Testing Skyrme energy-density functionals with the QRPA in low-lying vibrational states of rare-earth nuclei

TL;DR

This paper evaluates the effectiveness of Skyrme energy-density functionals, specifically SkM* and SLy4, in predicting low-lying vibrational states in rare-earth nuclei using the QRPA method, highlighting strengths and limitations.

Contribution

It systematically tests Skyrme functionals with QRPA for vibrational states in rare-earth nuclei, revealing their relative performance and areas needing improvement.

Findings

SkM* outperforms SLy4 in reproducing vibrational state properties.

QRPA captures gamma-vibrational trends but misses multi-particle-hole correlations.

Treatment of pairing energy significantly affects results in some nuclei.

Abstract

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.