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We revisit a sudden increase of the isotope shift of the charge radius of Pbisotope at $N>126$ based on a Skyrme Hartree-Fock-Bogoliubov theory. Newparametrizations of the pairing interaction optimized for selected four Skyrmeinteractions greatly improve a description of this phenomenon. Thedensity-dependent spin-orbit interaction is also investigated and furtherincreases the charge radius. The pairing correlations significantly change theproperties of the neutron orbits near the Fermi level and play a vital role inpulling out the well-bound protons in the Pb isotopes at $N>126$. Regarding$^{208}$Pb as a "core" nucleus, a novel pairing core swelling effect isproposed: The pairing interaction reduces the radius of "valence" neutronorbits by the shrinkage of diffused $1g_{9/2}$ orbit and the mixing of sharp$0i_{11/2}$ orbit. Simultaneously, the core nucleus swells, leading to thesudden enhancement of the charge radius at $N > 126$. This characteristicbehavior appears in the density profile near the nuclear surface and itsmeasurement is highly desirable.

Pairing core swelling effect in Pb isotopes at $N>126$