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Abstract An approximate description of a many-electron atom can be given by considering each electron to be in a stationary state in a suitable central field, and a method of calculating the wave functions of the different electrons, based on this description, has been developed by one of us. Further, in developing the theory of complex spectra Slater has shown how to calculate approximate energies from such a set of one-electron wave functions in many cases, including a number in which more than one electron is in an incomplete group, so that a given distribution of electrons among the different groups gives rise to a number of different stationary states. The object of the work described in this paper is firstly the calculation of one-electron wave functions for the normal electron arrangements of O+++, O++, O+ and neutral O; secondly the use of Slater’s results (slightly extended) and method for the calculation of the total energies of the various stationary states arising from the normal electron arrangements, and hence of the ionisation energies of those states; and thirdly the comparison with observation both of the absolute values of the ionisation energies so calculated (which correspond directly with the energies derived from the spectrum terms), and of the energy differences between the different terms arising from each electron arrangement (inter-multiplet separations).
Hartree et al. (Wed,) studied this question.