Dipole autocorrelation function for molecular pressure broadening: A quantum theory which satisfies the fluctuation-dissipation theorem

Abstract

The dipole autocorrelation function for spectral line broadening is treated in a quantum theory which rigorously satisfies the fluctuation-dissipation theorem on a microscopic level. The basic approximation in the theory is the binary-collision approximation. In the present paper, the two-body interaction is decomposed into one part which commutes with the internal coordinates and another part which does not. The theory, as developed, is appropriate for broadening mechanisms for which the noncommuting term may be treated within the framework of perturbation theory, while the commuting term is to be treated exactly. The theory gives, at long times, a result for the dipole autocorrelation function consistent with the well-known impact approximation. At short times, an autocorrelation function of Gaussian form, with renormalization of the initial-state occupancy is obtained. It is found that the qualitative features discussed above are unaltered in higher-order perturbation theory. The results are consistent with the requirement that all time derivatives of the autocorrelation function at $t=0$ exist. This further satisfies the requirement that all moments of the line-shape function in the frequency domain exist, hence that the line-shape function decays "exponentially" sufficiently far in the wings.