Incoherent scattering of gamma rays by inner-shell electrons

Using the form factor approximation and nonrelativistic Coulomb wavefunctions, cross section profiles for Compton scattering of gamma rays are calculated for all subshells of the atom. Spherical coordinate are used in order to facilitate a straightforward application of self-consistent wavefunctions. Relativistic energy and momentum relations are applied. Numerical data are presented, for Egamma =279 keV and the K-, L- and M-subshells of copper and lead. Comparisons are made with cross section profiles obtained by replacing the final-state Coulomb wavefunction by a plane wave. Reasonable agreement between the two methods of calculation has been found for the L- and M-shells of copper for energies close to the centre of the profile. Larger differences occur for the K-shell of copper and the K-, L- and M-shells of lead even close to the centres of the profiles. Secondary maxima occur which are related to the nodes in the bound-state wavefunctions.