Tensor force effect on single-proton energy levels of oxygen isotopes

In the framework of the Hartree-Fock approach the proton spin-orbital splittings of the 1p orbits and the shell gaps in the oxygen isotopes are investigated with the interactions SLy5+T,SLy5+Tw, SGII+Te1, SGII+Te2, SGII+Te3 and many sets of the TIJ interactions. All of the interactions are the Skyrme interactions and contain a tensor component (tensor force). It is shown that the evolution of the single-proton levels for the oxygen isotopes is sensitive to a parameter β _T which is associated with the tensor force strength of the Skyrme interactions. To understand this phenomenon, we systematically analyze the dependence of the spin-orbit splittings and shell gaps on the parameter β _T in terms of the spin-orbit potential and the corresponding wave function. We find that the Skyrme interactions can be classified into two groups: (a) T21, T32, T43, T54, SLy5+T, SLy5+Tw, SGII+Te1 and SGII+Te2, which can roughly reproduce the experimental shell gaps of the oxygen isotopes; (b) T1J and SGII+Te3, which can not reproduce the experimental shell gaps.