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

TL;DR

This paper explores the geometric mapping of algebraic models in nuclear physics, emphasizing the need to renormalize coherent state variables based on physical observables rather than Hamiltonian interactions.

Contribution

It introduces a novel approach to renormalize coherent state variables in algebraic models, improving the connection between algebraic and geometric descriptions.

Findings

Coherent state variables depend on the total number of bosons.

Renormalization of variables improves the mapping accuracy.

Physical observables guide the renormalization process.

Abstract

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.