Testing Skyrme energy-density functionals with the quasiparticle random-phase approximation in low-lying vibrational states of rare-earth nuclei

Although nuclear energy-density functionals are determined primarily by fitting to ground-state properties, they are often applied in nuclear astrophysics to excited states, usually through the quasiparticle random-phase approximation (QRPA). Here we test the Skyrme functionals SkM∗ and SLy4 along with the self-consistent QRPA by calculating properties of low-lying vibrational states in a large number of well-deformed even-even rare-earth nuclei. We reproduce trends in energies and transition probabilities associated with γ -vibrational states, but our results are not perfect and indicate the presence of multiparticle-hole correlations that are not included in the QRPA. The Skyrme functional SkM∗ performs noticeably better than SLy4. In a few nuclei, changes in the treatment of the pairing energy functional have a significant effect. The QRPA is less successful with “β-vibrational” states than with the γ -vibrational states.