Algebraic benchmark for prolate-oblate coexistence in nuclei

We present a symmetry-based approach for prolate-oblate and spherical-prolate-oblate shape coexistence, in the framework of the interacting boson model of nuclei. The proposed Hamiltonian conserves the SU(3) and SU(3) symmetry for the prolate and oblate ground bands and the U(5) symmetry for selected spherical states. Analytic expressions for quadrupole moments and E2 rates involving these states are derived and isomeric states are identified by means of selection rules.