Incoherent Scattering of Gamma Rays byK-Shell Electrons

The differential cross section for the incoherent scattering of 662-keV gamma rays by the $K$-shell electrons of tin, tantalum, and lead was determined by experiment. The scattered photons were selected in coincidence with accompanying $K$ x rays from the scatterer foil, using the NaI(Tl) scintillation detectors and the slow-fast coincidence method. The cross section $\frac{d{\sigma }_K}{d\Omega }$ was compared with that predicted by the Klein-Nishina formula, $\frac{d{\sigma }_F}{d\Omega }$, at scattering angles 20°, 35°, 50°, 65°, and 100°. The experimental results show that for all cases with these scatterer elements the cross-section ratio $\frac{d{\sigma }_K}{d{\sigma }_F}$ is less than unity for small scattering angles and approaches zero as the angle decreases to zero, as predicted by nonrelativistic calculation. For large angles, this ratio is greater than unity and at 100° it is found to be equal to about 1.2 for tin, 1.3 for tantalum, and 1.5 for lead. The experimental approximate dependence of the cross-section ratio on the binding energy of the struck $K$-shell electrons was also obtained for various gamma-ray scattering angles. On the basis of certain assumptions an attempt was made to calculate theoretical values to be compared with the experimental results for small and large scattering angles. The calculated values indicate the general behavior of the dependence of the ratio on the scattering angle.