The tensor part of Skyrme's interaction

A tensor part is added to central and spin-orbit parts of Skyrme's effective interaction and its contribution to the Hartree-Fock spin-orbit coupling of spherical nuclei is analysed. Minor improvements to spin-orbit splittings can be achieved if the strengths of the tensor interaction are treated as free parameters, but the fit to experiment deteriorates if the tensor interaction contribution is estimated for a realistic interaction.