The octupole collective Hamiltonian. Does it follow the example of the quadrupole case?

TL;DR

This paper introduces a general octupole collective Hamiltonian, explores intrinsic frames with cubic symmetry, and discusses a unified quadrupole-octupole model, revealing new insights into octupole vibrations and shapes.

Contribution

It presents a comprehensive form of the octupole collective Hamiltonian and analyzes intrinsic frames and vibrations, extending the quadrupole model to octupole deformations.

Findings

Intrinsic octupole coordinates and deformations are defined.

An intrinsic angular momentum for octupole vibrations is identified.

Analysis of small oscillations around axially-symmetric shapes is performed.

Abstract

A general form of the octupole collective Hamiltonian is introduced and analyzed based on fundamental tensors in the seven-dimensional tensor space. Possible definitions of intrinsic frames of reference possessing cubic symmetry for the octupole tensor are considered. Cubic intrinsic octupole coordinates or deformations are introduced. Shapes of the octupoloid are investigated. The octupole collective Hamiltonian is expressed in intrinsic coordinates. An intrinsic angular momentum carried by the octupole vibrations is discovered. Small oscillations about an axially-symmetric pear shape are analyzed. Formulation of a unified quadrupole-octupole collective model is discussed.