12C within the Semimicroscopic Algebraic Cluster Model

TL;DR

This paper applies the Semimicroscopic Algebraic Cluster Model to 12C, treating it as a system of three alpha clusters, and demonstrates that the model reproduces experimental spectra and supports a triangular ground state structure.

Contribution

It introduces a PEP-observing microscopic model space for 12C and compares its results with phenomenological models, highlighting the importance of the Pauli principle.

Findings

12C can be effectively modeled as 8Be + alpha

The ground state has a triangular structure

Large shell excitations are present in the Hoyle state

Abstract

The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 12C as a system of three alpha- clusters. The microscopic model space, which observes the Pauli-Exclusion-Principle (PEP), is constructed. It is shown that the 12C nucleus can effectively be treated as a two-cluster system 8Be+alpha. The experimental spectrum is well reproduced. The geometrical mapping is discussed and it is shown that the ground state must correspond to a triangular structure, which is in agreement with other microscopic calculations. The non-zero B(E2; 0_2+ --> 2_1+) transition requires a mixing of SU(3) irreducible representations (irreps) whose consequences are discussed. The Hoyle state turns out to contain large shell excitations. The results are compared to another phenomenological model, which assumes a triangular structure and, using simple symmetry arguments, can reproduce the states observed at low energy. This model does not observe the PEP and one objective of our contribution is to verify the extend of importance of the PEP.