Origins of spin-orbit splitting inN15

The spin-orbit splitting of the ${\mathit{p}}_{1/2}$ and ${\mathit{p}}_{3/2}$ hole states in ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ is studied with realistic nuclear forces and the variational cluster Monte Carlo method. The results show that the two-nucleon L⋅S forces give approximately half of the observed splitting, while the other half comes from pion exchange interactions between three or more nucleons. The observed splitting is fairly well reproduced by these calculations based on nonrelativistic nuclear many-body theory.