Theory of Complex Spectra

A method for the calculation of the energy levels of an atom in terms of the experimentally observed energy levels of ions of higher ionization is developed. This method can be applied to a system of nonequivalent electrons, as well as equivalent electrons. The notion of fractional parentage is extended to systems of nonequivalent electrons. Tables of fractional parentage coefficients are calculated for $p^{2}s$, $p^{3}s$, and $d^{2}p$ configurations. Application is made by a least-squares calculation of the $3d^{2}4p$ configuration of Ti ii in terms of the experimentally observed energies of the $3d^2$ and $3d4p$ configurations of Ti iii. As a result, the root-mean-square deviation of our calculated values from the experimental energies is reduced to ±249 ${\mathrm{cm}}^{-1\mathrm{}}$.