0+ states in the large boson number limit of the Interacting Boson Approximation model

Studies of the Interacting Boson Approximation (IBA) model for large boson numbers have been triggered by the discovery of shape/phase transitions between different limiting symmetries of the model. These transitions become sharper in the large boson number limit, revealing previously unnoticed regularities, which also survive to a large extent for finite boson numbers, corresponding to valence nucleon pairs in collective nuclei. It is shown that energies of 0n+ states grow linearly with their ordinal number n in all three limiting symmetries of IBA [U(5), SU(3), and O(6)]. Furthermore, it is proved that the narrow transition region separating the symmetry triangle of the IBA into a spherical and a deformed region is described quite well by the degeneracies E(02+) = E(61+, E(03+) = E(101+), E(04+) = E(141+, while the energy ratio E(61+)/E(02+ turns out to be a simple, empirical, easy‐to‐measure effective order parameter, distinguishing between first‐ and second‐order transitions. The energies of 0n+ state...