Evolution of nuclear shells with the Skyrme density dependent interaction

We present the evolution of the shell structure of nuclei in Hartree-Fock calculations using Skyrme's density-dependent effective nucleon-nucleon interaction. The role of the tensor part of the Skyrme interaction to the Hartree-Fock spin-orbit splitting in spherical spin unsaturated nuclei is reanalyzed. The contribution of a finite range tensor force to the spin-orbit splitting in closed shell nuclei is calculated. It is found that the exact matrix elements of a Gaussian and of a one-pion exchange tensor potential could be written as a product Skyrme's short range expression times a suppression factor which is almost constant for closed shell nuclei with mass number A >= 48. The suppression factor is similar to 0.15 for the one-pion exchange potential.