Phenomenological and microscopic cluster models II. Phase transitions

TL;DR

This paper compares two algebraic cluster models, SACM and PACM, in analyzing phase transitions in nuclear cluster states, highlighting differences in their treatment of the Pauli principle and identifying types of phase transitions.

Contribution

It introduces a comparative analysis of SACM and PACM, emphasizing the impact of Pauli principle considerations on phase transition behavior in nuclear models.

Findings

Both models exhibit first- and second-order phase transitions.

SACM reveals a critical line in phase space.

Numerical studies on neon-20 and magnesium-24 support analytical results.

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 {\alpha}-cluster states of the neon-20 and magnesium-24 nuclei.