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According to the perturbation theory of the scattering of photons, the cross section for Compton scattering diverges, owing to the multiple scattering effects for low frequency photons. It is shown that by the application of the method of Block and Nordsieck this difficulty can be evaded, and that, to a first approximation, the cross section for Compton scattering is given by the Klein-Nishina formula.
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Res Jost (1947) studied this question.
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