Compton scattering from electrons in bound states: Binding and "off-mass"-shell effects

Abstract

The Compton scattering of a photon from an unpolarized electron bound in a central field is treated relativistically. The distribution of the emitted electrons for a photon scattering in a given direction is obtained as a function of the radial components of the initial Dirac wave function. This expression, in the lowest power of the coupling constant, leads to the Klein-Nishina formula. The off-mass shell and binding corrections to the free Compton scattering formula, which are important near the ionization threshold, are found. Using exact hydrogenlike wave functions, various approximate formulas as functions of the atomic number $Z$ are discussed, and some possible limitations of the usual description of Compton profiles are considered.