We present a detailed theoretical evaluation for the g j factor of a bound electron in hydrogenlike ions up to Zϭ94. All quantum electrodynamical corrections of order (␣/) are evaluated in detail and various other contributions to the g j factor are computed and listed for 61 Z. A comparison with all existing experiments is carried out and excellent agreement is found. The present uncertainty in our calculations is discussed. It is not possible to improve this precision with only minor effort since two-photon bound-state QED terms are uncalculated up to now.

In view of the current interest of QED in strong fields, a complete set of one-photon radiative corrections to the bound-electron g factor is evaluated for several hydrogenlike ions. The calculations are performed to all orders in the nuclear potential and compared to earlier results, based on the (Z␣) expansion, which includes the Schwinger and the Grotch terms. For low Z our all-order result approaches the (Z␣) expansion, but for high Z there is a substantial deviation. Furthermore, for high Z our calculations show that the uncertainty due to nuclear structure is small and thus strongly motivate the bound g-factor experiment in progress. ͓S1050-2947͑97͒50410-0͔

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A numerical scheme for evaluating the part of the one-photon vacuum-polarization effect not accounted for by the Uehling potential (the Wichmann-Kroll eKect) is presented. The method can be used with an arbitrary atomic model potential describing the bound electrons. Benchmark results for this effect are presented for hydrogenlike levels using a uniform nuclear-charge distribution. The effect of direct and exchange electron screening on the vacuum polarization are discussed in connection with the accurately measured 2pzyz-2szf 2 transition in lithiumlike uranium.PACS number(s): 31.10.+z, 31.20.Di, 31.30.Jv