Refinement Of The Robert-Bonamy Formalism: Taking Into Account Contributions From Line Coupling
Ma, Q., C. Boulet, Richard H. Tipping · Zenodo (CERN European Organization for Nuclear Research) · 2014
The Robert-Bonamy (RB) formalism has been used to calculate half-widths and shifts adopted in HITRAN for years. Besides its success, it contains several approximations whose applicability has not been thoroughly justified. One of them is an assumption that lines of interest are well separated. When these authors developed the formalism, they have relied on this assumption twice. First, in calculating the spectral density F(ω), they have only considered the diagonal matrix elements of the relaxation operator. Due to this simplification, effects from line mixing are ignored. Secondly, when they applied the linked cluster theorem to remove the cut-off appearing in Anderson’s theory, they have assumed that the operator (-iS1 - S2) is diagonal within the linespace so that matrix elements of the operator exp(- iS1 - S2) can be replaced by the exponential of the matrix elements of (- iS1 - S2). With this replacement, effects on calculated half-widths and shifts from the line coupling are also ignored. Although both these two simplifications relied on the same approximation, their validity criteria are completely different and the latter is more stringent than the former. As a result, in many cases where the line mixing becomes negligible, significant effects from the line coupling have been completely missed. Recently, by abandoning the second simplification and accurately evaluating the matrix elements of exp(- iS1 - S2), we have refined the RB formalism such that the line coupling can be taken into account. Our numerical calculations for the Raman Q lines of auto-perturbed N2, and also the Raman Q lines and the infrared P and R lines of C2H2 in a N2 bath have demonstrated that effects on calculated half-widths from the line coupling are important. In comparison with values derived without the line coupling, new calculated values for these lines are significantly reduced and become closer to measurements.1 With respect to the H2O molecule immersed in a N2 bath, we have found that for most of the H2O lines, it is unnecessary to consider the line coupling. However, for several dozens of lines, effects on the calculated half-widths from the line coupling are small, but remain noticeable and the reductions due to including the line coupling could reach to 5 %. Meanwhile, effects on the calculated shifts are very significant and the variations could be as large as 25 %.