  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.
