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Tensor effects on gap evolution of N=40 from non-relativistic and relativistic mean-field theory

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 component are compared with the experimental data. When the tensor force is included, both of the two different approaches are found to give the same trend and agree with the experimental one, which indicates the necessity of introducing the tensor force in the evolution of N=40 subshell and on the other hand the reliability of the methods. Furthermore, it is shown that the gap evolution is primarily determined by the corresponding tensor contributions from $π$ and $ρ$-tensor coupling in the relativistic framework.