Intra-collision Effects in the Collision-broadening of Spectral Line Profiles

Some details of events occurring during collisions that affect the profiles of collision-broadened spectral lines are reviewed. Emphasis is on the impact and quasi-static approximations. Rotational level mixing and collisional propagation are shown to be important processes. The general principles are illustrated through consideration of the infrared spectrum of the hydrogen molecule. Collision-broadened spectral line shapes carry important information on the time-dependent dynamical and collisional processes occurring in the radiating medium. The physical description involves the dynamical evolution of the radiator as it undergoes a series of multiple collisions with a large number of perturbers, while the interaction between the radiator dipole moment and the external electromagnetic field results in absorption and emission processes. This article reviews, in an informal manner, a particular aspect of collisional broadening, namely some details of what can transpire during the collisions that are ultimately responsible for the broadening phenomenon. Both allowed and collision-induced electric-dipole transitions are treated. The material is not new but consideration of these phenomena within a single context provides insight into their character. The infrared spectrum of the hydrogen molecule provides an ideal illustration of some of the general phenomena involved. 1. COMMON APPROXIMATIONS To begin, recall some basic principles employed in the consideration of allowed transitions. Many treatments of collisional line broadening are presented within the impact approximation (or limit) where the time between collisions controls the spectral line width. This approximation is often taken to mean that the time of duration of collisions may be considered small compared to the time between collisions, thereby rendering the details of what happens during the collision unimportant. This last statement can mislead. More correctly, and mathematically, the approximation applies in the regime where1 ( ) 1 0 << τ ω − ω C ... (1) Here ( ) 0 ω − ω is the detuning from the line centre at ω0 and τC is the time duration of the collision. The major part of this paper concerns the situation where the collision does indeed have a finite duration and, moreover, where collisional propagation, i.e. inelastic transitions occurring during the collision process, but not due to radiative processes, are prominent. Only the modifications to the shape and intensity of the profile are discussed; the more subtle changes in frequency shift are not considered. The work of Boulet, Robert, Galatry and Marteau2, 3 provides an introduction to the concept. The absorption coefficient at frequency ω is given by: α (ω) = ( ) ω φ             ω − − ω       π kT c nR   exp 1 3 4 , ... (2)