THE FREQUENCY DETUNING AND BAND-AVERAGE APPROXIMATIONS IN A FAR-WING LINE-SHAPE THEORY SATISFYING DETAILED BALANCE

We develop the basic formalism of a far-wing line shape theory that sa tisfies the detailed balance principle. For molecular systems of inter est, e.g., CO2-Ar at room temperature or higher, there are many indivi dual vibration-rotational lines in a given band and many bands in the spectrum. In such cases, one must make additional approximations in or der to carry out accurate calculations of the absorption coefficient u sing a reasonable amount of computer time. In the present paper, we di scuss two such simplifications: the frequency detuning approximation o f the line-coupling functions and the band-average approximation. We t hen apply the theory to a calculation of the far-wing absorption of th e nu(3) band of CO2 perturbed by Ar, successively including the effect s of more lines in the calculations by increasing J(max) from 40 to 10 8, From the results of this work, we find that the frequency detuning approximation is good only for frequencies of interest far from the ba nd center. In addition, we find that contrary to previous assertions o f the adequacy of the first-order band-average approximation, the high er-order terms are significant. To a good approximation these can be i ncorporated by introducing a frequency shift in the first-order result s so that extensive additional calculations are not required. (C) 1996 American Institute of Physics.