The Theory of Complex Spectra

Part I. Calculation of the first order energies for configurations involving almost closed shells. A method is developed for calculating the electrostatic energy matrix for a configuration consisting of a closed shell minus ε electrons plus η other electrons with the same simplicity as for the corresponding configuration consisting of ε+η electrons. One classifies the states according to the quantum numbers of the "missing" and of the added electrons and calculates Slater's integral (J-δK) for each pair of electrons in the usual way except that one attaches a negative sign to an integral connecting a "missing" with an added electron. It is then shown quite generally that the matrices of magnetic interaction are identical in LS coupling for the two configurations mentioned above except for a reversal of sign of the spin-orbit coupling parameter corresponding to the almost closed shell.Part II. On two-electron spectra. It is shown that one is completely justified, when calculating the matrix of magnetic interaction in LS coupling by Johnson's method, in neglecting the equivalence of the two electrons of the atom. Similar results are shown to obtain for the addition of an electron to an ionic multiplet. The method of calculation of the matrix of magnetic interaction between configurations by this method is considered and it is shown that neglect of the equivalence of the electrons in case one of the configurations is composed of equivalent electrons leads to an error of a factor of (2)^. One does not obtain a magnetic interaction between configurations which differ by more than the n value of one electron. This holds quite generally for any type of atom.