A new boson approach for the wobbling motion in even-odd nuclei

TL;DR

This paper introduces a novel boson-based model for describing wobbling motion in even-odd nuclei, capturing complex phenomena like chiral structures and phase transitions with analytical and classical methods.

Contribution

It develops a new boson expansion approach and Schrödinger-like eigenvalue equation to analyze wobbling motion, including phase diagrams and wobbling frequencies.

Findings

The model reveals three minima in the potential energy, indicating different wobbling regimes.

Analytical expressions for energies at potential minima are derived.

The model successfully describes wobbling frequencies and transition probabilities in $^{135}$Pr.

Abstract

A triaxial core rotating around the middle axis, i.e. 2-axis, is cranked around the 1-axis, due to the coupling of an odd proton from a high j orbital. Using the Bargmann representation of a new and complex boson expansion of the angular momentum components, the eigenvalue equation of the model Hamiltonian acquires a Schr\"{o}dinger form with a fully separated kinetic energy. From a critical angular momentum, the potential energy term exhibits three minima, two of them being degenerate. Spectra of the deepest wells reflects a chiral-like structure. Energies corresponding to the deepest and local minima respectively, are analytically expressed within a harmonic approximation. Based on a classical analysis, a phase diagram is constructed. It is also shown that the transverse wobbling mode is unstable. The wobbling frequencies corresponding to the deepest minimum are used to quantitatively describe the wobbling properties in $^{135}$Pr. Both energies and e.m. transition probabilities are described.