Approximation of off-shell scattering operators for non-lorentzian line shape calculations

A previously derived approximation for the matrix elements of the Fano relaxation operator m(ω), which gives rise to non-Lorentzian line wings, is examined. This approximation is expressed in terms of an off-the-energy shell scattering operator. Calculation of this operator by a second-order Born expansion is unsuitable because this procedure limits the radiation frequency dependence to the same order. The main part of this paper is devoted to expressing the off-shell scattering operator in the time-ordered formalism. In this form, a scattering operator approximation suggested by Dillonet al.⁽⁶⁾ can be applied which is not restrictive to the frequency dependence.