Optical potentials derived from microscopic separable interactions including binding and recoil effects

We first consider a projectile scattering from a nucleon bound in a fixed potential. A separable Galilean invariant projectile-nucleon interaction is adopted. Without using the fixed scatterer approximation or using closure on the intermediate target nucleon states we obtain various forms for the projectile-bound nucleon $t$ matrix. Effects due to intermediate target excitation and nucleon recoil are discussed. By making the further approximations of closure and fixed scatterers we make connection with the work of previous authors. By generalizing to projectile interaction with several bound nucleons and examining the appropriate multiple scattering series we identify the optical potential for projectile elastic scattering from the many-body system. Different optical potentials are obtained assuming different projectile-bound nucleon $t$ matrices and we study the differences predicted by these dissimilar optical potentials for elastic scattering. In a model problem, we study pion-nucleus elastic scattering and compare the predictions obtained by adopting procedures used by (1) Landau, Phatak, and Tabakin and (2) Piepho-Walker to the predictions obtained in a less restrictive, but computationally difficult treatment.