Eur. Phys. J. A (2019) 55: 71
https://doi.org/10.1140/epja/i2019-12744-0

Regular Article - Theoretical Physics

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

¹ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior S/N, A.P. 70-543, 04510, México D.F., Mexico
² Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe Universität, Ruth-Moufang-Str.1, 60438, Frankfurt am Main, Germany

^* e-mail: hess@nucleares.unam.mx

Received: 22 January 2019
Accepted: 28 March 2019
Published online: 15 May 2019

Abstract

The Semimicroscopic Algebraic Cluster Model (SACM) is applied to ¹⁶O, assumed to consist of a system of four -clusters. For the 4- cluster system we take the model space already obtained in the past, which observes the Pauli Exclusion Principle (PEP) and is symmetric under permutation of the -particles. A phenomenological Hamiltonian is used. 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 for the ground state the ¹⁶O shows evidence of a tetrahedral structure which can be explained easily by symmetry arguments. We show that the 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, especially to an accumulation of parity doublets.