  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.

Nuclear Theory