Tensor-force effects on single-particle levels and proton bubble structure around the $Z$ or $N=20$ magic number

Abstract

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

Comments: 5 pages, including 3 figures; to appear in PRC (Brief Report)