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The spin-flip M1 giant resonance is explored in the framework of Random PhaseApproximation on the basis of the Skyrme energy functional. A representativeset of eight Skyrme parameterizations (SkT6, SkM*, SLy6, SG2, SkO, SkO', SkI4,and SV-bas) is used. Light and heavy, spherical and deformed nuclei ($^{48}$Ca,$^{158}$Gd, $^{208}$Pb, and $^{238}$U) are considered. The calculations showthat spin densities play a crucial role in forming the collective shift in thespectrum. The interplay of the collective shift and spin-orbit splittingdetermines the quality of the description. None of the considered Skyrmeparameterizations is able to describe simultaneously the M1 strengthdistribution in closed-shell and open-shell nuclei. It is found that theproblem lies in the relative positions of proton and neutron spin-orbitsplitting. Necessity to involve the tensor and isovector spin-orbit interactionis called for.

Skyrme-Rpa Description of Spin-Flip M1 Giant Resonance