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

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 $N=28\mathrm{}$ isotones. The data are well represented by the relation ${\sigma }_{\mathrm{R}}=\pi {(r_0{A}^{\frac{1}{3}}+\overline{\lambda })}^2$ with $r_0=1.23\mathrm{}\pm 0.01$ 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 $\frac{\mathrm{}(N-Z)\mathrm{}}{A}$ dependence for the product $W_D{a}^{\prime }$. 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, $W_0=(1.2\mathrm{}\pm 0.09E_p)$ MeV; surface absorption potential, $W_D=[4.2-0.05\mathrm{}{E}_p+15.5\mathrm{}\frac{\mathrm{}(N-Z)\mathrm{}}{A}]$ MeV; imaginary diffusivity, $a^{\prime }=[0.74-0.008\mathrm{}{E}_p+1.0\mathrm{}\times \frac{\mathrm{}(N-Z)\mathrm{}}{A}]$ F.