Self-consistent tilted-axis-cranking study of triaxial strongly deformed bands in $^{158}$Er at ultrahigh spin

TL;DR

This study uses a self-consistent tilted-axis-cranking approach within the Skyrme-Hartree-Fock model to analyze triaxial strongly deformed bands in $^{158}$Er at ultrahigh spins, clarifying the nature of multiple minima and predicting new configurations.

Contribution

It introduces a tilted-axis-cranking method to distinguish physical minima from saddle points in the analysis of TSD states in $^{158}$Er, advancing understanding of nuclear deformation at high spins.

Findings

Identification of a saddle point for the higher-energy TSD minimum.

Prediction of several TSD configurations, including a highly deformed band.

The predicted quadrupole moment of the candidate band matches experimental data.

Abstract

Stimulated by recent experimental discoveries, triaxial strongly deformed (TSD) states in $^{158}$Er at ultrahigh spins have been studied by means of the Skyrme-Hartree-Fock model and the tilted-axis-cranking method. Restricting the rotational axis to one of the principal axes -- as done in previous cranking calculations -- two well-defined TSD minima in the total Routhian surface are found for a given configuration: one with positive and another with negative triaxial deformation $\gamma$. By allowing the rotational axis to change direction, the higher-energy minimum is shown to be a saddle point. This resolves the long-standing question of the physical interpretation of the two triaxial minima at a very similar quadrupole shape obtained in the principal axis cranking approach. Several TSD configurations have been predicted, including a highly deformed band expected to cross lesser elongated TSD bands at the highest spins. Its transitional quadrupole moment $Q_t \approx 10.5$\,eb is close to the measured value of $\sim$11\,eb; hence, it is a candidate for the structure observed in experiment.