A unified description of charge radii throughout the entire nuclide chart plays an essential role for our understanding of nuclear structure and fundamental nuclear interactions. In this work, the influence of new term, which catches the spirit of neutron- and proton-pair condensation around Fermi surface, on the charge radii has been investigated based on the Skyrme density functionals with effective forces SLy5 and ${\mathrm{SkM}}^{*}$. The differential charge radii of even-even Ca, Ni, Sn, and Pb isotopes are employed to evaluate the validity of this theoretical model. Meanwhile, the results obtained by relativistic density functional with effective Lagrangian NL3 are also shown for the quantitative comparison. Calculated results suggest that the modified model can improve the trend of changes of differential charge radii along Ca, Ni, Sn, and Pb isotopic chains, especially the shell closure effect at neutron numbers $N=28$, 82, and 126. The shell quenching phenomena of charge radii can also be predicted at neutron number $N=50$ along Ni and Sn isotopes, respectively. The inverted parabolic-like shapes between two fully filled shells can also be observed, but the amplitude is gradually weakened from Ca to Pb isotopic chains. Combining the existing literatures, it suggests that the discontinuous behavior in nuclear charge radii can be described well by considering the influence of neutron Cooper pair condensation around Fermi surface.

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• Nuclear forces
• Nuclear radii
• Nuclear structure & decays
• Nuclear density functional theory
• Shell model