Abstract
A formally exact perturbation theory with a model potential is developed as a zeroth approximation for atomic systems. A potential of zeroth approximation for a complex system with an arbitrary number of electrons in an open shell and an arbitrary number of vacancies in the core is constructed semiempirically using experimental data for the simplest spectra of one-electron states in an open shell. A field form of perturbation theory is used to calculate energy corrections. Diagrams of the first two orders are considered and an effective summation is performed of diagrams describing major interactions in the system. Energies of all positive Fe ions with open shells n=3 and 4 and one vacancy (1s, 2s, 2p or 3p) are calculated.

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