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The full Klein-Nishina cross section for the inverse Compton scatteringinteractions of electrons implies a significant reduction of the electronenergy loss rate compared to the Thomson limit when the electron energy exceedsthe critical Klein-Nishina energy E_K = gamma_K * m_e c^2 = 0.27 m_e^2c^2/(k_BT), where T denotes the temperature of the photon graybodydistribution. As a consequence the total radiative energy loss rate of singleelectrons exhibits sudden drops in the overall energy loss rate ~ gamma ^2 -dependence when the electron energy reaches the critical Klein-Nishina energy.The strength of the drop is proportional to the energy density of the photonradiation field. The diffuse galactic optical photon fields from stars ofspectral type B and G-K lead to critical Klein-Nishina energies of 40 and 161GeV, respectively. Associated with the drop in the loss rate are suddenincreases (Klein-Nishina steps) in the equilibrium spectrum of cosmic rayelectrons. Because the radiative loss rate of electrons is the main ingredientin any transport model of high-energy cosmic ray electrons, Klein-Nishina stepswill modify any calculated electron equilibrium spectrum irrespective of theelectron sources and spatial transport mode. To delineate most clearly theconsequences of the Klein-Nishina drops in the radiative loss rate, we chose asillustrative example the simplest realistic model for cosmic ray electrondynamics in the Galaxy, consisting of the competition of radiative losses andsecondary production by inelastic hadron-hadron collisions. We demonstrate thatthe spectral structure in the FERMI and H.E.S.S. data is well described andeven the excess measured by ATIC might be explained by Klein-Nishina steps.

Klein-Nishina steps in the energy spectrum of galactic cosmic ray electrons