Geometric symmetries in light nuclei

TL;DR

This paper uses the algebraic cluster model to analyze light nuclei, revealing how geometric symmetries like triangles and tetrahedra explain observed nuclear energy levels and rotational bands.

Contribution

It demonstrates how discrete geometric symmetries underpin the structure of cluster states in 12C and 16O nuclei.

Findings

Level sequences correspond to equilateral triangle and tetrahedral symmetries.

Rotational band structures serve as fingerprints of geometric configurations.

Discrete symmetries explain the observed nuclear spectra.

Abstract

The algebraic cluster model is is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences 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.