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 which gives the observed change in the single-particle gap ε(h_11/2)-ε(g_7/2) going from ¹¹⁴Sn to ¹³²Sn. However, the experimental ℓ dependence of the spin-orbit splittings in ¹³²Sn and ²⁰⁸Pb is not well described when the tensor is added, owing to a change in the radial dependence of the total spin-orbit potential. The gap shift and a good fit to the ℓ dependence can be recovered when the like-particle tensor interaction is opposite in sign to that required for the G matrix.