The relativistic theory of an atom with many electrons

This paper derives the ordinary classification of multiplets, and the selection and summation rules, from Dirac's relativistic equation. The non-relativistic theory of the inner quantum number j and the magnetic quantum number u , and their selection rules, was worked out for an atom with any number of point-electrons by Born, Heisenberg and Jordan, using matrices, and by Dirac, using q -numbers. The two methods are equivalent, and depend principally upon the properties of the total angular momentum. 2 points out that the total angular momentum has the same properties in the new theory, so that the previous work can be taken over with scarcely any amendment. 3. deals with a selection rule that has received little theoretical attention. The azimuthal quantum number for a single electron is denoted by k , and Σ k is the sum for all the orbits involved in a given state. It is known empirically that Σ k always changes by an odd number. This is the basis of the distinction between S, P, D, ... and S', P', D', ... terms. The rule is proved rigorously in the absence of external fields. A practical consequence is that the O ++ lines of nebular spectra, if rightly identified, can occur only in electric or non-uniform magnetic fields, for they have ∆Σ k = 0.