A survey is made of the varied empirical structure-types to be expected for ${}_{}{}^2{}_{}{}^{}P\to {}_{}{}^2{}_{}{}^{}S$ and ${}_{}{}^2{}_{}{}^{}S\to {}_{}{}^2{}_{}{}^{}P$ bands, and examples of these types are discussed individually. In agreement with Kemble's theory, the arrangement of the rotational levels in the ${}_{}{}^2{}_{}{}^{}P$ state changes continuously with the parameter $\frac{\Delta E}{B}$ ($\Delta E=\mathrm{electronic}\mathrm{doublet}\mathrm{separation}$), and these changes are responsible for a large part of the observed variations in band structure. Fig. 1 and Table I show how the arrangement of the ${}_{}{}^2{}_{}{}^{}P$ levels changes with $\frac{\Delta E}{B}$, and Figs. 2-5 show, for the MgH, OH, HgH, and NO $\gamma$ bands, how observed branches are related to energy levels. In Table II, data on $\Delta E$ and $B$ are listed for a number of molecules. The mode of variation of the arrangement of the rotational levels in ${}_{}{}^2{}_{}{}^{}P$ states appears to be in striking agreement with the quantitative formulas of Hill and Van Vleck. For example, if $\frac{\Delta E}{B}=+2\mathrm{}$, their equation becomes formally identical with the Kramers and Pauli formula which holds exactly for the ${}_{}{}^2{}_{}{}^{}P$ state of CH.

A consistent notation, as proposed in VI of this series, is given here for the known branches of the MgH, CaH, OH, ZnH, CdH, HgH, and NO bands; this notation has already been applied to the OH and BO bands (Kemble, Jenkins) and to CH $\lambda 3900$. A more or less detailed discussion is given of the spectra mentioned, especially MgH and OH; some term values are given for ${}_{}{}^2{}_{}{}^{}P$ and ${}_{}{}^2{}_{}{}^{}S$ states of MgH, CaH and OH.

In the bands just mentioned, band-structure and missing lines show good agreement with theory. In the cases where $\left|\frac{\Delta E}{B}\right|$ is small for the ${}_{}{}^2{}_{}{}^{}P$ state (CH, MgH) there is agreement with the case $b$ intensity theory (six main branches, four weak satellite branches). As $\left|\frac{\Delta E}{B}\right|$ increases, the satellite branches get stronger, and two new branches become evident. This tendency first appears distinctly in OH, where the satellite branches, although very weak, are much too strong for Hund's case $b$, and where a previously unclassified very weak branch is found to be one of the two new branches just mentioned. As $\left|\frac{\Delta E}{B}\right|$ increases still further, the six weak branches finally become equal to the other six in intensity. This metamorphosis has also been discussed by Hulthén. The observed relations, in particular the equality of intensity of the six "weak" and the six "strong" branches when $\left|\frac{\Delta E}{B}\right|$ is very large, appear to be in excellent agreement with the quantitative intensity formulas of Hill and Van Vleck.

A conclusion of interest for the empirical study of ${}_{}{}^2{}_{}{}^{}P\to {}_{}{}^2{}_{}{}^{}S$ and ${}_{}{}^2{}_{}{}^{}S\to {}_{}{}^2{}_{}{}^{}P$ bands is the following: in four-headed bands of these types the first head should always be weaker than the rest unless $\left|\frac{\Delta E}{B}\right|$ is large, and should disappear if $\left|\frac{\Delta E}{B}\right|$ is near zero.

Intensity relations in ${}_{}{}^3{}_{}{}^{}P\to {}_{}{}^3{}_{}{}^{}S$, ${}_{}{}^3{}_{}{}^{}P\to {}_{}{}^1{}_{}{}^{}S$, and other types of bands are briefly discussed for the case that one electronic state falls under Hund's case $a$, the other under his case $b$; some predictions are made.

• Received 5 June 1928

DOI:https://doi.org/10.1103/PhysRev.32.388