Strength of reduced two-body spin-orbit interaction from chiral three-nucleon force

TL;DR

This paper estimates how chiral three-nucleon forces enhance the effective spin-orbit interaction in nuclei, addressing the longstanding discrepancy with empirical data and exploring isospin dependence.

Contribution

It introduces a method to derive a reduced two-body interaction from three-nucleon forces and evaluates its impact on spin-orbit strength using nuclear matter calculations.

Findings

Chiral three-nucleon forces significantly increase spin-orbit strength.

The spin-orbit interaction is weaker in neutron-rich environments.

Little uncertainty exists due to fixed low-energy constants.

Abstract

The contribution of a chiral three-nucleon force to the strength of an effective spin-orbit coupling is estimated. We first construct a reduced two-body interaction by folding one-nucleon degrees of freedom of the three-nucleon force in nuclear matter. The spin-orbit strength is evaluated by a Scheerbaum factor obtained by the $G$-matrix calculation in nuclear matter with the two-nucleon interaction plus the reduced two-nucleon interaction. The problem of the insufficiency of modern realistic two-nucleon interactions to account for the empirical spin-orbit strength is resolved. It is also indicated that the spin-orbit coupling is weaker in the neutron-rich environment. Because the spin-orbit component from the three-nucleon force is determined by the low-energy constants fixed in the two-nucleon sector, there is little uncertainty in the present estimation.