Quadrupole shape invariants in the interacting boson model

In terms of the interacting boson model (IBM), shape invariants for the ground state, formed by quadrupole moments up to sixth order, are studied in the dynamical symmetry limits and over the whole structural range of the IBM-1. The results are related to the effective deformation parameters and their fluctuations in the geometrical model. New signatures that can distinguish vibrator and γ-soft rotor structures, and one that is related to shape coexistence, are identified.