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

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.

7 pages, 1 figure, 5 tables

References in corpus (7)

• Evidence for Triangular D_3h Symmetry in 12C
• Alpha-particle condensation in 16O via a full four-body OCM calculation
• Evidence for tetrahedral symmetry in 16O
• Symmetry-guided large-scale shell-model theory
• Alpha particle clusters and their condensation in nuclear systems
• Tetrahedral $4\alpha$ and ${}^{12}\text{C}+\alpha$ cluster structures in ${}^{16}$O
• Open Problems in $\alpha$ Particle Condensation

Cited by in corpus (3)

• Semi-microscopic construction of multi-$\alpha$ cluster spaces
• Symplectic symmetry approach to clustering in atomic nuclei: The case of ${}^{24}$Mg
• Quantum Phase Transitions within a nuclear cluster model and an effective model of QCD