Compton Scattering byK-Shell Electrons

Abstract

The differential cross section $d{\ensuremath{\sigma}}_{K}$, for the Compton scattering of 660-kev photons by the $K$-shell electrons of tin and gold, is determined by an experimental method in which a scattered photon is selected in coincidence with an accompanying $K$ x ray. This cross section is compared with the Klein-Nishina cross section $d{\ensuremath{\sigma}}_{F}$ for an electron initially free and at rest. The results show that the ratio $\frac{d{\ensuremath{\sigma}}_{K}}{d{\ensuremath{\sigma}}_{F}}$ approaches zero as the photon scattering angle decreases to zero. This behavior agrees qualitatively with the small angle behavior predicted by exact nonrelativistic calculations for the hydrogen atom. For large angles, this ratio is greater than unity and at 110 degrees is equal to approximately 1.2 for tin and 1.4 for gold. The experimental values for $d{\ensuremath{\sigma}}_{K}$ at large angles agree with the theoretical values for the Compton cross section (averaged over the angle between the incident photon and electron) for electrons initially free but with velocities corresponding to the $K$-shell binding energy. Also, the results indicate that the small- and large-angle behavior for $d{\ensuremath{\sigma}}_{K}$ has a compensating effect in which the ratio of the total cross sections $\frac{{\ensuremath{\sigma}}_{K}}{{\ensuremath{\sigma}}_{F}}$ (integrated over the photon scattering angle) is approximately equal to unity for both tin and gold.