Renormalization of coherent state variables, within the geometric mapping of algebraic models

We investigate the geometrical mapping of algebraic models. As particular examples we consider the Semimicriscopic Algebraic Cluster Model (SACM) and the Phenomenological Algebraic Cluster Model (PACM), which also contains the vibron model, as a special case. In the geometrical mapping coherent states are employed as trial states. We show that the coherent state variables have to be renormalized and not the interaction terms of the Hamiltonian, as is usually done. The coherent state variables will depend on the total number of bosons and the coherent state variables. The nature of these variables is extracted through a relation obtained by comparing physical observables, such as the distance between the clusters or the quadrupole deformation of the nucleus, to their algebraic counterpart.

Phenomenological and microscopic cluster models II. Phase transitions

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.

Phenomenological and microscopic cluster models I. The geometric mapping

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.