Theoretical and experimental study of the scattering of photons byK-shell bound electrons: Energy and angular dependence of the cross sections

We present an analytic calculation of the differential cross section $\frac{d^2\sigma }{d{\Omega }_{{\overrightarrow{\mathrm{k}}}_f}d{\omega }_f}$ using relativistic wave functions for the initial ($s$ wave only) and final electron states. Comparisons are made with other theoretical calculations. Experimental results are given as a test of the theoretical calculation: energy spectra for 662-keV $\gamma$ rays scattered incoherently through 90° and 135° by Ge bound electrons, and for 60-keV photons scattered by Cu and Mo $K$-shell electrons through 50°. Good agreement has been obtained between experimental and theoretical results.