# Coherent quadrupole-octupole states from a SUSY-QM Hamiltonian hierarchy and shape invariance

## TL;DR

This paper demonstrates that the coherent quadrupole-octupole model in nuclei exhibits a supersymmetric quantum mechanics structure, with shape-invariant potentials forming a hierarchy of Hamiltonians, revealing underlying symmetries in nuclear spectra.

## Contribution

It introduces a SUSY-QM framework within the CQOM model, showing the potential for supersymmetric structures in nuclear spectra and explaining deviations from perfect symmetry.

## Key findings

- The potential generates a SUSY-QM hierarchy of Hamiltonians.
- The model reveals a generic supersymmetric structure in nuclear spectra.
- Signs of supersymmetry can be identified in experimental nuclear spectra.

## Abstract

We show that the potential in the radial equation in the model of coherent quadrupole-octupole motion (CQOM) in nuclei generates a sequence of superpotentials and subsequent series of effective potentials which satisfy the shape-invariance condition and correspond to a SUSY-QM hierarchy of Hamiltonians. On this basis we suggest that the original CQOM level scheme possesses a generic supersymmetric structure of the spectrum inherent for the coherent quadrupole-octupole mode. We outline the mechanism in which the real quadrupole-octupole spectra in even-even and odd-even nuclei deviate from the genuine symmetry. By using it we illustrate the possibilities to identify the signs of supersymmetry in the alternating-parity spectra of even-even nuclei and the quasi-parity-doublet levels of odd-mass nuclei described within the CQOM model approach.