Total-Reaction-Cross-Section Measurements for 30-60-MeV Protons and the Imaginary Optical Potential

Abstract

We have measured total reaction cross sections for 30-, 40-, 49.5-, and 60.8-MeV protons incident on thin, separated isotopes covering the range from $^{12}\mathrm{C}$ to $^{208}\mathrm{Pb}$. Our results are consistent with previous data at 30 MeV, but disagree with earlier data at 60 MeV. We find a strong dependence of the reaction cross section on neutron excess for a series of Fe and Ni isotopes. Little, if any, such dependence is observed for the $N=28$ isotones. The data are well represented by the relation ${\ensuremath{\sigma}}_{\mathrm{R}}=\ensuremath{\pi}{({r}_{0}{A}^{\frac{1}{3}}+\overline{\ensuremath{\lambda}})}^{2}$ with ${r}_{0}=1.23\ifmmode\pm\else\textpm\fi{}0.01$ F. When analyzed with the conventional optical model, our data require the volume absorption to increase and the surface absorption to decrease with increasing proton energy ${E}_{p}$. The analysis reveals a striking $\frac{(N\ensuremath{-}Z)}{A}$ dependence for the product ${W}_{D}{a}^{\ensuremath{'}}$. Using the Oak Ridge parameters for the real and spin-orbit potentials, we arrive at the following parametrization for the imaginary potential: volume absorption potential, ${W}_{0}=(1.2\ifmmode\pm\else\textpm\fi{}0.09{E}_{p})$ MeV; surface absorption potential, ${W}_{D}=[4.2\ensuremath{-}0.05{E}_{p}+15.5\frac{(N\ensuremath{-}Z)}{A}]$ MeV; imaginary diffusivity, ${a}^{\ensuremath{'}}=[0.74\ensuremath{-}0.008{E}_{p}+1.0\ifmmode\times\else\texttimes\fi{}\frac{(N\ensuremath{-}Z)}{A}]$ F.