Inhomogeneous broadening, narrowing and shift of molecular lines under frequent velocity-changing collisions

Abstract

We demonstrate that speed-dependent hard-collision profiles collapse into a simple Lorentz profile in the regime dominated by the velocity-changing collisions. We present simple analytical formulas for the effective width and shift of the Lorentzian, derived from the speed-dependent collisional broadening and shift. While the effective width increases with speed dependence of collisional shift, it is reduced by speed dependence of collisional width. On the other hand, the effective shift is modified by thermal average of speed dependence of the product of collisional width and shift. We validate these formula numerically applying the quadratic speed dependence of the collisional width and shift.