Phenomenological and microscopic cluster models I. The geometric mapping

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.

arXiv comment13 pages, 0 figures, part one of a two part work

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Cited by in corpus (5)

• 12C within the Semimicroscopic Algebraic Cluster Model
• Phenomenological and microscopic cluster models II. Phase transitions
• A Semimicroscopic Algebraic Cluster Model for Heavy Nuclei
• Application of the cranking method to the semimicroscopic algebraic cluster model and nuclear molecules
• Quantum Phase Transitions within a nuclear cluster model and an effective model of QCD