Robust correlations between quadrupole moments of low-lying $2^+$ states within random-interaction ensembles

TL;DR

This paper identifies robust proportional correlations between quadrupole moments of low-lying 2+ states in nuclear models, linking them to underlying symmetries and vibrational limits, with implications for understanding nuclear structure.

Contribution

It reveals three universal correlations between quadrupole moments in random-interaction ensembles and connects them to fundamental nuclear symmetries and vibrational models.

Findings

Three proportional correlations between quadrupole moments are robustly observed.

Correlations are linked to SU(3) symmetry and U(5) vibrational limit.

The $Q(2^+_2)=-rac{3}{7}Q(2^+_1)$ correlation is specific to the $sd$-boson space.

Abstract

In the random-interaction ensembles, three proportional correlations between quadrupole moments of the first two $I^{\pi}=2^+$ states robustly emerge, including $Q(2^+_1)=\pm Q(2^+_2)$ correlations consistently with realistic nuclear survey, and the $Q(2^+_2)=-\frac{3}{7}Q(2^+_1)$ correlation, which is only observed in the $sd$-boson space. These correlations can be microscopically characterized by the rotational SU(3) symmetry and quadrupole vibrational U(5) limit, respectively, according to the Elliott model and the $sd$-boson mean-field theory. The anharmonic vibration may be another phenomenological interpretation for the $Q(2^+_1)=- Q(2^+_2)$ correlation, whose spectral evidence, however, is insufficient.