Anomalous Magnetic Moment of a Bound Electron

We study binding corrections to the gyromagnetic factor ge of an electron in hydrogen-like ions. We argue that the leading order binding effects in radiative corrections Δgrad are universal to all orders in α/π and the complete result reads Δgrad = (gfree - 2) · [1 + (Zα)2/6] + Ο (α/π · (Zα)4). The theoretical uncertainty in the prediction for the experimentally interesting carbon ion is decreased by a factor of about 3