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.Comment: 10 pages, 9 figure