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

Abstract

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${}^{\ast }$. 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 a low and high $2_{\gamma }^{+}$ -collectivity are related with the structure of the lowest 2-quasiparticle states and conservation of the Nilsson selection rules. The description of $2_{\gamma }^{+}$ states with SV-bas and SkM${}^{\ast }$ 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.

16 pages, 10 figures, 2 tables

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• Enhanced collectivity of gamma vibration in neutron-rich Dy isotopes with N=108 - 110
• Low-energy spectra of nobelium isotopes: Skyrme random-phase-approximation analysis
• Theoretical description of nuclear collective excitations