$g$-factor and static quadrupole moment of $^{135}$Pr, $^{105}$Pd, and $^{187}$Au in wobbling motion

TL;DR

This study investigates the $g$-factor and static quadrupole moments of specific nuclides in wobbling motion, revealing how these properties vary with spin and differ between proton and neutron valence configurations.

Contribution

It provides a detailed analysis of the spin-dependent behavior of $g$-factors and quadrupole moments in wobbling nuclei using the particle-rotor model, highlighting differences between proton and neutron valence cases.

Findings

$^{105}$Pd's $g$-factor increases with spin due to neutron valence.

$^{135}$Pr and $^{187}$Au show decreasing $g$-factors with spin.

Quadrupole moments vary between yrast and wobbling bands depending on wobbling type.

Abstract

The $g$-factor and static quadrupole moment of the nuclides $^{135}$Pr, $^{105}$Pd, and $^{187}$Au in the wobbling motion are investigated in the particle-rotor model as functions of the total spin $I$. The $g$-factor of $^{105}\mathrm{Pd}$ increases with increasing $I$, due to the negative gyromagnetic ratio of a neutron valence-neutron. This behavior is in contrast to the decreasing $g$-factor of the other two nuclides, $^{135}$Pr and $^{187}$Au, which feature a valence-proton. The static quadrupole moment $Q$ depends on all three expectation values of the total angular momentum. It is smaller in the yrast band than in the wobbling band for the transverse wobblers $^{135}$Pr and $^{105}$Pd, while larger for the longitudinal wobbler $^{187}$Au.