Electronic States and Band Spectrum Structure in Diatomic Molecules. IV. Hund's Theory; Second Positive Nitrogen and Swan Bands; Alternating Intensities

After a brief review of Hund's theory of molecular electronic states and band spectra, and a discussion of intensity relations and selection principles in terms of the correspondence principle, it is shown that practically all the available evidence, as embodied in previous papers of this series and elsewhere, is in agreement with the theory. The occurrence of $\rho$-type $S$ terms and $\sigma$-type $P$ and $D$ terms is explained by the theory, as also the existence of $\rho$-type and $\sigma$-type doubling. Selection rules and other relations in ${}_{}{}^2{}_{}{}^{}P\to {}_{}{}^2{}_{}{}^{}S$ and ${}_{}{}^2{}_{}{}^{}S\to {}_{}{}^2{}_{}{}^{}P$ transitions (including, in agreement with Mecke and Hulthén, the CH, OH, MgH, and CaH bands) are discussed. Hund's interpretation of the second positive nitrogen bands as a ${}_{}{}^3{}_{}{}^{}P\to {}_{}{}^3{}_{}{}^{}P$ transition is further developed, and extended to the Swan bands; the apparent absence of $Q$ branches, and other intensity relations in these bands, are explained; the rotational doubling in these bands (accompanied by alternating intensities) is interpreted as $\sigma$-type doubling. It is shown that the alternating intensities or alternate missing lines in the ${\mathrm{He}}_2$, ${\mathrm{N}}_2$, Swan, and ${\mathrm{N}}_2^{+}$ bands can all be accounted for formally by the postulate that they are due to alternate (partially or completely) suppressed levels such that the suppressed values of ($j_k-{\sigma }_k$) are always as follows: $B$ rotational sub-states, $(j-\frac{1}{2}-{\sigma }_k)=0, 2, 4, \cdots$; $A$ sub-states, 1, 3, 5,...; here ${\sigma }_k$ is the part of $\sigma$ which is due to the orbital angular momentum of the electron, and $j_k$ is the resultant of ${\sigma }_k$ and the quantity $m$ which measures the nuclear angular momentum in quantum units.—Finally, the questions of term-notation and -formulation, $j$ values for odd and even molecules, etc., are considered. The NH $\beta$ bands (${}_{}{}^3{}_{}{}^{}P\to {}_{}{}^3{}_{}{}^{}S$) are briefly discussed.