Generalized impulse approximation for relativistic proton scattering

A complete set of Lorentz invariant nucleon-nucleon amplitudes, based on a meson-exchange model and on-mass-shell kinematics, is used to construct the impulse approximation optical potential for use in the Dirac equation. Relativistic nuclear densities are also used in the construction. No free parameters enter. The analysis provides a dynamical basis for the virtual pair couplings which are implicit in the Dirac equation for proton-nucleus scattering. A momentum space potential and a localized potential suitable for coordinate space analysis are developed. Initial numerical calculations are presented for proton scattering by ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ at 200, 500, and 800 MeV. The generalized impulse approximation provides a successful description of the elastic scattering data for these cases. Low energy results are improved substantially in comparison with the original form of Dirac impulse approximation based on using five Fermi amplitudes to represent nucleon-nucleon scattering.