Tensor effects on the proton sd states in neutron-rich Ca isotopes and bubble structure of exotic nuclei

In the framework of the Hartree-Fock-Bogoliubov (HFB) approach with Skyrme interactions SLy5+T, SLy5+T-omega and several sets of the TIJ parametrizations, the evolution of the proton single-particle energy difference between the 2s(1/2) and 1d(3/2) orbits in Ca isotopes is investigated for the cases with and without the tensor force. It is shown that the energy difference evolution trends by using different Skyrme interactions without the tensor force are similar to each other. However, the energy differences are obviously influenced by the tensor force. Meanwhile, it is found that the inversion between the two orbits (2s(1/2)-1d(3/2) inversion) induced by the tensor force occurs around Ca-48 (by SLy5+T-omega) as well as in the nuclei very far from the stability. We understand the inversion phenomenon by analyzing the tensor contributions to the spin-orbit potentials and the radial wave functions of the two orbits. Finally, the proton density distributions of Ar-46 and Hg-206 are calculated by using several sets of Skyrme interactions with and without the tensor component. It is found that the parametrization SLy5+T-omega favors the bubble structure of Ar-46 resulting from the 2s(1/2)-1d(3/2) inversion. However, for Hg-206 any tensor parametrizations do not favor its bubble structure.