Compton scattering in the Klein-Nishina Regime Revisited
  In blazars such as 3C 279, GeV gamma-rays are thought to be produced by inverse Compton scattering of soft photons injected from external sources into the jet. Because of the large bulk Lorentz factor of the jet, the energy of soft photons is Doppler shifted in the comoving frame of the jet, and the scattering is likely to occur in the Klein-Nishina regime. Although the Klein-Nishina effects are well known, the properties of the electron and emission spectra have not been studied in detail in the environment of blazars. We solve the kinetic equation of electrons with the spatial escape term of the electrons to obtain the electron energy spectrum in the jet and calculated the observed emission spectrum. In calculations of the Compton losses in the Klein-Nishina regime, we use the discrete loss formalism to take into account the significant energy loss in a single scattering. Although the scattering cross section decreases because of the Klein-Nishina effects, ample gamma rays are emitted by inverse Compton scattering. When the injection spectrum of electrons obeys a power law, the electron spectrum does not follow a broken power law, as a result of the Klein-Nishina effects, and a large number of high-energy electrons remain in the emitting region. 
Masaaki Kusunose, Fumio Takahara