On the symmetries of the 12C nucleus

TL;DR

This paper compares two algebraic models describing the symmetries of the 12C nucleus, highlighting their different symmetry assumptions and how they align with experimental data.

Contribution

It analyzes and contrasts the D3h geometric symmetry-based ACM with the U(3) multichannel dynamical symmetry SACM for the 12C nucleus.

Findings

Both models are consistent with available data.

The models use different symmetry frameworks (D3h vs. U(3)).

The comparison enhances understanding of nuclear symmetries.

Abstract

The consequences of some symmetries of the three-alpha system are discussed. In particular, the recent description of the low-energy spectrum of the 12C nucleus in terms of the Algebraic Cluster Model (ACM) is compared to that of the Semimicroscopic Algebraic Cluster Model (SACM). The previous one applies interactions of a D3h geometric symmetry [1], while the latter one has a U(3) multichannel dynamical symmetry, that connects the shell and cluster pictures. The available data is in line with both descriptions.