Expansion of the Spectrum in Powers of the Density in the Adiabatic Theory of Pressure Broadening

Abstract

Within the framework of the adiabatic theory of pressure broadening, an expansion of the spectrum in powers of the density is obtained by making use of a technique of local averaging in the time domain. The first term of the expansion, $I_c\left(\omega \right)$, is essentially the impact distribution; the second term is $n{J}_w\left(\omega \right)$ folded into $I_c\left(\omega \right)$, where $J_w\left(\omega \right)$ is the wing of the one-perturber distribution, that is, the intensity distribution obtained if there is only one perturbing atom interacting with the radiating atom. Higher-order terms are successive convolution powers of $n{J}_w\left(\omega \right)$, all folded into $I_c\left(\omega \right)$. The expansion should be useful mostly for understanding and predicting qualitative features of the spectrum. In particular, the results imply that structure in the wings, such as satellite bands, is broadened and shifted in the same way as the line center under increasing pressure, in agreement with experimental observations.