The Shape of an X-ray Line

An x-ray emission line as measured by the double-crystal spectrometer ("anti-parallel" position) can be represented very accurately by means of a simple empirical formula. Some uses for the formula are (1) location of background under the $K\alpha$ doublet, (2) the calculation of the separation of close components from measured points used in the empirical formula. This formula appears to be a function of a very useful type since it is also a good representation of rocking curves obtained in the "parallel" position of the spectrometer. A search for theoretical justification of this type of formula has brought to light the curious result that although the application of the Dirac quantum theory of the radiation field yields a formula of the same type, the maximum ordinate predicted is independent of the spontaneous transition probability; whereas, certain experimental work indicates that the maximum ordinate is a good measure of the line intensity. This is very disturbing since the assumption is usually made that the line intensity is proportional to this Einstein coefficient of spontaneous transition.