Elastic Scattering of 61.4-MeV Protons

Abstract

Proton elastic scattering angular distributions were measured for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ with a 61.4-MeV beam from the Oak Ridge isochronous cyclotron. An optical-model analysis of the data was performed. The results show a nuclear symmetry dependence of the optical-model potential; this dependence can be related to either the real well depth or the radius parameter of the real well. This study, combined with previously reported studies at lower bombarding energies, shows that for targets of $A\ge 27$ a potential with fixed-geometry parameters and an energy-dependent real well depth, $-\left(\frac{V-0.4Z}{A^{\frac{1}{3}}}\right)\approx \frac{\mathrm{}[49.9-0.215E+26.0(N-Z)\mathrm{}}{A}] \mathrm{MeV},$ will predict angular distributions in reasonable agreement with experiment for bombarding energies of 30-61 MeV. Data from light targets show a preference for large volume absorption and small surface absorption terms in the potential, while heavy-target data show a preference for small volume absorption and large surface absorption terms. The mean free path for a reaction of a 61-MeV proton in nuclear matter is estimated to be about 7½ F.