Nucleon-Nucleon Interactions and Polarization of High-Energy Protons Elastically Scattered from Carbon

The transition matrix element in momentum space derived by Riesenfeld and Watson has been used to calculate the polarization and the triple-scattering parameter $\beta$ of high-energy protons elastically scattered at small angles from carbon. As the nucleon-nucleon phase shifts which represent two-body interactions, those by Signell and Marshak, by Gammel and Thaler, and by Feshbach and Lomon have been considered. In evaluating nuclear as well as Coulomb scattering amplitudes, the first Born approximation has been employed with the assumption that, in carbon, the distribution of protons is equal to that of neutrons. Final results are then independent of the assumed distribution of nucleons. It has been found that, while one cannot discriminate between Signell-Marshak and Gammel-Thaler phase shifts, both of them being in semiquantitative agreement with experimental data, Feshbach-Lomon phase shifts may be ruled out because of the wrong sign of the resulting $\beta$. Since only the first-order transition matrix element in momentum space has been used in the present work, the calculation does not depend on the optical model potential in the usual sense.