Spin-flip M1 giant resonance as a challenge for Skyrme forces

Despite a great success of the Skyrme mean-field approach in the exploration of nuclear dynamics, it seems to fail in the description of the spin-flip M1 giant resonance. The results for different Skyrme parameterizations are contradictory and poorly agree with experiment. In particular, there is no parameterization which simultaneously describes the one-peak gross structure of M1 strength in doubly magic nuclei and two-peak structure in heavy deformed nuclei. The reason of this mismatch could lie in an unsatisfactory treatment of spin correlations and spin-orbit interaction. We discuss the present status of the problem and possible ways of its solution. In particular, we inspect (i) the interplay of the collective shift and spin-orbit splitting, (ii) the isovector M1 response versus isospin-mixed responses and (iii) the role of tensor and isovector spin-orbit interaction.