  It was pointed out [Phys. Rev. C \textbf{91}, 021302(R)] that the isotope
shifts of the Pb nuclei, the kink at $N=126$ in particular, can be well
described by the 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 semi-realistic M3Y-P6
interaction and its LS modified variant M3Y-P6a, as in the Pb case. It is found
that almost equal charge radii between $^{40}$Ca and $^{48}$Ca 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.
