# Symmetries and order in cluster nuclei

## TL;DR

This paper demonstrates that the rotational band structures in 12C and 16O nuclei reflect their underlying alpha-particle geometrical symmetries, revealing a link between nuclear configurations and observable spectra.

## Contribution

It introduces a symmetry-based framework to understand cluster states in nuclei, connecting geometric arrangements to rotational spectra, and extends initial insights to odd-cluster nuclei.

## Key findings

- Rotational bands correspond to equilateral triangle and tetrahedral symmetries.
- Geometrical configurations serve as fingerprints for nuclear structure.
- Initial results suggest similar symmetry principles apply to odd-cluster nuclei.

## Abstract

It is shown that the rotational band structure of the cluster states in 12C and 16O can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle for 12C, and a regular tetrahedron for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles. Finally, some first results are presented for odd-cluster nuclei.