Significance of tensor force in pseudospin symmetry

We point out that the pseudospin symmetry (PSS) of nuclei significantly depends on the proton ($Z$) and neutron numbers ($N$), sometimes giving rise to characteristic structures. By using the nonrelativistic spherical Hartree-Fock calculation with a realistic tensor force, we show that the tensor force may be deeply relevant to the $Z$ and $N$ dependence of the PSS. While the PSS has often been discussed in the context of relativistic symmetry, the tensor-force effects on the PSS sometimes look analogous to the $Z$ and $N$ dependence of the PSS in relativistic mean-field (RMF) calculations without explicit tensor force. The observed variation of the $p0{d}_{3/2}\ensuremath{-}p1{s}_{1/2}$ levels from $^{40}\mathrm{Ca}$ to $^{34}\mathrm{Si}$ is consistent with the tensor-force-driven $Z$ dependence of the PSS, but not necessarily with the RMF result. The present analysis elucidates the significance of the tensor force when discussing the PSS.