowest-order approximations requires the use of the off-shell extension due to Alt, Grassberger, and Sandhas along with a consistent set of dynamical equations for the optical potential. In nucleon-nucleus scattering a lowest-order optical potential is obtained as part of a systematic, exact, inclusive connectivity expansion which is expected to be useful at moderately high energies. This lowest-order potential consists of an energy-shifted ($t\rho$)-like term with three-body kinematics plus a heavy-particle exchange or pickup term. The natural appearance of the exchange term additively in the optical potential clarifies the role of the elastic distortion in connection with the treatment of these processes. The relationship of the relevant aspects of the present analysis of the optical potential to conventional multiple scattering methods is discussed.