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

Regularities and symmetries of subsets of collective 0+ states