The magic nature of the ${}^{54}\mathrm{Ca}$ nucleus is investigated in light of recent experimental results. We employ both Hartree-Fock-Bogoliubov and Hartree-Fock (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: ${}^{60}\mathrm{Fe}$, ${}^{58}\mathrm{Cr}$, ${}^{56}\mathrm{Ti}$, and ${}^{54}\mathrm{Ca}$. 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 ${}^{54}\mathrm{Ca}$ a magic nucleus candidate. Quasiparticle random-phase approximation 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 ${}^{52}\mathrm{Ca}$ and ${}^{54}\mathrm{Ca}$ nuclei. We confirm that the tensor part of the interaction is quite essential in explaining the neutron subshell closure in ${}^{52}\mathrm{Ca}$ and ${}^{54}\mathrm{Ca}$ nuclei.

• Received 2 April 2014

DOI:https://doi.org/10.1103/PhysRevC.89.064322