The question of the reasonable form of a line intensity distribution function for representation of molecular spectra is discussed. A distribution function which is proportional to 1/S in the low-intensity region is shown to be reasonable on a physical basis. A curve of growth is obtained for a continuous distribution of Lorentz lines which is proportional to 1/S, but cut off at a small value of S and decreases exponentially for large S to permit normalization. The limiting curve of growth for no cutoff (i.e., for a continuous exponential-tailed 1/S intensity distribution for O <S < ∞) is found to be a simple, conveniently handled expression. A comparison is made with the curve of growth presented by Godson for a distribution proportional to 1/S up to a maximum S and zero above. A comparison is also made with the curve of growth for a model with a discrete 1/S distribution (consisting of lines whose intensities are in geometric progression), which is calculated numerically from existing tables of the Ladenburg—Reiche function for several values of the intensity ratio. Criteria for the applicability of the curves of growth for the 1/S models are discussed; the curve developed here and the Ladenburg—Reiche curve form (approximate) lower and upper limits, respectively, to the curve of growth for any physically reasonable band model consisting of Lorentz lines.
W. MALKMUS, "Random Lorentz Band Model with Exponential-Tailed S-1 Line-Intensity Distribution Function," J. Opt. Soc. Am. 57, 323-329 (1967)