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 ¹⁴⁰Ce, ¹³⁹Ce, ¹⁴¹Ce, ¹⁴²Ce, and ⁴⁰Ca, ⁴⁴Ca from 6–60 MeV and have made comparisons with experimental data. Except for ¹⁴²Ce, reasonable agreement with the mass 140 data was achieved with proton densities ρ_p of the nuclei determined by μ^- data and neutron densities determined by the relationship ρ_n=(N/Z)ρ_p which implies Δr_np =〈r_n²〉^1/2 -〈r_p²〉^1/2=0. Satisfactory agreement with the ¹⁴²Ce data was obtained by choosing a ρ_n for ¹⁴²Ce with Δr_np=0.05 fm and by a 10% increase in the strength of the ¹⁴²Ce imaginary potential. Similar choices of Δr_np and imaginary potential strength were made for ⁴⁴Ca in trying to fit the ⁴⁴Ca 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.