Optical-model analysis of $p+{}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ elastic scattering from 15 - 1000 MeV

Measurements have been made of the differential cross sections for $p+{}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ elastic scattering at mean proton energies of 21.0, 24.1, 26.3, 30.5, 35.0, 45.0, and 47.3 MeV. Measurements have also been made of the differential cross sections and polarizations at 185 MeV. These data together with the data in the energy range 15-1000 MeV available in the literature have been analyzed in terms of a standard 11-parameter optical model. Relativistic corrections to the optical-model analysis were introduced. The energy dependence of the real central potential (as indicated by the volume integral per nucleon and by the strength parameter) can be represented by a linear relation if a limited energy range is chosen. This linear energy relation cannot be extrapolated to higher energies since it makes the real central potential repulsive at too low an energy as indicated by the results of optical-model analyses of proton scattering data above 200 MeV. A logarithmic energy dependence gives a reasonable presentation of the volume integral per nucleon of the real central potential for energies up to 1 GeV.

NUCLEAR SCATTERING ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}\mathrm{}(p,p)\mathrm{}$, $T=21.0, 24.1, 26.3, 30.5, 35.0, 45.0, \mathrm{and} 47.3$ MeV, measured $\sigma \left(\theta \right)$, $\theta =15\mathrm{}-167.5°$; $T=185\mathrm{}$ MeV measured $\sigma \left(\theta \right)$, $P\left(\theta \right)$, $\theta =4\mathrm{}-38°$; optical-model analysis, previous data $\sigma \left(\theta \right)$, $P\left(\theta \right)$, ${\sigma }^R$ included.