Comparison of Dirac and Schrödinger descriptions of spin observables for proton-nucleus elastic scattering at 650 and 800 MeV

We compute the analyzing power, ${\mathit{A}}_{\mathit{y}}$, and spin rotation, Q, for proton elastic scattering at 650 and 800 meV from target nuclei ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, using both nonrelativistic multiple-scattering theory and a relativistic impulse approximation model. We show that the nonrelativistic theory, based on the Schrödinger equation with relativistic kinematics, and the relativistic model, based on the Dirac equation, provide very similar and equally good descriptions of these spin observables when electromagnetic spin-orbit contributions are included in both approaches. The nonrelativistic model calculations include contributions from nuclear medium effects (Pauli blocking and binding energy corrections) and also target nucleon two-body correlations. Medium effects and correlations are not expected to be significant in the relativistic model based on the Dirac equation, and were not included.