Incoherent scattering of gamma rays in heavy atoms

Exact relativistic differential cross sections for the incoherent scattering of gamma rays by the inner shell electrons of heavy atoms are developed from the second order S matrix element for the electron-photon interaction in the Furry (1951) picture. Electron binding is accounted for completely by using the bound electron propagator and Dirac eigenfunctions for the initial and final electron states. A pure Coulomb potential is used to calculate the energy spectrum and the differential cross section for 662 keV gamma rays scattered by the K electrons of lead. In contrast with the results of Di Lazzaro and Missoni (1966) the energy spectrum maximum is displaced by 10% from the Compton energy towards higher photon energies, and there is no increase in the spectrum at the low-energy end. The relativistic results for the ratio of the bound electron to feed electron cross sections are larger than the incoherent scattering function calculations and exceed unity for scattering angles above 52 degrees .