Magicity of the $^{52}$Ca and $^{54}$Ca isotopes and tensor contribution within a mean--field approach

We investigate the magicity of the isotopes $^{52}$Ca and $^{54}$Ca, that 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, we show that the like--particle tensor contribution induces shell effects that render these nuclei more magic than they would be predicted by neglecting it. In particular, such induced shell effects are stronger in the nucleus $^{52}$Ca 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 $^{58}$Fe to $^{52}$Ca, and from $^{60}$Fe to $^{54}$Ca, respectively. The mean--field calculations are perfomed by employing one Skyrme parameter set, that was introduced in a previous work by fitting the tensor parameters together with the spin--orbit strength. The signs and the 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 $^{52}$Ca and $^{54}$Ca within a pure mean--field picture with the effective two--body Skyrme interaction.