A near-wing correction to the quasistatic far-wing line shape theory

Abstract

A new representation is introduced in which the rapidly varying time-dependent part of the time displacement operator can be factored out and the remaining part, which varies with time more slowly, can be expanded in the usual perturbational fashion. The lowest order approximation leads to the far-wing quasistatic line shape theory developed previously, whereas the next order approximation, related to the noncommutation of the Liouville operators describing the unperturbed absorber and bath molecules and the interaction between them, leads to a near-wing correction. Explicit expressions are derived for both the corrections to the spectral density and the statistical band-average line shape function assuming an anisotropic dipole–dipole interaction. Detailed computations for the case of self-broadened H2O are carried out for the line-shapes and the corresponding absorption coefficients for several temperatures and for frequencies to 10 000 cm−1. From these results, we conclude that the near-wing corrections generally increase the line shape function between 10 and 200 cm−1, and that this increase is more important for lower temperatures than for higher ones. This in turn leads to increased absorption nearer the band centers, especially for lower temperatures, and thus to improved agreement between theory and experiment.