Generalized Skyrme random-phase approximation for nuclear resonances: Different trends for electric and magnetic modes

Abstract

We discuss major differences between electric and magnetic excitations in nuclei appearing in self-consistent calculations based on Skyrme energy-density functionals (EDFs). For this we calculate collective low- and high-lying electric and magnetic excitations in $^{208}\mathrm{Pb}$ within a self-consistent Skyrme EDF approach using the random-phase approximation (RPA) and a more sophisticated particle-hole plus phonon-coupling model, coined the time-blocking approximation (TBA). Tools of analysis are Landau-Migdal parameters for bulk properties and the RPA and TBA results for finite nuclei. We show that the interplay between the effective mass and the effective particle-hole interaction, well known in the Landau-Migdal theory, renders the final results rather independent of the effective mass by virtue of the ``backflow effect.'' It explains the success of self-consistent calculations of electric transitions in such approaches. This effect, however, is absent in the magnetic case and leads to higher fluctuations in the results. It calls for further developments of the Skyrme functional in the spin channel.