On the intensity of total scattering of X-rays

Abstract We shall here investigate theoretically the intensity of total scattering of X-rays by atoms distributed at random, e. g., the scattering by the atoms of a monatomic gas. In the scattered radiation we shall not include the characteristic X-rays excited by the incident radiation. The scattered radiation consists then partly of radiation having the same frequency as the incident radiation (coherent scattered radiation) and partly of radiation having other frequencies (incoherent scattered radiation). For sufficiently high frequency of the incident radiation the incoherent scattered radiation is then nearly monochromatic for a given scattering angle, and consists practically entirely of radiation whose wave-length and intensity is given by the formulæ for the Compton effect for the scattering by free electrons. Generally, however, it must be taken into account that several frequencies occur in the scattered radiation for each direction of scattering. The total intensity of the scattered radiation for a given direction has therefore to be taken as a sum of the intensities of the different components, each having a definite frequency. General expressions for the scattered radiation are given by a scattering formula derived by one of us. In this formula “relativity corrections” are neglected; for the intensity of scattering in the Compton effect for free electrons, this approximation, and a further one which we also make, lead to the classical Thomson formula. This means that our intensity formula gives a useful approximation only if the incident radiation is not too hard (e. g., has a wave-length not shorter than about 1 Å., in which case the error arising from the approximation just mentioned should not exceed a few per cent.).