Magicity of theCa52andCa54isotopes and tensor contribution within a mean-field approach

Abstract

I investigate the magicity of the isotopes $^{52}\mathrm{Ca}$ and $^{54}\mathrm{Ca}$, which was recently confirmed by two experimental measurements, and relate it to like-particle and neutron-proton tensor effects within a mean-field description. By analyzing Ca isotopes, it is shown that the like-particle tensor contribution induces shell effects that render these nuclei more magic than would be predicted by neglecting it. In particular, such induced shell effects are stronger in the $^{52}\mathrm{Ca}$ nucleus, and the single-particle gaps are increased in both isotopes due to the tensor force. By studying $N=32$ and $N=34$ isotones, neutron-proton tensor effects may be isolated and their role analyzed. It is shown that neutron-proton tensor effects lead to increasing $N=32$ and $N=34$ gaps, when going along isotonic chains, from $^{58}\mathrm{Fe}$ to $^{52}\mathrm{Ca}$ and from $^{60}\mathrm{Fe}$ to $^{54}\mathrm{Ca}$, respectively. Mean-field calculations are perfomed by employing one Skyrme parameter set, which was introduced in a previous work by fitting the tensor parameters together with the spin-orbit strength. The signs and values of the tensor strengths are thus checked within this specific application. The obtained results indicate that the employed parameter set, even if generated with a partial adjustment of the parameters of the force, leads to the correct shell behavior and provides, in particular, a description of the magicity of $^{52}\mathrm{Ca}$ and $^{54}\mathrm{Ca}$ within a pure mean-field picture with the effective two-body Skyrme interaction.