Quadrupole Rotation-Vibration Spectrum of H_{2}

Abstract

The theory of the quadrupole radiation of homonuclear diatomic molecules is de- veloped for the case of transitions between `»=~ states. The results are applied in a theoretical treatment of the rotation-vibration spectrum of H2, which, as Herzberg has suggested, may be observable in the absorption spectra of planetary atmospheres. The quadrupole moment of the system is computed as a function of the nuclear separation by the use of electronic wave functions obtained by a variational process. Matrix ele- ments of this quantity are calculated, using the vibrational functions of the Morse and Pöschl-Teller potential-curves. Absolute values are found for the Einstein absorption coefficient B for fundamental, first, and second overtone bands, and are compared with the corresponding quantities for the dipole spectrum of HC1. It is found that the first and second overtone bands have intensities in the ratios 0.91 and 0.19, respectively, to that of the fundamental, and that, while this is an exceptional case, one should, in general, expect the ratios to be higher in quadrupole than in dipole bands