Resonance Absorption Line Shapes in Monatomic Gases: The Role of Off-Diagonal Resolvent Matrix Elements

A new derivation is given for the resonance absorption line shape in monatomic gases in terms of resolvent-operator matrix elements. This derivation is believed to be simpler and more rigorous than the one given previously by Reck, Takebe, and Mead. In contrast to the earlier result, in which only diagonal resolvent matrix elements appeared in the expression for the susceptibility, it is shown that off-diagonal elements also contribute. In the classical path approximation, with neglect of excitation transfer via virtual transverse photons, it is shown that the line shapes for emission and absorption are identical. The effect of the off-diagonal elements on the line shape is calculated for the static (statistical) limit, and it is shown to lead to a shift toward the blue. It was previously shown that the off-diagonal terms cause a red shift in the opposite "impact" limit.