Energy-Corrected Sudden approach to the non-Markovian relaxation matrix for two linear colliders
A finer picture of collisional effects on spectral band shapes is urgently demanded by a number of atmospheric and combustion explorations . For that, simulations of band profiles in large spectral intervals should be done at various thermodynamic conditions, in particular for elevated gas densities where the line-mixing effects are strongly pronounced. The problem is solved when the fundamental, frequency-dependent relaxation (super)matrix Γ(ω) is known. Presently, the only affordable receipt to calculate Γ(ω) without limitations of the perturbation theory is due to the Energy- and Frequency Corrected Sudden Approximation (EFCSA) model developed initially for the structureless bath  and extended recently to linear perturbers , assuming collision durations to be finite, yet much shorter than the period of collider's rotation.
In a previous study , we suggested an approach based on spectral moments to model the translational interaction spectral functions (ISF). This approach requires, however, refined potential energy surfaces available only for a limited number of molecular systems. To make non-Markovian calculations feasible for an arbitrary molecular pair, we develop here a semi-empirical approach to ISF simulation based on the Energy-Corrected Sudden model. While there exist papers presenting ECS-modeling of the Markovian relaxation matrix for a linear perturber  or the non-Markovian ECS matrix for a structureless perturber , to our knowledge, there is no published work describing non-Markovian relaxation matrices that accounts for the anisotropy of the perturbing molecule.
After having applied the basic hypotheses of the ECS approximation and having factorized the ISFs into frequency- and anisotropy-dependent parts, we consider the particular case of the isotropic Q-branch, which allows identification of the frequency-dependent factor with the adiabaticity factor and enables relating the anisotropy-dependent factor to the bimolecular transition rates. We propose various analytical multi-parameter models for bimolecular basic transition rates that are used, together with a Lorentzian-type adiabaticity factor, for ISF modeling and are shown, on the example of high-pressure anisotropic Raman spectra of nitrogen, to be suitable for theoretical prediction of large-band spectra of dense gases of linear molecules.
AS and AK acknowledge the financial support from the RFBR (project number 19-33-90244).
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