Contribution to the Theory of the Compton-Line

Abstract

Starting from Wentzel's theory of the Compton scattering of bound electrons, and assuming that the motion of the electrons in the atom can be described by hydrogenic eigenfunctions, general formulae are developed for the calculation of the intensity distribution in the Compton line. It is shown that the interaction of the electrons with the atomic nucleus gives not only a broadening of the Compton line but makes it also asymmetrical, shifting at the same time the position of the maximum intensity from Compton's value $\Delta \lambda =\left(\frac{h}{m_{0}c}\right)(1-cos\theta )$. The "defect of the Compton shift" is shown to be quadratic in the wave-length of the incident radiation. This law as well as the value of the constant entering into it are found to agree satisfactorily with experiment.