New signature of a first order phase transition at the O(6) limit of the IBM

Shape invariants within the interacting boson model are used to describe the γ deformation of the ground state and 02+ state along the β-rigid leg of the extended Casten triangle between the symmetry limits SU(3) and SU(3)̄ via the O(6) limit. Similarly to the recently discovered β-deformation crossing of the ground state with the 02+ state between the symmetry limits U(5) and SU(3), a crossing of those states with respect to the γ deformation is observed between SU(3) and SU(3)̄. The newly introduced order parameter K3(01+)-K3(02+) shows a peaking behavior at O(6), which is a signature of a first-order phase transition and is observed at O(6) for the first time. Comparison with existing data and experimental prospects for measuring this signature are presented and differences and similarities between spherical-deformed and prolate-oblate first-order phase transitions are discussed.