Tensor-force effects on single-particle levels and proton bubble structure around theZorN=20magic number

Abstract

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 $\ensuremath{\varepsilon}(p1{s}_{1/2})$ and $\ensuremath{\varepsilon}(p0{d}_{3/2})$ (denoted by $\ensuremath{\Delta}{\ensuremath{\varepsilon}}_{13}$) 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 $\ensuremath{\Delta}{\ensuremath{\varepsilon}}_{13}$ also in neutron-rich Ca nuclei. While the $p1{s}_{1/2}$--$p0{d}_{3/2}$ inversion is predicted in heavier Ca nuclei as in ${}^{48}$Ca, it takes place only for $N\ensuremath{\ge}46$, delayed by the tensor force. We further investigate the possibility of proton bubble structure in Ar, which is suggested by the $p1{s}_{1/2}$--$p0{d}_{3/2}$ 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 $p1{s}_{1/2}$ and $p0{d}_{5/2}$.