Theoretical calculations of H 2O linewidths and pressure shifts: Comparison of the Anderson theory with quantum many-body theory for N 2 and air-broadened lines

Abstract

Comparisons of theoretical predictions for line-widths and pressure shifts of water vapor transitions broadened by N 2 or air are presented using the Anderson-Tsao-Curnutte (ATC) theory of pressure broadening and a more recent formalism derived by using quantum many-body techniques. The theoretical predictions are also compared to available experimental results, including 110 measurements of half widths, and eight measured ν 2-band line shifts. The standard ATC theory for multipole interactions is generalized to yield second-order pressure shifts. It is also shown that a scaling transformation from the momentum transfer variable to the impact parameter variable converts the quantum theory to a form very similar to the ATC equations. The essential modification is to replace the ATC resonance functions ⨍( k), F( k) by new functions g( k), G( k), which, however, have a very different shape. In particular, g( k) is a Gaussian, which results from the simultaneous constraints of a Boltzmann distribution of velocities, coupled with strict momentum and energy conservation in the collision processes. The implication is that highly non-resonant collisions, i.e. collisions involving large inelasticities, are given much less weight in the quantum-derived formalism. The results are analyzed for both high and low J transitions, including the behavior of the anomalously narrow lines measured by Eng and others at high J, and the theoretical dependence of such transitions on the parameter b min used in the earlier calculations of Benedict and Kaplan. Limited comparisons are made for individual level shifts, and for the temperature dependence of the half width Some specific suggestions for additional experimental studies are also offered.