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 2-3 2 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 S~ ground state to a 1 2~ state. Formulae are also found for the transitions 1 2-3 n, x 2-3 A when the triplet state comes under either of Hund's cases (a) or (b). T HEORETICAL investigations of intensities in electronic bands havehitherto dealt with transitions between states of the same multiplicity. Certain bands are however known from their structure to be due to "intersystem" combinations between terms of different multiplicities. In this paper only singlet-triplet combinations are considered, since all inter-system bands so far described are of this kind.The proof of the selection rule for molecular spectra that only terms of like multiplicity combine depends on the possibility of separating the wave function of any state of the stationary molecule into the product of two factors, one depending on the orbital motions, and the other on the electron spins. This separation can be made only when the orbit-spin interaction is negligibly small; the effect of the interaction will be to modify the wave functions in such a way as to permit inter-system transitions of small intensity. In the analogous case of intercombinations between singlet and triplet terms in an atom with two electrons 1 it is necessary to solve this perturbation problem completely before the intensities can be calculated. The molecular problem is simpler in that for our purpose the perturbation problem need not be completely solved, nor indeed would this be possible without definite knowledge of the complete molecular wave functions. We are here concerned with the way in which the intensities depend on the rotation quantum number J for a given electronic transition, and not, as in the atomic case, with the intensities of different electronic transitions. STATIONARY MOLECULEElectronic orbital wave functions. The position of an electron with respect to the molecule with nuclei held fixed is specified by Cartesian coordinates 1 W. V, Houston, Phys. Rev. 33, 297 (1929). 806

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