Proton total reaction cross sections for the doubly magic nucleiO16,Ca40, andPb208in the energy range 20-50 MeV

Proton total reaction cross sections have been measured for the doubly magic nuclei ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ in the energy range 20-50 MeV. For the $p$+ ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ system, total reaction cross sections were measured in 400 keV steps over practically the entire energy range. The $p$+ ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and $p$+ ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ total reaction cross sections were measured at six and nine different energies, respectively. The experimental total reaction cross sections are compared with results based on optical model analyses in which preliminary data from the present experiment were included. An evaluation of the imaginary potential parameters is reported. Using the proton total reaction cross section information for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ available in the literature, general characteristics of these cross sections in the energy range 10-1000 MeV are shown. A comparison has been made between the measured total reaction cross sections and those predicted by global optical model parameter sets.