The structure of the Compton shifted line

According to Wentzel's(1) wave mechanical theory of modified x-ray scattering and also according to Jauncey's (2) classical-quantum theory of the same effect (though not explicitly so stated by Jauncey), the modified scattered x-radiation is regarded as due to many Smekal transitions (3) in each of which the initial state of the electron is a discrete negative energy level and the final state is one of the continuum of positive energy levels. In both of these theories the shifted "line" is predicted as a diffuse band, the diffuseness being due to the momenta of bound electrons in the dynamic atom model. Indeed, the natural breadth of the Compton modified line can be regarded as a Doppler broadening for x-rays scattered by moving electrons in much the same way as the temperature broadening is regarded in the case of optical spectra. The broadening of the Compton line is the most direct evidence for a dynamic atom model yet found. The structure of the line can be interpreted in such a way as to give the probability distribution of electron momenta in atoms. The breadth for circular orbits should be proportional to the effective atomic number of the scatterer.