Collisional influences on vibration–rotation spectral line shapes: A scaling theoretical analysis and simplification

Abstract

The recently developed energy corrected sudden (ECS) scaling theory for nonreactive molecular collisions is combined with the impact theory of spectral line shapes. Through the use of angular momentum algebra, we show that only a restricted fundamental set of collisional transitions enter into the linewidth and line shift determination. This development significantly reduces the complexity and difficulty in dynamical calculations of the line shape parameters. A further simplification in the linewidth and line shift equations is derived based upon the physical properties of the ECS theory; the result is a relationship between linewidths (or line shifts) and a small set of dynamical quantities: rotationally inelastic rates, modified vibrationally inelastic rates, impact parameter correlation functions and vibration-to-vibration inelastic rates. The theory is sufficiently general to treat pure rotation, fundamental, overtone and hot bands, and vibrationally hot perturbers. A brief consideration of the physical implications of such a relationship is presented here; future articles will contain more detailed discussions with special emphasis on the direct extraction of the dynamical quantities from experimental linewidth and line shift data.