Systematic study of tensor effects in shell evolution

In the framework of the Hartree-Fock-Bogoliubov approach with the Skyrme interactions SLy5, SLy5+T, SLy5+T-w, and several sets of the TIJ parametrizations (Skyrme effective interaction parametrizations including the tensor terms), the effect of the tensor force on the shell evolution at Z, N = 8, 20, and 28 is investigated. It is shown that the evolution of the gap (defined as the energy difference between the last occupied and first unoccupied single-particle orbits) with SLy5+T is similar to thatwith SLy5+T-w, and the gap values with SLy5+T are smaller than those with SLy5+T-w in the cases of Z, N = 8, 20. At Z, N = 28, the gap values with SLy5 are smaller than those with SLy5+T and larger than those with SLy5+T-w. To understand these features, we analyze the spin-orbit potentials with and without the tensor contributions and the radial wave functions of relevant orbits. Meanwhile, we find that the deviation of the calculated gaps with SLy5+T-w from the experimental ones is larger than that with SLy5+T. This indicates that SLy5+T-w is not suitable for investigating the properties of the ground-state gap evolution. Finally, it is seen that the gap evolutions with different sets of the TIJ parametrizations are similar to each other except for the ones with T22, and there is almost no difference between the tensor effect in gap evolution with the perturbative method and the one with the complete fitting method.