The g-factor of highly charged ions

Highly charged ions provide a unique opportunity to test our understanding of atomic properties under extreme conditions: The electric field strength seen by an electron bound to a nucleus at the distance of the Bohr radius ranges from 10¹⁰ V/cm in hydrogen to10¹⁶ V/cm in hydrogenlike uranium. The theory of quantum electrodynamics (QED) allows for calculation e.g. of binding energies, transition probabilities or magnetic moments. While at low fields QED is tested to very high precision, new, hypothetical nonlinear effects like photon- photon interaction or a violation of Lorentz symmetry may occur in strong fields which then would lead to an extension of the Standard Model. The ultra-high precision determination of the magnetic moment of a bound electron in a highly charged ion provides a unique possibility to probe the validity of the current Standard Model in extreme conditions. (paper)