Skyrme random-phase-approximation description of spin-flip M1 giant resonance

The spin-flip M1 giant resonance is explored in the framework of the random-phase-approximation (RPA) on the basis of the Skyrme energy functional. A representative set of eight Skyrme parametrizations (SkT6, SkM*, SLy6, SG2, SkO, SkO', SkI4, and SV-bas) is used. Light and heavy, spherical and deformed nuclei (Ca-48, Gd-158, Pb-208, and U-238) are considered. The calculations show that spin densities play a crucial role in forming the collective shift in the spectrum. The interplay of the collective shift and spin-orbit splitting determines the quality of the description. None of the considered Skyrme parametrizations is able to describe simultaneously the M1 strength distribution in closed-shell and open-shell nuclei. It is found that the problem lies in the relative positions of proton and neutron spin-orbit splitting. This calls for a better modeling of the tensor and isovector spin-orbit interaction.