Tensor interaction contributions to single-particle energies

We calculate the contribution of the nucleon-nucleon tensor interaction to single-particle energies with finite-range $ G $ matrix potentials and with zero-range Skyrme potentials. The Skx Skyrme parameters including the zero-range tensor terms with strengths calibrated to the finite-range results are refitted to nuclear properties. The fit allows the zero-range proton-neutron tensor interaction as calibrated to the finite-range potential results and that gives the observed change in the single-particle gap $\epsilon$(h$_{11/2}$)-$\epsilon$(g$_{7/2}$) going from $^{114}$Sn to $^{132}$Sn. However, the experimental $\ell$ dependence of the spin-orbit splittings in $^{132}$Sn and $^{208}$Pb is not well described when the tensor is added, due to a change in the radial dependence of the total spin-orbit potential. The gap shift and a good fit to the $\ell$-dependence can be recovered when the like-particle tensor interaction is opposite in sign to that required for the $ G $ matrix.