Theory of resonance pressure broadening: Resolvent operator formalism and classical path approximation

Abstract

The problem of resonance pressure broadening of spectral lines in monatomic gases is discussed using a resolvent operator formalism. A differential equation is developed to determine the resolvent, and it is shown how its solution for a limiting case yields the familiar classical path approximation for the translational motion of the atoms, and how quantum corrections may be systematically studied. Commonly used limiting cases within the classical path approximation (two-body static and impact approximations) are also exhibited as limiting cases, with methods for systematic evaluation of corrections. Closed form solutions are obtained for the two-body static and impact cases. The results are compared with available experimental data, and generally satisfactory agreement is obtained. Of some theoretical interest is the formalism, which embraces all the usual approximations and permits them to be studied together with corrections to them from a unified point of view. New results of more practical interest are the closed form solutions for the limiting cases, and the estimation of the lowest-order quantum corrections, which are appreciable under some experimental conditions.