Pairing core swelling effect in Pb isotopes at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>N</mml:mi><mml:mo>></mml:mo><mml:mn>126</mml:mn></mml:mrow></mml:math>
W. Horiuchi, T. Inakura
Abstract
We revisit a sudden increase of the isotope shift of the charge radius of Pb isotopes at $N>126$ based on a Skyrme Hartree-Fock-Bogoliubov theory. New parametrizations of the pairing interaction optimized for four selected 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 $^{208}\mathrm{Pb}$ 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 the diffused $1{g}_{9/2}$ orbit and the mixing of the sharp $0{i}_{11/2}$ 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.