Connecting the X(5)-β2, X(5)-β4, and X(3) models to the shape/phase-transition region of the interacting boson model

The parameter independent (up to overall scale factors) predictions of the X(5)-{beta}{sup 2}, X(5)-{beta}{sup 4}, and X(3) models, which are variants of the X(5) critical point symmetry developed within the framework of the geometric collective model, are compared to two-parameter calculations in the framework of the interacting boson approximation (IBA) model. The results show that these geometric models coincide with IBA parameters consistent with the shape/phase-transition region of the IBA for boson numbers of physical interest (close to 10). Nuclei within the rare-earth region and select Os and Pt isotopes are identified as good examples of X(3), X(5)-{beta}{sup 2}, and X(5)-{beta}{sup 4} behavior.