Effects of three-nucleon spin-orbit interaction on isotope shifts of Pb nuclei

Abstract

We investigate the effects of the $3N$ interaction, which effectively adds a density-dependent term to the LS channel, on the isotopes shifts of the Pb nuclei. With the strength so as to keep the $\ensuremath{\ell}s$ splitting of the single-nucleon orbits, the density dependence in the LS channel tends to shrink the wave functions of the $j=\ensuremath{\ell}+1/2$ orbits while making the $j=\ensuremath{\ell}\ensuremath{-}1/2$ functions distribute more broadly. Thereby the kink in the isotope shifts of the Pb nuclei at $N=126$ becomes stronger, owing to the attraction from neutrons occupying $0{i}_{11/2}$ in $N>126$. The density dependence in the LS channel enables us to reproduce the data of the isotope shifts by the Hartree-Fock-Bogoliubov calculations in a long chain of neutron numbers, even without degeneracy between the $n1{g}_{9/2}$ and $n0{i}_{11/2}$ levels. We exemplify it by the semirealistic M3Y-P6 interaction.