Energy dependence of nucleon-nucleus scattering

A model-insensitive data-to-data formula based on an analytic expression for the scattering of a Dirac particle from a nucleus is derived for the energy dependence of the scattering. Using this formula, the Dirac impulse approximation is found to account for the energy dependence of proton scattering from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ in the 500-800 MeV regime. The energy dependence cannot, however, be accounted for to energies below 200 MeV. The method introduced in the analysis is applicable to a wide variety of scattering problems.