Investigation of neutron density distribution of $^{208}$Pb nucleus when the proton density is constrained to its experimental distribution

Abstract

In this study, two novel improvements for the theoretical calculation of the neutron distributions are presented. First, the available experimental proton distributions are used as a constraint rather than inferred from the calculation. Second, the recently proposed distribution formula, d3pF, is used for the neutron density, which is more detailed than the usual shapes, for the first time in nuclear structure calculation. A semi-microscopic approach for binding energy calculation is considered in this study, however, the proposed improvements can be introduced to any other approach. The ground state binding energy and neutron density distribution of $^{208}$Pb nucleus are calculated by optimizing the binding energy considering three different distribution formulae. The implementation of the proposed improvements leads to a qualitative and quantitative improvement in the calculation of the binding energy and neutron density distribution. The calculated binding energy agrees with the experimental value, and the calculated neutron density shows fluctuations within the nuclear interior, which agrees with the predictions of self-consistent approaches.