On the temperature dependence of half-widths and line shifts for molecular transitions in the microwave and infrared regions

An expression was developed that correctly models the temperature dependence of the half-width over large temperature ranges and the temperature dependence of the line shift, even for cases where the line shift changes sign. The expression was derived from the expansion of the collisional cross-sections in a series of powers of the relative velocity of the radiator and perturber. Cutting offat two terms yields a complex double power law (DPL) expression, where the real and imaginary parts describe the temperature dependence of the half-width and line shift, respectively. Data were collected for more than 100 thousand transitions and the standard power law expression for the half-width and line shift were compared with the new double power law expression. It is shown that the double power law works well for all transitions, even those that exhibit unusual structure, which the standard power law cannot model. The DPL expression gives better results than the standard power law for all transitions studied and the DPL model gives good results for the temperature dependence of the line shift when it changes sign. The DPL model for the temperature dependence of the line shift was compared with the linear model, which is currently used on the HITRAN database. In all cases the DPL model gave much better results than the linear model no matter what temperature range was considered. The new formalism allows a substantial reduction in the number of parameters that need to be stored in databases and the same expression can be utilized in radiative transfer and simulation codes for both the half-width and line shift.