Abstract
Two algebraic cluster models of nuclear structure which use the same Hamiltonian are explored: a Phenomenological Algebraic Cluster Model (PACM), and a Semi-microscopic Algebraic Cluster Model (SACM). The PACM does not incorporate the Pauli exclusion principle, while the SACM does. The Hamiltonian considered is an admixture of three dynamical symmetries; the SU(3), SO(4), and SO(3), with weighting of each determined by parameters. The classical potential is constructed using coherent states, and the model Hilbert space of the SACM is constructed in such a way as to include all shell model states which correspond to the cluster structure of interest. Phase transitions and their orders are investigated for each model, and parameter phase diagrams are presented, wherein it is found that consideration of the Pauli principle has significant consequences. Also shown are fits of Hamiltonian parameters for a nucleus of 2 spherical clusters, when moving between the symmetry limits.
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