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 ∆grad are universal to all orders in α/π and the complete result reads ∆grad = (gfree − 2) · [1 + (Zα) 2/6] + O ( α π · (Zα)4 ) . The theoretical uncertainty in the prediction for the experimentally interesting carbon ion is decreased by a factor of about 3. Typeset using REVTEX e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] 1 The interaction of an electron with an external magnetic field B is described by the potential V = −μ ·B. (1) The electron magnetic moment μ is μ = ge e 2m s. (2) where m and s = σ/2 denote the mass and spin of the electron and ge is the so-called gyromagnetic or Landé factor. We adopt the convention that e = −|e|. For a free electron, ge is known with very high precision. If an electron is bound in a ground state of a hydrogen-like ion, ge becomes a function of the nuclear charge Z and its measurements provide a sensitive test of the bound-state theory based on the Quantum Electrodynamics (QED). With a novel spectroscopic method precise experiments can be carried out with hydrogen-like ions in a wide range of nuclear charges Z [1–3]. A unique feature of those measurements is that results obtained with different values of Z may be used to rigorously test various bound-state effects [4]. To fully exploit these experimental results, the QED prediction for ge (Z) must be known with comparable precision. At the present level of experimental uncertainty, accounting for the QED interactions (including leading effects of the nuclear recoil) is sufficient; other nuclear effects and weak interactions can be neglected. The theoretical prediction can be cast in the following form [5] ge (Z) = gD +∆grec +∆grad. (3) The first term corresponds to the lowest order expansion in α/π and has been calculated to all orders in Zα [6],