  The energies of subsets of excited 0+ states in geometric collective models
are investigated and found to exhibit intriguing regularities. In models with
an infinite square well potential, it is found that a single formula, dependent
on only the number of dimensions, describes a subset of 0+ states. The same
behavior of a subset of 0+ states is seen in the large boson number limit of
the Interacting Boson Approximation (IBA) model near the critical point of a
first order phase transition, in contrast to the fact that these 0+ state
energies exhibit a harmonic behavior in all three limiting symmetries of the
IBA. Finally, the observed regularities in 0+ energies are analyzed in terms of
the underlying group theoretical framework of the different models.
