Phenomenological and microscopic cluster models. II. Phase transitions

Abstract

Based on the results of a previous paper (Paper I), by performing the geometrical mapping via coherent states, phase transitions are investigated and compared within two algebraic cluster models. The difference between the semimicroscopic algebraic cluster model (SACM) and the phenomenological algebraic cluster model (PACM) is that the former strictly observes the Pauli exclusion principle between the nucleons of the individual clusters, while the latter ignores it. From the technical point of view the SACM is more involved mathematically, while the formalism of the PACM is closer to that of other algebraic models with different physical content. First- and second-order phase transitions are identified in both models, while in the SACM a critical line also appears. Analytical results are complemented with numerical studies on $\ensuremath{\alpha}$-cluster states of the ${}^{20}$Ne and ${}^{24}$Mg nuclei.