Tensor effects in shell evolution are studied within the mean-field approach. Particular attention is paid to the analysis of the magic gaps in different regions of the nuclear chart, namely, $Z,N=8$, 20, and 28. Hartree-Fock calculations with Skyrme and Gogny interactions are performed where the tensor term has a zero and finite range, respectively. Results obtained with and without the tensor component are compared between them and with the experimental data, when available. To complete this analysis, the tensor effect is also investigated within the relativistic Hartree-Fock model, where the exchange of $\rho$ mesons and pions is taken into account. It turns out that the tensor effect in the evolution of the magic gaps can be more easily identified in the cases $Z,N=8$ and 20, whereas the interpretation of the effect is more complicated for $Z$ or $N=$ 28. Consequently, we indicate the regions defined by the magic numbers 8 and 20 as suitable for fitting the tensor parameters in a mean-field approach: We suggest to include explicitly the data associated to these gap evolutions in the fitting procedures. In general, with the parametrizations used in this work (which have not been fitted on these data), the mean-field results obtained with the tensor contribution do not reproduce the experimental trend, that is, the reduction of the gaps at 8 and 20 that is observed when going toward the drip lines. Since some of the considered nuclei have $N=Z$, a discussion will be devoted to the interpretation of the experimental data concerning these nuclei and to the Wigner-energy correction.

• Received 22 April 2010

DOI:https://doi.org/10.1103/PhysRevC.81.064327