Differential charge radii: self-consistency and proton-neutron interaction effects

The analysis of self-consistency and proton-neutron interaction effects in the buildup of differential charge radii has been carried out in covariant density functional theoretical calculations without pairing interaction. Two configurations of the $^{218}$Pb nucleus, generated by the occupation of the neutron $1i_{11/2}$ and $2g_{9/2}$ subshells, are compared with the ground state configuration in $^{208}$Pb. The interaction of added neutron(s) and the protons forming the $Z=82$ proton core is responsible for a major contribution to the buildup of differential charge radii. It depends on the overlaps of proton and neutron wave functions and leads to a redistribution of single-particle density of occupied proton states which in turn modifies the charge radii. Self-consistency effects affecting the shape of proton potential, total proton densities and the energies of the single-particle proton states provide only secondary contribution to differential charge radii. The buildup of differential charge radii is a combination of single-particle and collective phenomena. The former is due to proton-neutron interaction, the impact of which is state dependent, and the latter reflects the fact that all occupied proton single-particle states contribute to this process. The neglect of either one of these aspects of the process by ignoring proton-neutron interaction and self-consistency effects as it is done in macroscopic+microscopic approach or by introducing the core as in spherical shell model introduces uncontrollable errors and restricts the applicability of such approaches to the description of differential charge radii.