Note on Fock Equations for Complex Configurations

Abstract

Fock's equations for a general atomic state are written in terms of the coefficients of Slater's $F\text{'}\mathrm{s}$ and $G\text{'}\mathrm{s}$ in the energy of that state. With the special formulas which are given to take care of the closed shells, this enables the Fock equations to be written down immediately for any desired state. For a complex configuration, in order to obtain one particular set of radial factors to use as a basis for a first-order perturbation calculation, a process is given for obtaining that set of radial factors for which the center of gravity of the configuration is a minimum, for any coupling. Finally, it is shown how equations may be obtained for finding the best radial factors with which to form the eigenfunctions of a given term of a configuration in $\mathrm{LS}$ coupling, and suggested that this may be made the basis of a perturbation theory in which the different types of terms are considered independently.