Extension of the Theory of Complex Spectra

This paper extends the tabular and formular material of the theory of complex spectra to configurations involving $f$ and $g$ electrons. In making these computations it was found that in practically every case significant simplification could be made over the methods previously used. In particular, for the computation of the electrostatic energies for two-electron-like almost-closed-shell configurations a simple closed formula was found which entirely replaces the previous lengthy diagonal-sum calculation. The explicit content of the paper is best exhibited by listing the section headings: I. Extension of Tables of $c^k$, $b^k$, and $a^k$ to $\mathrm{gp}$, $\mathrm{gd}$, $\mathrm{gf}$, $\mathrm{gg}$. II. Explanation of the Regularities in the Electrostatic Energies of Two-Electron Configurations and Formulas for $\mathrm{gp}$, $\mathrm{gd}$, $\mathrm{gf}$, $\mathrm{gg}$, $g^2$. III. Formula Determining the Electrostatic Energies of Two-Electron-Like Configurations with Almost-Closed Shells. Values for $p^{5}g$ and $d^{9}g$. IV. Matrices for Transformation of $\mathrm{pf}$, $\mathrm{df}$, $\mathrm{pg}$, $\mathrm{dg}$ from $\mathrm{LS}$ to $\mathrm{jj}$ Coupling. V. Matrices of Electrostatic Interaction in $\mathrm{jj}$ Coupling for $p^{5}f$, ($d^{9}p$), $d^{9}d$, $d^{9}f$, $d^{9}g$.