The geometric interpretation of the semimicroscopic algebraic cluster model and the role of the Pauli principle

Abstract

The geometrical mapping of the Semimicroscopic Algebraic Cluster Model (SACM) is performed via coherent states. The SACM strictly observes the Pauli exclusion principle. It is shown that the resulting mapping can be reproduced by the mapping of other algebraic nuclear cluster model, the Phenomenological Algebraic Cluster Model (PACM), which does not observe the Pauli exclusion principle, but with a more complicated Hamiltonian. The phase transitions are investigated and compared within two algebraic cluster models. First-and second-order phase transition are observed. For the SACM also a critical line appears. The general discussion of phase transitions is reduced to at most three effective parameters, which are functions of all possible interaction parameters in the model.