Rotational bands in Quadrupole-Octupole Collective Model

TL;DR

This paper develops a comprehensive theoretical model for quadrupole-octupole collective vibrations and rotations in nuclei, comparing predictions with experimental data in $^{156}$Dy, and exploring implications for nuclear symmetries.

Contribution

It introduces a consistent collective Hamiltonian incorporating quadrupole and octupole vibrations coupled with rotation, enabling detailed analysis of negative-parity bands and symmetry fingerprints.

Findings

The model accurately reproduces experimental energies and transition probabilities.

It distinguishes scenarios for the disappearance of E2 transitions in negative-parity bands.

Potential identification of high-order symmetries in nuclear structures.

Abstract

A collective bands of positive and negative parity could be composed of the vibrations and rotations. The rotations of the octupole configurations can be based either on the axial or the non-axial octupole vibrations. A consistent approach to the quadrupole-octupole collective vibrations coupled with the rotational motion enables to distinguish between various scenarios of disappearance of the E2 transitions in negative-parity bands. The here presented theoretical estimates are compared with the recent experimental energies and transition probabilities in and between the ground-state and low-energy negaive-parity bands in $^{156}$Dy. A realistic collective Hamiltonian contains the potential energy term obtained through the macroscopic-microscopic Strutinsky-like method with particle-number-projected BCS approach and deformation-dependent mass tensor defined in vibrational-rotational, nine-dimensional collective space. The symmetrization procedure ensures the uniqueness of the Hamiltonian eigensolutions with respect to the laboratory coordinate system. This quadrupole-octupole collective approach may also allow to find and/or verify some fingerprints of possible high-order symmetries (e.g. tetrahedral, octahedral,...) in nuclear collective bands.