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)−β2,X(5)−β4, 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 geometricmodels coincide with IBA parameters consistentwith the phase/shape transition region of the IBA for boson numbers of physical interest (close to 10). 186Pt and 172Os are identified as good examples of X(3), while 146Ce, 174Os, and 158Er, 176Os are identified as good examples of X(5)−β2 and X(5)−β4 behavior, respectively