Prolate-oblate shape-phase transition in the O(6) description of nuclear rotation

Recently it has been shown that the O(6)-based Hamiltonian of the interacting boson model (IBM) with three-body interactions parallels the traditional SU(3) description of nuclear rotation in a way which is closely related to the Bohr-Mottelson model. Here we focus on properties of quantum phase transitions between prolate and oblate ground-state shapes induced by the sign inversion of the cubic interaction. The classical-limit analysis shows that the phase structure of our model is partly analogous to that of the standard IBM with only two-body interactions. A triple point of spherical, prolate and oblate phases is identified within the O(6) dynamical symmetry. Quadrupole shape invariants and wave-function overlaps are applied to measure the phase-transitional rate at a realistic number of bosons