Modified complex Robert–Bonamy formalism calculations for strong to weak interacting systems

Abstract

In 1979 Robert and Bonamy published a complex formalism (CRB) for the calculations of the pressure broadened half-width and collision-induced line shifts [J. Phys. Paris 40, 923 (1979)]. Application of the linked cluster theorem produced expressions that no longer needed the cut-off procedure that plagued earlier line shape theories. Recently, Ma, Tipping and Boulet (MTB) suggested that the application of the linked cluster theorem in their derivation of Robert and Bonamy was based on an invalid assumption. In their work MTB gave the modified expressions and state that the effect of the modification is more important for strong interaction systems. Here the effect of the MTB modification on the formalism of Robert and Bonamy is studied for systems which range in interaction strength from strong to weak. In particular, complex Robert–Bonamy calculations and calculations based on the modified formalism are made in the mean-relative thermal velocity approximation for the systems H₂O–H₂O, H₂O–N₂, H₂O–O₂, O₃–N₂, O₃–O₂, and CH₄–N₂ and the results from the formalisms compared for both the pressure-broadened half-width and pressure-induced line shift. The results of the two methods of computation are compared with the measurement database. It is shown that the difference between the two methods of computation is proportional to the strength of the radiator–perturber interaction and for some systems is larger than the uncertainty desired by the spectroscopy and remote sensing communities. Comparison with the measurement database shows better agreement with the CRB calculations.

Acknowledgements

We thank Q. Ma, R.H. Tipping and C. Boulet, for providing us with their manuscript on their theoretical modification to CRB formalism prior to its publication. The authors are pleased to acknowledge support of this research by the National Science Foundation through Grant No. ATM-0242537. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.