Optical-Model Analysis of Excitation Function Data and Theoretical Reaction Cross Sections for Alpha Particles

Abstract

The complex alpha particle-nuclear potential is determined with small uncertainty at the nuclear surface by experiments with alpha particles in the range of bombarding energies up to 50 Mev in conjunction with this optical-model analysis which assumes that the shape of the complex potential is exponential at the nuclear surface. The potential is given by the expression ${V}_{\ensuremath{\alpha}}+{W}_{\ensuremath{\alpha}}=\left\{\ensuremath{-}1100\mathrm{exp}\left[\ensuremath{-}\left(\frac{r\ensuremath{-}1.17{A}^{\frac{1}{3}}}{0.574}\right)\right]\ensuremath{-}45.7i\mathrm{exp}\left[\ensuremath{-}\left(\frac{r\ensuremath{-}1.40{A}^{\frac{1}{3}}}{0.578}\right)\right]\right\} \mathrm{Mev},$ for values of $r$ (in units of ${10}^{\ensuremath{-}13}$ cm) where the real part is \ensuremath{\gtrsim}-10 Mev. The elastic scattering data has been used to determine the potential. The calculated reaction cross sections are found to be in satisfactory agreement with excitation function data.The total reaction cross section ${\ensuremath{\sigma}}_{R}$ for alpha particles in the energy range 0-50 Mev on nuclei with charge $Z=10, 20, 30, 50, 70, \mathrm{and} 90$ has been calculated using the potential ${V}_{\ensuremath{\alpha}}+i{W}_{\ensuremath{\alpha}}$ obtained from the analysis of elastic scattering data. The calculated values may be interpolated to obtain ${\ensuremath{\sigma}}_{R}$ for other values of $Z$.