  Using all the available empirical information, we analyse the spacing
distributions of low-lying 2+ levels in even-even nuclei by comparing them with
a theoretical distribution characterized by a single parameter (the chaoticity
parameter f). We use the method of Bayesian inference. We show that the
necessary unfolding procedure generally leads to an overestimate of f. We find
that f varies strongly with the ratio of the excitation energies of the first
4+ and 2+ levels and assumes particularly small values in nuclei that have one
of the dynamical symmetries of the Interacting Boson Model.
