A method is developed for calculating the energy of a definite state of an N-electron system. The method uses a form of the Bethe–Goldstone equation to calculate the correlation energy of an interacting electron pair moving in the nuclear Coulomb field and in the average field of the other electrons. A calculation on the ground state of the lithium atom gives an energy which differs from the accurate value by less than 0.1%.
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W. R. Conkie (1965) studied this question.
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