# 16O within the Semimicroscopic Algebraic Cluster Model and the importance of the Pauli Exclusion Principle

## TL;DR

This paper applies the Semimicroscopic Algebraic Cluster Model to 16O, emphasizing the critical role of the Pauli Exclusion Principle in accurately modeling its structure and spectrum, contrasting it with models that neglect PEP.

## Contribution

It demonstrates the importance of including the Pauli Exclusion Principle in cluster models of 16O, providing a more accurate description of its spectrum and structure.

## Key findings

- PEP significantly affects the predicted spectrum and structure.
- Neglecting PEP leads to incorrect low-energy state predictions.
- The model supports a tetrahedral symmetry in 16O when PEP is considered.

## Abstract

The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 16O, assumed to consist of a system of four alpha-clusters. For the 4-alpha cluster system a microscopic model space is constructed, which observes the Pauli-Exclusion-Principle (PEP) and is symmetric under permutation of the 4-alpha-particles. A phenomenological Hamiltonian is used, justifying the name Semi in the SACM. The spectrum and transition values are determined. One of the main objectives is to test the importance of the Pauli Exclusion Principle (PEP), comparing the results with the Algebraic Cluster Model (ACM), which does not include the PEP, and claims that the 16O shows evidence of a tetrahedral structure, which can be explained easily by symmetry arguments. We show that PEP is very important and cannot be neglected, otherwise it leads to a wrong interpretation of the band structure and to too many states at low energy.