Semi-classical and boson descriptions of scissors states

TL;DR

This paper models nuclear wobbling and chiral motion using a semi-classical and boson expansion approach on a two-rotor Hamiltonian, explaining experimental phenomena like twin chiral bands in $^{156}$Gd.

Contribution

It introduces a combined semi-classical and Dyson boson method to describe scissors states, wobbling, and chiral symmetry breaking in nuclei, providing a new framework for understanding these phenomena.

Findings

The model reproduces wobbling frequencies and chiral twin bands.

Application to $^{156}$Gd demonstrates the model's effectiveness.

The approach links phonon amplitudes to inter-band transition probabilities.

Abstract

A two interacting rotors Hamiltonian is alternatively treated semi-classically and by a Dyson boson expansion method. The linearized equations of motion lead to dispersion equation for the wobbling frequency. One defined a ground band with energies consisting in a rotational part and one half of the vibrational wobbling energy. Adding to each state energy the corresponding wobbling quanta one obtains the first excited band. Phonon amplitudes are used to calculate the reduced probability for the inter-band M1 transitions. The states exhibit a shears character. One points out a chiral symmetry which is broken by the interaction term, leading to a pair of twin chiral bands. Applications are made for $^{156}$Gd. One outlines the ability of the two rotor model to account for the wobbling and chiral motion in nuclei. Although the chosen trial function has not a definite total angular momentum, for two particular ansatz of the pairs $I_p,I_n$ the average value of the total angular momentum approximates, to a certain accuracy, the partial angular momentum $I_p$ In this context, the rotational bands defined throughout this present paper could be labeled by the total I.