The Semimicroscopic Algebraic Cluster Model (SACM) is applied to 16 O, assumed to consist of a system of four α-clusters. For the 4-α cluster system a microscopic model space is constructed, which observes the Pauli-Exclusion-Principle (PEP) and is symmetric under permutation of the 4α-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 16 O 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.

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The Pauli Exclusion Principle (PEP) is one of the most basic concepts in physics, but also the most difficult to implement in many-fermion systems, which are common in nuclear physics. To investigate the consequences of ignoring the PEP, we discuss several algebraic models in nuclear structure physics, in particular cluster models. Sometimes they tend to ignore the Pauli Exclusion Principle for practical reasons, leading to flawed interpretations. Though at first sight there seems to be an agreement to experiment, often it is due to the limited number of states known experimentally. We discuss several models which include or not the PEP, illustrating through their differences the importance of the PEP. This contribution is also a review of recently published results.