Abstract
The MCDF-EAL method is shown to be closely related to the procedure used to solve the Bethe-Salpeter equation by Douglas and Kroll (1974) in their study of helium 3P fine structure. The authors interpret the former as a method based on a well defined effective Hamiltonian derived from QED which yields a solution within a finite set of CSF which is exact to all orders of perturbation theory. This interpretation allows one to examine the contribution of higher-order terms in the perturbation series for 23P in helium-like F VIII, 1s2p2 4P levels in the lithium isoelectronic sequence and 1s22s22p2 3P levels in the carbon isoelectronic sequence. These terms are shown to be essential if the theoretical predictions are to match the precision obtainable in current experiments. In the case of the carbon sequence, the authors identify discrepancies due to missing (non-relativistic) correlation contributions, and show how these may be taken into account in some cases.
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