Tests of quantum electrodynamics with EBIT

A Feynman-diagram-based approach to calculating the spectra of highly charged ions is described and applied to lithiumlike and sodiumlike ions. Discrepancies between calculations excluding the two-loop Lamb shift and experiment allow that shift to be determined, as the accuracy of EBIT experiments is well below the size of the effect. The present status of the theory of hyperfine splitting is described, where a large quantum electrodynamics (QED) effect is made difficult to observe because of nuclear physics uncertainties. The importance of a correct treatment of nuclear recoil at present levels of accuracy is stressed, and prospects for a full QED treatment of copperlike ions are discussed.