Phenomenological and microscopic cluster models I. The geometric mapping

TL;DR

This paper explores the geometric mapping of algebraic nuclear cluster models using coherent states, comparing a Pauli-principle-observing model with a phenomenological limit, and discusses potential phase transitions.

Contribution

It introduces a new SO(3) dynamical symmetry limit and third-order Hamiltonian terms, linking the SACM and PACM through geometric and energetic analyses.

Findings

The potential energy surfaces of both models are constructed.

Higher-order interactions in PACM can mimic Pauli principle effects.

The study provides a foundation for analyzing phase transitions in algebraic cluster models.

Abstract

The geometrical mapping of algebraic nuclear cluster models is investigated within the coherent state formalism. Two models are considered: the Semimicroscopic Algebraic Cluster Model (SACM) and the Phenomenological Algebraic Cluster Model (PACM), which is a special limit of the SACM. The SACM strictly observes the Pauli exclusion principle while the PACM does not. The discussion of the SACM is adapted to the coherent state formalism by introducing the new SO(3) dynamical symmetry limit and third-order interaction terms in the Hamiltonian. The potential energy surface is constructed in both models and it is found that the effects of the Pauli principle can be simulated by higher-order interaction terms in the PACM. The present study is also meant to serve as a starting point for investigating phase transitions in the two algebraic cluster models.