The Theory ofΣ+3−Σ−3Transitions in Band Spectra

Abstract

G. Herzberg has recently studied certain faint absorption bands in ${\mathrm{O}}_2$ which show $Q$ branches ($\Delta K=0\mathrm{}$) but not the customary $P$ and $R$ branches ($\Delta K=\pm 1$). These bands he attributes on the basis of the configuration theory to a "forbidden" transition ${}_{}{}^3{}_{}{}^{}{\Sigma }_g_{}^{-}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}{\Sigma }_u_{}^{+}{}_{}{}^{}$. There exist two alternative explanations for the occurrence of these bands: (1) spin-orbit interaction, (2) rotational distortion. For the case of spin-orbit interaction the intensities have been calculated in case (a) and transformed to case (b) where the theory predicts twelve branches with $\Delta K=\pm 2,0$, provided that the $J$ structure is resolved. When this structure is unresolved it is found that transitions with $\Delta K=0\mathrm{}$ should be more intense than transitions with $\Delta K=\pm 2$ in the ratios: 6: 1 for $Kė\infty$, 5: 1 for $K=4\mathrm{}$ and 4: 1 for $K=1\mathrm{}$. In view of the faintness of the observed bands this appears to be sufficient to account for the absence of branches with $\Delta K=0\mathrm{}$. With rotational distortion, calculations show that only $Q$ branches will occur. The intensities with spin-orbit interaction vary asymptotically as the first power of $K$, while for rotational distortion they increase asymptotically as $K^3$. Further experiments are needed to decide between the two explanations, although theory would favor the first from considerations of relative intensity. An explanation is given of the non-enhancement of the ${}_{}{}^3{}_{}{}^{}{\Sigma }_g_{}^{-}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}{\Sigma }_u_{}^{+}{}_{}{}^{}$ bands in ${\mathrm{O}}_4$, despite the proximity of the triple-headed ultraviolet bands of Wulf, Finkelnburg and Steiner which we attribute to a ${}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ upper state. Transitions of the type ${}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}\Sigma _{}^{-}{}_{}{}^{}$ are also discussed.