Experimental Compton-scattering cross sections for Si and Ge

Compton-scattering cross sections of Si and Ge for $\mathrm{Cu}K\alpha$ radiation are determined by direct absolute measurement of the intensity scattered from a single crystal. Parasitic components are eliminated by an evacuated specimen chamber and by combined use of a scintillation counter and a Si(Li) solid-state detector. The contribution of the thermal diffuse scattering is subtracted by a calculation based on independently determined phonon frequecies. At large scattering angles the contribution of the Compton scattering is separated directly by the Si(Li) detector. In the case of Si, a good agreement with the Waller-Hartree theory is obtained above $\frac{sin\theta }{\lambda }=0.2\mathrm{}$ ${\mathrm{\AA }\mathrm{A}}^{-1\mathrm{}}$. The experimental values for Ge are considerably larger than the theoretical ones, particularly at small scattering angles. To explain the origin of these discrepancies theoretical calculations which allow for electron binding in the Compton process and include the effects of the band structure of Ge crystal are needed.