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

A method for the solution of the pair equation, by summation over a complete and finite basis set, is presented. The basis set is obtained by diagonalization of a discretized Hermitian one-particle Hamiltonian. The number of operations required to solve the radial pair equation is proportional to N where N is the number of radial lattice points used. An application to the ground state of helium, evaluating the total energy to an accuracy of a few parts in 10, is presented. The method is equally well applicable to the study of pair correlation in many-electron atoms.

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