The kinks in charge radii across $N$ = 82 and 126 revisited

We revisit the studies of the isotopic shift in the charge radii of {\it even-even} isotopes of Sn and Pb nuclei at $N$ = 82, and 126, respectively, within the relativistic mean-field and Relativistic-Hartree-Bogoliubov approach. The shell model is also used to estimate isotopic shift in these nuclei, for the first time, to the best of our knowledge. The ground state single-particle energies ($spe$) are calculated for non-linear NL3 \& NL3$^*$ and density-dependent DD-ME2 parameter sets compared with the experimental data, wherever available. We establish a correlation between the filling of single-particle levels and the isotopic shift in occupation probabilities. The obtained $spe$ from the relativistic mean-field and Relativistic-Hartree-Bogoliubov approaches are in line with those used in the shell model and experimental data for both the Sn and Pb isotopic chains. The shell model calculated isotopic shift agrees with relativistic mean-field and Relativistic-Hartree-Bogoliubov approaches that explain the experimental data quite well.