Relativistic impulse approximation in an additive potential model

Based on some arguments from relativistic field theory, the individual nucleons in a nucleus at rest are assumed to act as static sources for potentials which then enter the Dirac equation describing a projectile proton additively. The two-component version of the eikonal approximation is then used to estimate the scattering amplitude both for the full model and using the relativistic impulse approximation. In both cases the lowest order corrections to simple Glauber theory are quadratic in the nuclear densities, but dependence on the nucleon-nucleon interaction differs: In the complete model the corrections depend on the range of the nucleon-nucleon interaction even in the short range approximation, while in the relativistic impulse approximation they do not. Some numerical results are presented for the elastic scattering of 800 MeV protons on ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$.