Models for Spectral Band Absorption*

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Abstract
An exhaustive, theoretical study is made of the various models that have been proposed to represent band absorption. These models are compared with each other; a derivation is given of the regions where they predict the same absorption. The regions of validity for various useful approximations to these models are also given. The statistical model is extended to include the random superposition of a finite number of Elsasser bands. Thus a continuous spectrum of absorption curves is obtained between the results for the Elsasser and the pure statistical models. The absorption predicted by the statistical model when there is a specific number of spectral lines in the frequency interval under consideration is compared with the limit as the number of lines approaches infinity. It is shown that the shape of the absorption curve obtained from the statistical model is independent of the distribution of line intensities in the band for most cases of interest. The absorption from the statistical model including the effects of overlapping is shown to depend only on an average equivalent width for a single line. This result is used to derive the band absorption for the statistical model with Lorentz, Doppler, and other line shapes.