Abstract
The contribution of the chiral three-nucleon force to the strength of effective spin-orbit coupling is estimated. We construct a reduced two-body interaction by folding single-nucleon degrees of freedom of the three-nucleon force in nuclear matter. The spin-orbit strength is evaluated by the Scheerbaum factor obtained by a $G$-matrix calculation in nuclear matter with the two-nucleon interaction plus the reduced two-nucleon interaction. The inability of modern realistic two-nucleon interactions to account for the empirical spin-orbit strength is overcome. We found that spin-orbit coupling is weaker in a neutron-rich environment. Because the spin-orbit component of the three-nucleon force is determined by low-energy constants fixed in the two-nucleon sector, the present estimation has a small uncertainty.
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