Intensities in Singlet-Triplet Bands of Diatomic Molecules

Abstract

Intensity formulae are found for the rotational structure of bands arising from transitions between a singlet and a triplet state of a diatomic molecule. These intercombinations occur because the wave functions which diagonalize the orbit-spin interaction contain both singlet and triplet terms. In the transition $^{1}\ensuremath{\Sigma}\ensuremath{-}^{3}\ensuremath{\Sigma}$ two cases arise, according as the two states have the same or opposite symmetry as regards reflection of the orbital motions in a plane containing the nuclei, a different set of branches appearing in either case. A comparison is made with measurements of intensities in the atmospheric absorption bands of oxygen; the agreement is satisfactory on the assumption that these bands are due to dipole transitions from the $^{3}\ensuremath{\Sigma}^{\ensuremath{-}}$ ground state to a $^{3}\ensuremath{\Sigma}^{\ensuremath{-}}$ state. Formulae are also found for the transitions $^{1}\ensuremath{\Sigma}\ensuremath{-}^{3}\ensuremath{\Pi}$, $^{1}\ensuremath{\Sigma}\ensuremath{-}^{3}\ensuremath{\Delta}$ when the triplet state comes under either of Hund's cases (a) or (b).