Theory of spectral line shape. II. Collision time theory and the line wing

Abstract

In this second part of a theory on spectral line shapes, applicable to conditions of atmospheric transmission, a means of evaluation of the frequency dependence of the collision operator is developed. An extension of formal scattering theory relates the off-the-energy shell matrix elements of the transition operator to their on-shell values through an operator Φ which is a function of the energy increment, a collision time operator T(E) and a free propagation time operator script T sign(E). In the spectral line near-wing application, a first-order perturbation solution is obtained in terms of Φ as a function of the displacement from the line center. The real and imaginary parts of the (reduced) Fano collision operator are expressed in terms of shift and width functions and the impact approximation shift Δ(0) and width Γ(0) parameters. In addition, other impact approximation quantities are required which do not play a role in line shape in the impact approximation theory. A preliminary comparison with experiment for the CO2 continuum near 4.3 μm shows excellent agreement. The derived values of the collision times are in the expected picosecond range. There also seems to be little temperature dependence for N2-CO2 broadening over a wide range of temperatures. © 1994 American Institute of Physics.