Theory of Resonance Absorption Line Shapes in Monatomic Gases

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Abstract
It is pointed out that the usual theories of pressure broadening disagree with direct experimental measurements of the widths of resonance-broadened alkali doublet lines, although the theories are at least qualitatively confirmed for the wings of resonance lines and for foreign-gas broadening. There are also two conflicting sets of experimental data (both in strong disagreement with theory). Some qualitative arguments are given for doubting the validity, near the center of a resonance line, of the "two-body" approximation generally used in theoretical treatments, and some formal objections to the usual procedure are also presented. The basic equation relating the susceptibility to a resolvent operator matrix element is derived from a more fundamental point of view than usual; the result contains in principle all effects due to translational motion, to the quantized nature of the radiation field, and to "spatial dispersion." In the limit of large absorber mass it is proved rigorously that the two-body approximation can never be valid near the center of a line, even for very low densities. By using different approximations for the wings and the line center, we obtain satisfactory agreement with experiments in both regions for the alkali doublet lines. We are also able to decide between the two conflicting experiments, favoring the square-root density dependence of the line-width observed by Lauriston and Welsh.

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