Unified description of 0+ states in a large class of nuclear collective models

A remarkably simple regularity in the energies of 0+ states in a broad class of collective models is discussed. A single formula for all 0+ states in flat-bottomed infinite potentials that depends only on the number of dimensions and a simpler expression applicable to all three interacting boson approximation symmetries in the large N(B) limit are presented. Finally, a connection between the energy expression for 0+ states given by the X5 model and the predictions of the interacting boson approximation near the critical point of the first order phase transition is explored.