Two-dimensional collective Hamiltonian for chiral and wobbling modes

TL;DR

This paper introduces a two-dimensional collective Hamiltonian model for analyzing chiral and wobbling modes in triaxial nuclei, effectively restoring symmetries and matching exact solutions at high frequencies.

Contribution

The paper develops a novel 2D Hamiltonian approach based on TAC calculations to study chiral and wobbling modes, restoring broken symmetries and providing accurate spectra.

Findings

The 2DCH reproduces PRM results at high frequencies.

Energies are overestimated at low frequencies due to mass parameter issues.

Transitions from chiral vibration to wobbling are demonstrated.

Abstract

A two-dimensional collective Hamiltonian (2DCH) on both azimuth and polar motions in triaxial nuclei is proposed to investigate the chiral and wobbling modes. In the 2DCH, the collective potential and the mass parameters are determined from three-dimensional tilted axis cranking (TAC) calculations. The broken chiral and signature symmetries in the TAC solutions are restored by the 2DCH. The validity of the 2DCH is illustrated with a triaxial rotor ($\gamma=-30^\circ$) coupling to one $h_{11/2}$ proton particle and one $h_{11/2}$ neutron hole. By diagonalizing the 2DCH, the angular momenta and energy spectra are obtained. These results agree with the exact solutions of the particle rotor model (PRM) at high rotational frequencies. However, at low frequencies, the energies given by the 2DCH are larger than those by the PRM due to the underestimation of the mass parameters. In addition, with increasing angular momentum, the transitions from the chiral vibration to chiral rotation and further to longitudinal wobbling motion have been presented in the 2DCH.