Behavior of the collective rotor in wobbling motion

TL;DR

This paper investigates the behavior of the collective rotor in wobbling motion within the particle-rotor model for $^{135}$Pr, revealing the transition from transverse to longitudinal wobbling with detailed angular momentum analysis.

Contribution

It introduces a method to analyze wobbling modes by transforming wave functions and provides detailed insights into the evolution of wobbling modes in $^{135}$Pr.

Findings

Reproduces experimental spectra and wobbling frequencies.

Shows the transition from transverse to longitudinal wobbling with spin.

Analyzes coupling schemes of rotor and particle angular momenta.

Abstract

The behavior of the collective rotor in wobbling motion is investigated within the particle-rotor model for the nucleus $^{135}$Pr by transforming the wave functions from the $K$-representation to the $R$-representation. After reproducing the experimental energy spectra and wobbling frequencies, the evolution of the wobbling mode in $^{135}$Pr, from transverse at low spins to longitudinal at high spins, is illustrated by the distributions of the total angular momentum in the intrinsic reference frame (azimuthal plot). Finally, the coupling schemes of the angular momenta of the rotor and the high-$j$ particle for transverse and longitudinal wobbling are obtained from the analysis of the probability distributions of the rotor angular momentum ($R$-plots) and their projections onto the three principal axes ($K_R$-plots).