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

TL;DR

This study explores how three-nucleon spin-orbit interactions influence isotope shifts in lead nuclei, demonstrating improved data reproduction through density-dependent modifications in nuclear models.

Contribution

It introduces a density-dependent term in the spin-orbit channel to better explain isotope shifts without requiring level degeneracy, advancing nuclear structure modeling.

Findings

Enhanced isotope shift predictions matching experimental data.

Strengthening of the kink at N=126 due to neutron occupation effects.

Successful application of the modified interaction in Hartree-Fock-Bogolyubov calculations.

Abstract

We investigate 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 $\ell s$ splitting of the single-nucleon orbits, the density-dependence in the LS channel tends to shrink the wave functions of the $j=\ell+1/2$ orbits while makes the $j=\ell-1/2$ 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 $0i_{11/2}$ in $N>126$. The density-dependence in the LS channel enables us to reproduce the data of the isotope shifts by the Hartree-Fock-Bogolyubov calculations in a long chain of neutron numbers, even without degeneracy between the $n1g_{9/2}$ and $n0i_{11/2}$ levels. We exemplify it by the semi-realistic M3Y-P6 interaction.