Application of the Dirac Vector Model to thed4Configuration

Formulae for the energies of multiplets belonging to $d^4$ are computed by the use of the vector model as developed by Van Vleck and Serber. Since insufficient data were available for $d^4$, the configuration $m{d}^4\mathrm{ns}$ was used to check the formulae against experiment. Even here the data are rather meager. In order to obtain out of the above configuration the proper energies of the multiplets arising from $d^4$ alone, it was necessary to subtract from it the exchange energy between the $s$ electron and the $d^4$ "core." The agreement with experiment is, at best, only fair, perhaps because of perturbations from neighboring levels.