Semiclassical and Classical Spectrum in the Adiabatic Theory of Pressure Broadening

Abstract

The semiclassical spectrum, defined by use of WKB wave functions, and the classical expression of the spectrum are interpreted in terms of Feynman amplitudes. The radiative electronic transition may be considered to occur instantaneously, and the different times at which it can occur define different "paths" from initial to final state. During a collision of the radiating atom with a perturbing atom, the electronic transition occurs preferably when the relative distance between the two atoms is such that their relative velocity is conserved in the transition (Franck-Condon principle). In a given collision, there are several such preferred transition times which define as many preferred paths. Interference between these paths can result in interference patterns in the spectrum. In general, an interference structure, associated with the repulsive part of the interatomic potential difference, will appear in the violet wing of the spectral line. This forms a highly plausible explanation for the violet satellites observed in the spectrum of various gas mixtures. Not much regarding the shape of the interference structure can, in general, be deduced outside of numerical computations; nevertheless, the general dependence of the position of the violet satellites on parameters such as temperature, reduced mass, and size of the repulsive core of the potential difference can be inferred in a rough manner, and qualitative agreement with experiment be obtained.