SU(3) quasidynamical symmetry underlying the Alhassid--Whelan arc of regularity

TL;DR

This paper identifies a quasi-dynamical SU(3) symmetry trajectory within the Interacting Boson Approximation model, explaining the Alhassid-Whelan arc of regularity as a symmetry-based phenomenon connecting SU(3) and U(5) regions.

Contribution

It provides the first empirical example of a quasi-dynamical symmetry trajectory in the model's interior, linking spectral regularities to underlying symmetries.

Findings

Spectra along the trajectory show SU(3)-like degeneracies.

The trajectory extends from SU(3) to near the critical line of phase transition.

It offers a symmetry-based interpretation of the Alhassid-Whelan arc of regularity.

Abstract

The first example of an empirically manifested quasi dynamical symmetry trajectory in the interior of the symmetry triangle of the Interacting Boson Approximation model is identified for large boson numbers. Along this curve, extending from SU(3) to near the critical line of the first order phase transition, spectra exhibit nearly the same degeneracies that characterize the low energy levels of SU(3). This trajectory also lies close to the Alhassid-Whelan arc of regularity, the unique interior region of regular behavior connecting the SU(3) and U(5) vertices, thus offering a possible symmetry-based interpretation of that narrow zone of regularity amidst regions of more chaotic spectra.