Electronic States and Band Spectrum Structure in Diatomic Molecules VI. Theory of Intensity Relations for casebDoublet States. Interpretation of CH Bandsλλ3900, 4300

Abstract

Theoretical intensity equations (Eqs. 8-22 of text) are obtained by means of the summation rule for all possible branches (including "main" and "satellite" branches) in transitions between doublet electronic states falling under Hund's case $b$. A revised notation is proposed, applicable to all known bands and capable of simply describing any band line, for any type of multiplicity. The energy differences between $F_1$ and $F_2$ terms ($s$ parallel or antiparallel to $j_k$ in case $b$) are considered qualitatively for a series of cases between case $a$ and case $b$, for normal and inverted doublets (cf. Fig. 1); with normal doublets, as is shown elsewhere in detail by Kemble, a special case is possible in which $s$ is oriented nearly as $\pm \epsilon$, while $\sigma \sim {\sigma }_k$, for all but the lowest values of $j$, so that the Kramers and Pauli formula should hold rather accurately; it is concluded that the ${}_{}{}^2{}_{}{}^{}P$ common final state of $\mathrm{CH}\lambda \lambda 3900$ and 4300 is an example of this case.