Radiative corrections in highly charged ions and tests of QED in strong electric and magnetic fields

To provide predictions of the Lamb shift of highly charged ions on the level of accuracy of about 10-6 has been achieved after exact results for the contributions of all two-photon self-energy diagrams have been performed. We report on the present status of our Lamb-shift calculations including all QED-corrections of first- and second-order in the fine-structure constant α and all relevant nuclear effects. An excellent agreement between the most recent experimental data for Lamb shift of the 1s-ground state in hydrogenlike uranium can be stated. This can serve as a sensitive test of QED in the strongest electric fields accessible in nature. In a second part of this article we report about an all-order numerical evaluation of the one-photon selfenergy at low nuclear charge (Z = 1,.., 5). A sensitive comparison of our numerical approach with analytical approach to the one-photon selfenergy confirms the consistency of these two different approaches (numerical and analytic) to very high precision. (orig.)