A Method for Improved Calculation of Energies of Two-Electron Configurations from Hartree Functions Application to2p2Terms in O III

A generalization of the method of the self-consistent field for two-electron configurations previously given by the author has now been simplified and improved in two ways. Firstly, it is now assumed that the radial functions are identical with the Hartree functions (or with simpler approximations to these), so that a considerable saving in labor results. Secondly, the core electrons are taken account of more accurately than in the original method. The final results are in general only valid if the valence electrons are equivalent or if the difference in their azimuthal quantum numbers exceeds two; they do not involve a great deal of computation once the Hartree functions are known. Numerical calculations have been made for the normal state of helium (as a test of the method) and for the $2p^2$ terms of O III. The improvement obtained with the present method, while not great, is significant; in particular, the separation ratio for the O III terms is markedly improved.