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

We revisit a sudden increase of the isotope shift of the charge radius of Pb isotope at $N>126$ based on a Skyrme Hartree-Fock-Bogoliubov theory. New parametrizations of the pairing interaction optimized for selected four Skyrme interactions greatly improve a description of this phenomenon. The density-dependent spin-orbit interaction is also investigated and further increases the charge radius. The pairing correlations significantly change the properties of the neutron orbits near the Fermi level and play a vital role in pulling 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 is proposed: The pairing interaction reduces the radius of "valence" neutron orbits 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 the sudden enhancement of the charge radius at $N > 126$. This characteristic behavior appears in the density profile near the nuclear surface and its measurement is highly desirable.