Halogen Molecule Spectra. II. Interval Relations and Relative Intensities in the Long Wave-Length Spectra

Quantum-theoretical expressions are obtained in Section II for energy-intervals among the levels belonging to related ${}_{}{}^3{}_{}{}^{}\mathrm{II}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{II}$ states of any diatomic molecule, for partial $\Omega$, $\omega$ ($J$, $j$-like) coupling. A theoretical expression is also obtained for the relative intensities of spectroscopic transitions from a ${}_{}{}^1{}_{}{}^{}\Sigma$ to the ${}_{}{}^3{}_{}{}^{}\Pi _1^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}\Pi$ states. The effect of partial case $c$ coupling (persistence of separate-atom $J$ quantization) on the foregoing relations is studied in Section III. Equations are obtained which (together with equations of Van Vleck) permit computation of case $c$ displacements of certain energy levels of the halogen molecules. The foregoing relations are applied in Sections IV and V to a refinement of the existing interpretations of the long wave-length absorption spectra of the diatomic halogen molecules (cf. Tables II, III). In the case of bromine, it is found impossible to decide between two alternative interpretations; suggestions are made for further work that could lead to a decision. Information is obtained bearing on the strength of the dissociation continuum overlying the bands in ${\mathrm{Cl}}_2$, ${\mathrm{Br}}_2$, and ${\mathrm{I}}_2$, on the positions of the ${}_{}{}^1{}_{}{}^{}\Pi$ and ${}_{}{}^3{}_{}{}^{}\Pi _{0^{-}u}^{}{}_{}{}^{}$ potential energy curves in ${\mathrm{I}}_2$ and on the cause of magnetic predissociation in ${\mathrm{I}}_2$. The desirability of quantitative measurement of the infra-red continuum of iodine and careful remeasurement of the visible continuum of iodine chloride are mentioned. Two mechanisms (proposed by Van Vleck and the writer) for explaining the remarkably high intensity of the ${}_{}{}^1{}_{}{}^{}\Sigma \to {}_{}{}^3{}_{}{}^{}\Pi _{0^{+}}^{}{}_{}{}^{}$ component in the halogen spectra are examined in Section VI. Both give calculated intensities approaching the observed in order of magnitude. The weak $\lambda 2250$ bromine continuum is discussed in Section VIII; its occurrence and intensity seem to be explainable by a case-$c$-allowed intersystem combination.