Vibration-dependent trajectories and their effects on vibrational dephasing

We show that the expression for S₁ (i.e., the first term in the expansion of the S matrix) that is essential in calculating vibration-rotation pressure-broadened shifts is not properly given in the usual Robert-Bonamy (RB) formalism. The problem resulted when they considered effects of the vibrational dephasing on S₁; they tacitly made an assumption that the trajectories of interest are vibrationally independent. As a result, the current RB expression is an approximate one. Based on a vibration-dependent trajectory model, which is physically sound, we derive the correct expression for S₁. We present numerical calculations of the broadening and shifting cross sections and of the line shape parameters for the H₂-He pair and find for this molecular system, new results differ significantly from those calculated using the existing formalism. In addition, by comparing with those derived from close coupling calculations, we find that the new results are better than the old ones. Finally, we discuss how important effects from this modification could be for other molecular systems. We conclude that for certain molecular systems where the short-range collisions are the dominant source responsible for the line widths and shifts, and in addition, the isotropic potential has small depth, the present modification is a worthwhile step to be taken in order to refine the current RB formalism. Meanwhile, for other systems it may not be necessary.