Scattering of 139-MeV Alpha Particles byNi58andPb208

Abstract

The elastic and inelastic scattering of $\alpha$ particles by ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been investigated at an incident energy of 139 MeV. The elastic cross sections have been analyzed in terms of the optical model using a six-parameter Woods-Saxon potential. The data for ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ are sufficient to eliminate the discrete ambiguity in the strength of the potential; the single potential which fits the data has a well depth of 116 MeV and a volume integral $\frac{J}{4A}$ of 298 MeV ${\mathrm{fm}}^3$. For ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ the discrete ambiguity could not be resolved. This outcome is consistent with recently developed criteria for experimental data necessary to resolve the discrete ambiguity. A discussion of the discrete ambiguity, in particular the $A$ dependence, is given, and it is shown that measurements at higher energies are required to resolve the ambiguity for ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$. The inelastic cross sections for transitions to the 1.45-MeV ($J^{\pi }=2^{+}$), 2.46-MeV ($4^{+}$), 4.47-MeV ($3^{-}$) states in ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$ and the 2.62-MeV ($3^{-}$) state in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ have been analyzed with distorted-wave Born-approximation (DWBA) calculations using collective-model form factors. The results are consistent with previous analyses of lower-energy data.