Compton Scattering of 279.1 and 661.6 keV Photons by K-shell Electrons

Abstract

The spectral distributions of 279?1 and 661? 6 keY photons incoherently scattered by the K electrons of U, Pb, Ta and Sm are calculated for a point-Coulomb potential using a theory previously developed by the author which accounts completely for electron binding and relativistic effects. WKB treatments of the regular and irregular continuum Dirac wavefunctions have been developed and used to mprove the computation of the 'absorption-first' radial matrix elements. The scattered photon spectra for the four elements and scattering angles for which the free electron Compton energy lies below the high energy cutoff due to conservation of energy have broad peaks shifted by 3 to 18 and by 30 to 50 keY, for 279?1 and 661? 6 keY photons respectively, from the free electron Compton energy towards higher scattered photon energies. An infrared divergence, whose magnitude increases strongly with atomic number, commences at ~ 56 keV and is present in those spectra where there is no peak or where the peak lies significantly above 56 keY. Differential cross sections daK' computed using a low energy cutoff, are nonzero for zero-angle scattering and are lower than the Klein-Nishina cross section daF for scattering angles ~ 50� for 661?6 keV photons and for all scattering angles for 279?1 keY photons (with the exception of 80�-130� in the case of Sm). The cross section ratio daK/daF increases with increasing scattering angle until about 100� and 80� for 279?1 and 661? 6 keY photons respectively and then subsequently decreases slowly.