Further evidence for three-nucleon spin-orbit interaction in isotope shifts of nuclei with magic proton numbers

It was pointed out [Phys. Rev. C 91, 021302(R) (2015)] that the isotope shifts of the Pb nuclei, the kink at N = 126 in particular, can be well described by Hartree-Fock-Bogolyubov calculations if a density-dependent LS interaction derived from the 3N interaction is incorporated. Effects of the density dependence in the LS channel on the isotope shifts are extensively investigated for the Ca, Ni, and Sn isotopes, using the semirealistic M3Y-P6 interaction and its LS modified variant M3Y-P6a, as in the Pb case. It is found that almost equal charge radii between Ca-40 and Ca-48 are reproduced, as well as the isotope shifts in a long chain of the Sn nuclei, owing to the density dependence in the LS channel. A kink is predicted at N = 82 for the isotope shifts of the Sn nuclei, in clear contrast to the interactions without the density dependence.