Proton Elastic Scattering Measurements at 16 MeV with Optical-Model Analysis

Differential cross-section measurements are presented for the elastic scattering of 16-MeV protons from ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. In general the angular range 15-160° was covered with a relative uncertainty in the cross sections of ±1%. The data are analyzed using an optical model in three ways: (1) by fitting individual data sets for each element with a nine-parameter model; (2) by fitting all the data simultaneously with a "global" search routine; and (3) by fitting individual data sets with the folding version of Greenlees, Pyle, and Tang. The lack of constraints on the spin-orbit parameters due to the absence of polarization data is overcome to some extent by procedure (2). The ambiguities associated with the spin-orbit term are investigated in some detail. The results confirm trends with mass number found at higher energies, and suggest that effects not included in the usual forms of the model are present in the interaction.