  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 gamma-vibrational states, but our results are not perfect and indicate the
presences of multi-particle-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 "beta-vibrational" states
than with the gamma-vibrational states.
