Target-Momentum and Nonlocal Effects in the High-Energy Optical Potential

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Abstract
A derivation of the optical potential for elastic scattering of high-energy nucleons by heavy nuclei is given under the multiple-scattering and impulse approximations. The momenta of the target nucleons and the dependence of the nucleon-nucleon scattering matrix on the sum p and difference q (momentum transfer) of final and initial relative momenta in the two-body center-of-mass system are taken into account in this derivation, and their effects are emphasized. The momenta of the target nucleons and the p dependence of the nucleon-nucleon scattering matrix, which are usually neglected in such derivations, introduce nonlocal terms in the optical potential. The contributions to this optical potential which arise from the one-pion exchange and phenomenological parts of the nucleon-nucleon scattering matrix are discussed. When the optical potential is used to describe scattering in Born approximation, the nonlocal terms have the effect of energy-dependent multiplicative operators. In particular, target-momentum effects lead to terms which, in Born approximation, can be readily interpreted as energy-dependent distortions of the optical potential in the direction of the momentum of the incident nucleon.