Studies on the goodness of IBA group symmetries. I. Centroids,widths and partial widths for irreducible representations of IBA group symmetries

We present explicit analytic expressions for the centroids, widths and partial widths of the eigenvalue distribution over an irreducible representation corresponding to various group symmetries of the interacting boson approximation model of Arima and Iachello. As an example we present a study of the goodness of IBA group symmetries for Sm isotopes.