Skyrme random-phase-approximation description of lowestKπ=2γ+states in axially deformed nuclei

The lowest quadrupole $\ensuremath{\gamma}$-vibrational ${K}^{\ensuremath{\pi}}={2}^{+}$ states in axially deformed rare-earth (Nd, Sm, Gd, Dy, Er, Yb, Hf, W) and actinide (U) nuclei are systematically investigated within the separable random-phase-approximation (SRPA) based on the Skyrme functional. The energies ${E}_{\ensuremath{\gamma}}$ and reduced transition probabilities $B(E2)$ of ${2}_{\ensuremath{\gamma}}^{+}$ states are calculated with the Skyrme forces SV-bas and ${\mathrm{SkM}}^{*}$. The energies of two-quasiparticle configurations forming the SRPA basis are corrected by using the pairing blocking effect. This results in a systematic downshift of ${E}_{\ensuremath{\gamma}}$ by 0.3--0.5 MeV and thus in a better agreement with the experiment, especially in Sm, Gd, Dy, Hf, and W regions. For other isotopic chains, a noticeable overestimation of ${E}_{\ensuremath{\gamma}}$ and too weak collectivity of ${2}_{\ensuremath{\gamma}}^{+}$ states still persist. It is shown that domains of nuclei with low and high ${2}_{\ensuremath{\gamma}}^{+}$ collectivity are related to the structure of the lowest two-quasiparticle states and conservation of the Nilsson selection rules. The description of ${2}_{\ensuremath{\gamma}}^{+}$ states with SV-bas and ${\mathrm{SkM}}^{*}$ is similar in light rare-earth nuclei but deviates in heavier nuclei. However SV-bas much better reproduces the quadrupole deformation and energy of the isoscalar giant quadrupole resonance. The accuracy of SRPA is justified by comparison with exact RPA. The calculations suggest that a further development of the self-consistent calculation schemes is needed for a systematic satisfactory description of the ${2}_{\ensuremath{\gamma}}^{+}$ states.