Anomalous magnetic moment of the positronium ion

We determine the gyromagnetic factor of the positronium ion, a three-body system consisting of two electrons and a positron, including first relativistic corrections. We find that the g-factor is modified by a term -0.51(1)alpha^2, exceeding 15 times the alpha^2 correction for a free electron. We compare this effect with analogous results found previously in atomic positronium and in hydrogen-like ions.