Spin-orbit and tensor mean-field effects on spin-orbit splitting including self-consistent core polarizations

A new strategy of fitting the coupling constants of the nuclear energy density functional is proposed, which shifts attention from ground-state bulk to single-particle properties. The latter are analyzed in terms of the bare single-particle energies and mass, shape, and spin core-polarization effects. Fit of the isoscalar spin-orbit and both isoscalar and isovector tensor coupling constants directly to the $f_{5/2}\text{−}{f}_{7/2}$ spin-orbit splittings in ${}^{40}\mathrm{Ca}$, ${}^{56}\mathrm{Ni}$, and ${}^{48}\mathrm{Ca}$ is proposed as a practical realization of this new program. It is shown that this fit requires drastic changes in the isoscalar spin-orbit strength and the tensor coupling constants as compared to the commonly accepted values, but it considerably and systematically improves basic single-particle properties including spin-orbit splittings and magic-gap energies. Impact of these changes on nuclear binding energies is also discussed.