THE INFLUENCE OF KLEIN-NISHINA STEPS ON THE SPATIAL DIFFUSION OF GALACTIC COSMIC-RAY ELECTRONS
The full Klein-Nishina cross section for the inverse Compton scattering interactions of electrons implies a significant reduction of the electron energy loss rate compared to the Thomson limit when the electron energy exceeds the critical Klein-Nishina energy E{sub K} = 0.27m{sup 2}{sub e} c{sup 4}/(k{sub B}T), where T denotes the temperature of the photon graybody distribution. We investigate the influence of the Klein-Nishina reduction on the solution of the steady-state spatial diffusion transport equation for relativistic electrons. The modified electron spectrum at energies below 10{sup 4} GeV, where only the Klein-Nishina modifications from interstellar optical target photons are relevant, are derived in terms of the Green's function solution for one-, two-, and three-dimensional spatial diffusion. The modifications to the solutions of the one- and three-dimensional diffusion equations are calculated for a single point source of monoenergetic electrons. It is shown that significant enhancements in the local electron intensity occur at electron energies greater than the critical Klein-Nishina energy E{sub K} , and that the cosmic-ray electron anisotropy at the solar system resulting from a single steady point source exhibits a sharp drop near E{sub K} . These Klein-Nishina enhancements are potentially interesting for determining the contribution of point sources such as dark matter sources and/or electromagnetic particle accelerators (pulsars and micro-quasars) to the local electron intensity and the local positron fraction.