Wobbling motion in $^{135}$Pr within a collective Hamiltonian

TL;DR

This paper models the wobbling motion in $^{135}$Pr using a collective Hamiltonian derived from TAC and HFA methods, successfully reproducing experimental spectra and revealing a transition from transverse to longitudinal wobbling with increasing rotational frequency.

Contribution

It introduces a novel approach combining TAC and HFA to determine collective parameters, providing a detailed understanding of wobbling mode transitions in $^{135}$Pr.

Findings

Reproduces experimental spectra of $^{135}$Pr wobbling bands

Identifies transition from transverse to longitudinal wobbling

Analyzes moments of inertia and potential shapes

Abstract

The recently reported wobbling bands in $^{135}$Pr are investigated by the collective Hamiltonian, in which the collective parameters, including the collective potential and the mass parameter, are respectively determined from the tilted axis cranking (TAC) model and the harmonic frozen alignment (HFA) formula. It is shown that the experimental energy spectra of both yrast and wobbling bands are well reproduced by the collective Hamiltonian. It is confirmed that the wobbling mode in $^{135}$Pr changes from transverse to longitudinal with the rotational frequency. The mechanism of this transition is revealed by analyzing the effective moments of inertia of the three principal axes, and the corresponding variation trend of the wobbling frequency is determined by the softness and shapes of the collective potential.