Tensor effects on the $N=40$ gap evolution of $N=40$ isotones are studied by employing the Skyrme-Hartree-Fock-Bogoliubov (SHFB) and relativistic Hartree-Fock-Bogoliubov (RHFB) theories. The results with and without the inclusion of the tensor components are compared with each other. It is found that when the tensor force is included, both approaches present the same trend and qualitatively agree with the experimental one indicated by the $\beta$-decay studies, which implies an important role played by the tensor force in the gap evolution of $N=40$. Furthermore, it is shown that the gap evolution is dominated by the corresponding tensor contributions from $\pi$ and $\rho$-tensor coupling in the relativistic framework.

• Received 21 October 2012

DOI:https://doi.org/10.1103/PhysRevC.87.047301