Abstract
A quantum-mechanical unified theory of foreign-gas pressure broadening of atomic lines which includes the impact and statistical theories and duration-of-collision effects is developed. The model consists of an absorber atom with two internal states (upper) and (lower) interacting with a structureless perturber gas via two spherical pairwise additive potentials and , e.g., a simple model of an alkali-atom line perturbed by a rare gas. The dipolemoment correlation function is analyzed in the time domain using Liouville (tetradic) techniques. The correlation function reduces exactly to a two-body form containing the proper thermal weight factors. Detailed balance is obeyed and no restriction is required. The impact theory follows from a long-time analysis of . Sum rules or spectral moments are used to study short-time behavior revealing conventional statistical-theory effects (including satellite bands) and the important duration-of-collision effects which link the statistical and impact regimes. The sum rules are expressed as quadratures involving potential functions and the quantum-mechanical radial distribution function. Unified methods for calculating the total line shapes are suggested: (1) Padé approximants (ratios of polynomials) can be used to interpolate from the known short-time behavior to the known long-time beahvior; this requires the least computational effort; (2) exact results for this model may be obtained numerically from the overlap integrals of radial wave functions (Franck-Condon factors) for the two potentials and ; (3) classical phase (trajectory) expressions are given which are reasonable approximations in both the impact and statistical limits. A number of related topics are discussed including diabatic effects, collision-induced absorption, non-Lorentzian wings of molecular vibration-rotation bands, and the Condon approximation for the dipole-moment transition strength vs . The use of line shapes to probe atomic interactions, especially in excited states, is emphasized and the suggestion made that experiments be done over as wide a temperature range as possible with the measured line shapes in computer-readable form. The entire line-shape problem is described as the study of the spectrum of an atom-perturber "quasimolecule" (with primarily unbound states).
- Received 27 July 1971
DOI:https://doi.org/10.1103/PhysRevA.5.2162
©1972 American Physical Society