Effects of the tensor force on the ground and first $2^{+}$ states of the magic ${}^{54}$Ca nucleus

Abstract

The magic nature of the ${}^{54}$Ca nucleus is investigated in the light of the recent experimental results. We employ both HFB and HF+BCS methods using Skyrme-type SLy5, SLy5+T and T44 interactions. The evolution of the single-particle spectra is studied for the N=34 isotones: ${}^{60}$Fe, ${}^{58}$Cr, ${}^{56}$Ti and ${}^{54}$Ca. An increase is obtained in the neutron spin-orbit splittings of $p$ and $f$ states due to the effect of the tensor force which also makes ${}^{54}$Ca a magic nucleus candidate. QRPA calculations on top of HF+BCS are performed to investigate the first $J^{\pi }$=$2^{+}$ states of the calcium isotopic chain. A good agreement for excitation energies is obtained when we include the tensor force in the mean-field part of the calculations. The first $2^{+}$ states indicate a subshell closure for both ${}^{52}$Ca and ${}^{54}$Ca nuclei. We confirm that the tensor part of the interaction is quite essential in explaining the neutron subshell closure in ${}^{52}$Ca and ${}^{54}$Ca nuclei.

Comments: 8 pages, 3 figures