Geometrical symmetries of nuclear systems: D(3h) and T(d) symmetries in light nuclei

TL;DR

This paper explores how discrete geometrical symmetries like D(3h) and T(d) influence the structure of light nuclei, specifically 12C and 16O, through an algebraic cluster model that links symmetry to nuclear rotational bands.

Contribution

It introduces a framework connecting point-group symmetries to nuclear structure, providing a simple explanation for observed level sequences in light nuclei.

Findings

Level sequences in 12C and 16O are explained by underlying geometric symmetries.

Discrete symmetries determine the structure of rotational bands.

Geometrical configurations serve as fingerprints for nuclear states.

Abstract

The role of discrete (or point-group) symmetries in alpha-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the alpha-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the alpha-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle with D(3h) symmetry for 12C, and a tetrahedron with T(d) symmetry for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles.