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Physical Review

Generalization of Resonant Scattering Calculations

David L. Huber

Published Nov 5, 1969• 29 citations
Publisher

Abstract

Previous calculations of the differential cross section for the resonant scattering of monochromatic light in gases are generalized. The connection between the integrated and coherent cross sections and the absorption line shape is displayed.
DOI
10.1103/physrev.187.392

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The resonant scattering of monochromatic light in gases is analyzed. Explicit expressions for the differential cross section are obtained in the limits (Doppler width) \ensuremath{\gg} (natural width) \ensuremath{\gg} (collision width) and (collision width) \ensuremath{\gg} (natural width) \ensuremath{\gg} (Doppler width). In the former limit, the frequency distribution of scattered light is narrowed in the forward and backward directions, and has the full absorption width for right-angle scattering. In the collision-dominated limit, the cross section separates into a coherent and a fluorescent component. The motion of the atoms broadens the $\ensuremath{\delta}$ function distribution characterizing coherent scattering from a stationary target. The interference between light scattered by different atoms is assessed.
An analysis is presented of the redistribution of scattered light in resonant electronic Raman scattering from localized scattering centers. Results are obtained for the integrated cross sections characterizing the coherently scattered and the redistributed radiation. A statistical SSS-matrix theory is outlined which relates the cross section for the redistributed radiation to the coherent-scattering cross section. For the theory to be applicable it is necessary that the absorption lines from the various initial and final states to the resonant intermediate state have identical shapes. The conditions for this to occur are discussed.