Microscopic optical-model calculations of neutron total cross sections and cross section differences

Using the microscopic optical model of Jeukenne, Lejeune, and Mahaux we have calculated the absolute neutron total cross sections and cross section differences of ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$, ${}_{}{}^{139}{}_{}{}^{}\mathrm{Ce}$, ${}_{}{}^{141}{}_{}{}^{}\mathrm{Ce}$, ${}_{}{}^{142}{}_{}{}^{}\mathrm{Ce}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ from 6–60 MeV and have made comparisons with experimental data. Except for ${}_{}{}^{142}{}_{}{}^{}\mathrm{Ce}$, reasonable agreement with the mass 140 data was achieved with proton densities ${\rho }_p$ of the nuclei determined by ${\mu }^{\mathrm{-}}$ data and neutron densities determined by the relationship ${\rho }_n$=(N/Z)${\rho }_p$ which implies Δ$r_{\mathrm{np}}$ =〈$r_n^2$${〉}^{1/2}$ -〈$r_p^2$${〉}^{1/2}$=0. Satisfactory agreement with the ${}_{}{}^{142}{}_{}{}^{}\mathrm{Ce}$ data was obtained by choosing a ${\rho }_n$ for ${}_{}{}^{142}{}_{}{}^{}\mathrm{Ce}$ with Δ$r_{\mathrm{np}}$=0.05 fm and by a 10% increase in the strength of the ${}_{}{}^{142}{}_{}{}^{}\mathrm{Ce}$ imaginary potential. Similar choices of Δ$r_{\mathrm{np}}$ and imaginary potential strength were made for ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ in trying to fit the ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ data. Previous phenomenological analyses carried out for this data are in qualitative agreement with our results, which imply that the addition of a few neutrons to a nucleus with a closed neutron shell yields a nucleus with a slightly thicker neutron skin and a larger neutron reaction cross section when compared to their closed shell isotopes.