Tensor interaction contributions to single-particle energies

Abstract

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 $\ensuremath{\epsilon}({h}_{11/2}$)-$\ensuremath{\epsilon}({g}_{7/2}$) going from $^{114}\mathrm{Sn}$ to $^{132}\mathrm{Sn}$. However, the experimental $\ensuremath{\ell}$ dependence of the spin-orbit splittings in $^{132}\mathrm{Sn}$ and $^{208}\mathrm{Pb}$ 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 $\ensuremath{\ell}$ dependence can be recovered when the like-particle tensor interaction is opposite in sign to that required for the $G$ matrix.