Skyrme Random-Phase-Approximation description of lowest $K^{\pi}=2^+_{\gamma}$ states in axially deformed nuclei

The lowest quadrupole gamma-vibrational K-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-gamma and reduced transition probabilities B(E2) of 2(gamma)(+) states are calculated with the Skyrme forces SV-bas and 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-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-gamma and too weak collectivity of 2(gamma)(+) states still persist. It is shown that domains of nuclei with low and high 2(gamma)(+) collectivity are related to the structure of the lowest two-quasiparticle states and conservation of the Nilsson selection rules. The description of 2(gamma)(+) states with SV-bas and 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(gamma)(+) states.