Applying the semirealistic $NN$ interactions that include a realistic tensor force to the Hartree-Fock calculations, we investigate tensor-force effects on the single-particle levels in Ca isotopes. The semirealistic interactions successfully describe the experimental difference between $\varepsilon \left(p1s_{1/2}\right)$ and $\varepsilon \left(p0d_{3/2}\right)$ (denoted by $\Delta {\varepsilon }_{13}$) both at ${}^{40}$Ca and ${}^{48}$Ca, confirming the importance of the tensor force. The tensor force plays a role in the $N$ dependence of $\Delta {\varepsilon }_{13}$ also in neutron-rich Ca nuclei. While the $p1s_{1/2}$–$p0d_{3/2}$ inversion is predicted in heavier Ca nuclei as in ${}^{48}$Ca, it takes place only for $N\ge 46$, delayed by the tensor force. We further investigate the possibility of proton bubble structure in Ar, which is suggested by the $p1s_{1/2}$–$p0d_{3/2}$ inversion in ${}^{48}$Ca and more neutron rich Ca nuclei, by using spherical Hartree-Fock-Bogolyubov calculations. Even with the inversion at ${}^{48}$Ca the pair correlation prohibits prominent bubble distribution in ${}^{46}$Ar. Bubble structure in Ar is unlikely also near the neutron drip line because of either unboundness or deformation. However, ${}^{34}$Si remains a candidate for proton bubble structure, owing to the large shell gap between $p1s_{1/2}$ and $p0d_{5/2}$.

• Received 15 November 2012

DOI:https://doi.org/10.1103/PhysRevC.87.067305