Van Vleck-Weisskopf model

Faced with these difficulties, we shall presently illustrate that if a generalization of the Klein-Kramers equation, first proposed by Barkai and Silbey [30], where the fractional derivatives do not act on the Liouville terms, is used, then the desired return to transparency at high frequencies is achieved. Moreover, the Gordon sum mle, Eq. (85), is satisfied. In conclusion of this subsection, we remark that the divergence of the integral absorption is not unusual in models that incorporate inertial effects. For example, in the well-known Van Vleck-Weisskopf model [88], the divergence results from the stosszahlansatz used by them, just as in the present problem. 

Significantly they showed that the spectral profile of the water line could be accurately described by the van Vleck-Weisskopf model (Equation 1.36), indicating guidelines for the fitting of spectral profiles to other absorbers in a mixture. This would permit their deconvolution from the rest of the spectrum, spectral profile area measurement and hence analyte quantification. 

Fig. 10 Comparison of the functions n((ji)) and n(a))k(u)) with the real and imaginary parts of the complex susceptibility. The lines give experimental data while the prints give values calculated using a Van Vleck/Weisskopf model. (Reproduced by permission from J. Phys. Chem. 70, 1536, (1966)).

---