The collision induced spectroscopies: Concerning the desymmetrization of classical line shape

Classical spectral line shapes are symmetric and easy to compute. Measured broad profiles, on the other hand, are asymmetric (principle of detailed balance) and can be reproduced from a much more involved quantum theory. Various desymmetrization procedures are known which, when applied to classical profiles, result in a line shape that is formally consistent with the asymmetry required by detailed balance. It is an interesting fact that various desymmetrization procedures known give rise to very different profiles. Little is known about which (if any) results in a simple but accurate substitute for the quantum shape. An ab initio quantum calculation is in close agreement with a measurement of the binary collision induced, translational Raman spectrum of helium at 30 amagat. To a classical line shape based on the same input, four common desymmetrization procedures are applied. The comparison shows that the Egelstaff procedure simulates the quantum profile most closely and should have broad applications in the collision induced infrared and Raman spectroscopies, especially in the dense state where quantum line shape computations do not exist. A modification of the classical pair correlation function allows the computation of spectral 0th to 2nd moments which agree with the quantum moments to third order in a series expansion in powers of Planck's constant.