Multiplet Separations

Formulas for the separations of normal multiplets, arising from general configurations, are derived by reasoning from the fundamental assumption that they are due to the interaction energy between spin and orbital magnetism of the electrons. The separations are known for multiplets arising from groups of equivalent electrons, from considerations given in the preceding paper. It is shown in this investigation, by a simple treatment of the vector model, that the interaction energy for other configurations may be found in terms of that of the equivalent group and the interaction energy of the electron or group of electrons added, provided the quantum vectors of the original configuration remain unchanged. Our treatment applies only to multiplets showing reasonably close agreement with the interval rule, and which are therefore accounted for by the Russell-Saunders coupling. Examples given for illustration are taken from data on Fe and ${\mathrm{O}}^{+}$. Calculated results indicate the validity of our formulas to the extent permitted by agreement of data with the interval rule.