Theory of spectral line shape. I. Formulation and line coupling

Abstract

A theoretical expression for spectral line shape, applicable to the conditions for atmospheric infrared transmission, is derived. The theory is based on a previously derived kinetic equation for the density matrix for a system of absorbing molecules, in a thermal bath. An iterative solution for the linearized kinetic equation is developed as a density expansion about an isolated line approximation, based on Fano’s frequency-dependent collision operator. The absorption coefficient is determined by the application of linear response theory, together with the fluctuation-dissipation theory and detailed balance. The isolated line shape has non-Lorentzian wings due to frequency dependent shift and width parameters. New expressions are found for the line coupling terms, which depend on the line strengths of coupled lines as well as their width and shift parameters.