Energy Relations in Complex Spectra

Abstract

The manner in which the energy levels of extreme ($\mathrm{jj}$) coupling are split up by interaction of the electrons is calculated, and the results serve in special cases to determine energies in the condition intermediate between ($\mathrm{jj}$) and ($\mathrm{LS}$) coupling. Single-electron wave functions appropriate to large spin-orbit interaction are selected, and antisymmetric atomic wave functions are formed of them. With these the diagonal elements of the matrix of electrostatic interaction are reduced to combinations of radial integrals, the same integrals met by Slater in ($\mathrm{LS}$) coupling. Some configurations have only one such radial integral to express electrostatic interaction. It serves as a parameter in the extension to intermediate coupling by a method of Goudsmit. Coefficients in the general equation for the energies are determined by the energies in extreme couplings. Knowledge of electrostatic energies in ($\mathrm{jj}$) coupling, as here calculated, extends the applicability of the method to configurations having three states with the same angular momentum.