Line Strengths in Intermediate Coupling

The sum rules applicable to intermediate coupling are discussed in §1; in §2 proofs are given for two which are essentially new: the $J$-file sum rule which states that for any coupling, in a transition array in which the jumping electron is not equivalent to any electron in the ion in either the initial or final configuration, the sum of the strengths of the lines originating in (or terminating on) a common level of quantum number $J$ is proportional to $2J+1$; and the $J$-group-file sum rule which says that for any transition array of this type in which the valence electron jumps from $s$ to $p$ or $p$ to $s$, the individual $J$-groups may be split up in one direction into invariant files. The dispersion measurements of Ladenburg and Levy on the neon transition array $2p^{5}3p\to 2p^{5}3s$ furnish in §3 an interesting experimental verification of these rules. The predictions of the usual first-order quantum-mechanical theory regarding the line strengths in this neon array are investigated in §4. It is concluded that this approximation does not enable the eigenfunctions to be determined with sufficient accuracy from the observed energy levels for quantitative intensity predictions.