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 X(5) model and the predictions of the interacting boson approximation near the critical point of the first order phase transition is explored.

• Received 28 February 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.022501