Effect of Electron Binding upon the Magnitude of the Compton Shift

Precision measurements of the Compton shift for ninety degree scattering of the wave-lengths 0.435A, 0.496A and 0.631A by carbon and by beryllium have been performed, using the ring-target x-ray tube and a double spectrometer, under the assumption that the mean shift for two mutually supplementary angles of scattering equals the ninety degree shift. In all cases the observed shift is less than $\frac{h}{\mathrm{mc}}$, the value required by the Compton formula, the maximum percentage discrepancy being 2.4 percent, observed in the case of $\lambda 0.631\mathrm{A}$ scattered from carbon. These observations fulfill the predictions inherent in Wentzel's theory of scattering by bound electrons, and are consistent with the explicit shift formula previously deduced by the present authors, as regards dependence of the shift upon wave-length and upon ionization energy of the scatterer. They are also in satisfactory quantitative agreement with the theoretical shift formulas of F. Bloch.