A Dynamical Model for Complex Atoms

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Abstract
Following out the ideas of Hund and others on complex spectra, and of Goudsmit and Uhlenbeck on the spinning electron, a model for a complex atom is set up, consisting of electrons whose intrinsic and orbital angular momentum vectors act on each other with torques whose energies are proportional to the cosines of the angles between. The dynamical equations of this model are solved and the quantum conditions are applied. These agree with the quantum conditions previously set up empirically, as far as those go, but also yield new quantum numbers relating to the orientation of electrons. The formula for the energy in terms of the quantum numbers is set up. This is not only in qualitative agreement with what has been previously found, but it furnishes an explanation of inverted multiplets, of the fact that relativity doublets follow the same formula as alkali doublets but are inverted, and of the fact that doublets and triplets both fit on the same "relativity" doublet curve.

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