Quasidynamical symmetries in the backbending of chromium isotopes

TL;DR

This paper investigates quasidynamical symmetries in chromium isotopes during backbending, revealing persistent symmetries that help characterize nuclear band evolution despite complex shape changes.

Contribution

It introduces a group-theoretical decomposition method to analyze backbending in chromium isotopes, highlighting the role of quasidynamical symmetries across different groups.

Findings

Quasidynamical symmetries are present above and below backbending.

SU(3) shows the strongest evolution but does not indicate decreased deformation.

Mean-field and SU(3) configurations can depict different deformation pictures.

Abstract

Background: Symmetries are a powerful way to characterize nuclear wave functions. A true dynamical symmetry, where the Hamiltonian is block-diagonal in subspaces defined by the group, is rare. More likely is a quasidynamical symmetry: states with different quantum numbers (i.e. angular momentum) nonetheless sharing similar group-theoretical decompositions. Purpose: We use group-theoretical decomposition to investigate backbending, an abrupt change in the moment of inertia along the yrast line, in $^{48,49,50}$Cr: prior mean-field calculations of these nuclides suggest a change from strongly prolate to more spherical configurations as one crosses the backbending and increases in angular momentum. Methods: We decompose configuration-interaction shell-model wavefunctions using the SU(2) groups $L$ (total orbital angular momentum) and $S$ (total spin), and the groups SU(3) and SU(4). We do not need a special basis but only matrix elements of Casimir operators, applied with a modified Lanczos algorithm. Results: We find quasidynamical symmetries, albeit often of a different character above and below the backbending, for each group. While the strongest evolution was in SU(3), the decompositions did not suggest a decrease in deformation. We point out with a simple example that mean-field and SU(3) configurations may give very different pictures of deformation. Conclusions: Persistent quasidynamical symmetries for several groups allow us to identify the members of a band and to characterize how they evolve with increasing angular momentum, especially before and after backbending.