Other approaches to line shape

To the extent that the dipole induced in a cluster of atoms may be represented by a sum of pair dipoles induced in dissimilar atoms, i and i, fiu, = ft(Rw), we may write for the total dipole ft = Xw Mu - The summation is over all atoms i and all atoms i. The dipole correlation function can then be written as a sum of three parts (Poll 1980), 

The correlation function C2 (r) models the binary interactions. The three-particle function C3 (t) describes the interactions of one atom of one kind with two atoms of the other kind it includes the intercollisional effect. The four-particle function Czj(t) models the correlations between distinct pairs of dissimilar atoms. 

The function G (R, R t) can always be split into two parts that are symmetric and antisymmetric under interchange of Rr and R , respectively. The antisymmetric part does not contribute to C(t) so that we may write 

The correlation functions G are the same functions which Oppenheimer and Bloom introduced in their theory of nuclear spin relaxation [304], The function has been called the time-dependent pair distribution function it should not, however, be confused with the van Hove correlation function which is often referred to by the same name. The name time-dependent intermolecular correlation function (TDICF) has, therefore, been proposed for G [71]. 

Constant acceleration approximation. An approximation introduced to the time-dependent intermolecular correlation function G, which was commonly referred to as the constant acceleration approximation (CAA), was used to compute the line shapes of collision-induced absorption spectra of rare gas mixtures, but the computed profiles were found to be unsatisfactory [286], It does not give the correct first spectral moment. 

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