Optical-Model Analysis of Proton Elastic Scattering byPb208from 8 to 14 MeV

The uniqueness and energy dependence of optical-model parameters which describe the ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}(p, p){}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ scattering reaction have been studied in the bombarding range 8 to 14 MeV. In the analysis of data with a 3% error two discretely ambiguous well depths with mean values of 35 and 55 MeV are found which yield comparably good fits. The imaginary well depth is approximately 4 MeV for both. To select one well depth, a 1% measurement was made at the energy ($E_p=7.6\mathrm{}$ MeV) at which the difference between the two computed cross sections at backward angles is maximized, a difference of approximately 3%. These measurements select the 55-MeV well depth consistent with the number of occupied states in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The spin-orbit term is undetermined in this study, since the values of the imaginary potential render the analysis insensitive to it.