Quantum Electrodynamics of Highly Charged Ions

Abstract

Quantum electrodynamics (QED) provides a relativistic description of highly charged few-electron atomic systems. Despite inherent problems associated with renormalization the predictions of bound-state QED can be tested to very high precision by measurements of the Lamb shift of electron levels in highly charged ions. Dominant corrections to the energy spectrum are due to the finite nuclear size and to QED effects: self energy and vacuum polarization of the order of α, where α is the fine-structure constant. Both radiative corrections have to be evaluated to all orders in Zα in the interaction with the external Coulomb potential to achieve agreement with Lamb shift data for a hydrogen-like system measured with a relative precision of about 10−4. (Here Z is the nuclear charge number.) Aiming at the utmost experimental precision, it becomes essential to determine the level of accu racy at which one is leaving the framework of pure QED. The natural limitation for testing QED is set by nuclear polarization effects and by the uncertainties of nuclear parameters. In heavy systems nuclear structure becomes non-negligible at the level of relative precision of about 10−6. To provide predictions for the Lamb shift taking into account this ultimate standard requires the exact evaluation of all QED radiative corrections of order α2. This brief review is focused on QED of hydrogen-like systems. Particular emphasis is laid on the exact evaluation of the self-energy and vacuum-polarization correction as well as on the influence of nuclear effects. For hydrogen-like lead and uranium we discuss the current status of Lamb shift predictions.