Background: In any theoretical framework for nuclear structure, the quantitative description of $E0$ transition rates remains a nontrivial and persistent challenge. Moreover, these observables impose stringent constraints on the viable parameter space of such models.

Purpose: This work aims to systematically investigate the behavior of selected ${\rho }^2\left(E0\right)$ values and their ratios across the entire parameter space of the interacting boson model with a single configuration. As a concrete application, the even-even Xe isotopic chain is analyzed in detail.

Method: The interacting boson model will be employed to calculate ${\rho }^2\left(E0\right)$ values for selected key transitions and to investigate the evolution of these observables across the parameter space of the model.

Results: Several key ${\rho }^2\left(E0\right)$ quantities, either absolute values or ratios, are analyzed, and contour plots are generated within the parameter space of the interacting boson model, represented by the Casten triangle. The calculated results for even-even Xe isotopes are then mapped onto and compared with these contour plots.

Conclusions: The present analysis demonstrates that the ${\rho }^2\left(E0\right)$ values, and in particular specific ratios, provide stringent constraints on the parameter space of the interacting boson model. Furthermore, there exist regions of this parameter space in which the ${\rho }^2\left(E0\right)$ values are effectively invariant under fine tuning of the Hamiltonian parameters and, hence ${\rho }^2\left(E0\right)$ cannot be used to constrain the parameters.

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• Electromagnetic transitions
• Energy levels
• Nuclear radii
• 90 ≤ A ≤ 149
• Models based on symmetries