$g$-factor and static quadrupole moment for the wobbling mode in $^{133}$La

TL;DR

This study uses the particle rotor model to analyze the $g$-factor and static quadrupole moment in the wobbling mode of $^{133}$La, providing insights into angular momentum geometry and matching experimental data.

Contribution

It offers a detailed interpretation of the $g$-factor and quadrupole moment variations with spin, revealing the angular momentum alignment and wobbling excitation characteristics.

Findings

The rotor angular momentum is approximately 2 at the bandhead.

Proton-particle and total nuclear angular momenta are aligned parallel.

Negative static quadrupole moments indicate alignment along the short axis.

Abstract

The $g$-factor and static quadrupole moment for the wobbling mode in the nuclide $^{133}$La are investigated as functions of the spin $I$by employing the particle rotor model. The model can reproduce the available experimental data of $g$-factor and static quadrupole moment. The properties of the $g$-factor and static quadrupole moment as functions of $I$ are interpreted by analyzing the angular momentum geometry of the collective rotor, proton-particle, and total nuclear system. It is demonstrated that the experimental value of the $g$-factor at the bandhead of the yrast band leads to the conclusion that the rotor angular momentum is $R\simeq 2$. Furthermore, the variation of the $g$-factor with the spin $I$ yields the information that the angular momenta of the proton-particle and total nuclear system are oriented parallel to each other. The negative values of the static quadrupole moment over the entire spin region are caused by an alignment of the total angular momentum mainly along the short axis. Static quadrupole moment differences between the wobbling and yrast band originate from a wobbling excitation with respect to the short axis.