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Astron. Astrophys. 357, 301-307 (2000) 2. Theory of relativistic inverse Compton scatteringFor the sake of completeness we summarize in Sects. 2.1 and 2.2 the basic formulars describing the relativistic non-resonant and resonant inverse scattering processes. 2.1. Non-resonant inverse Compton scatteringLet us begin with Thomson case without a magnetic field 1. The average rate of photons scattered by relativistic electrons is given (e.g. Feenberg & Primakoff, 1948) by where for the differential energy loss of the electron per moving unit
with Taking a closer look at the cross section we have to distinguish
between Thomson case and Klein-Nishina case i.e., between
Here, are approximately the average energy loss of the primary in a
single Compton collision for 2.2. Resonant inverse Compton scatteringIn the presence of a (strong) magnetic field the cross section for inverse Compton scattering has a resonance when the Doppler shifted frequency of the infalling photon equals the gyro-resonance frequency of the electron in its rest frame. The later one can be written as where in the laboratory frame (here we made use of the fact, that
electrons in pulsar magnetospheres travel along the magnetic field
lines, which leads to For a description of the resonance we use the Breit-Wigner formula. In general, the maximum cross section within the resonance can be expressed as both formulated in the laboratory frame. 2 The width of the Breit-Wigner resonance is described by is independent on the magnetic field strength. To find a similar expression to Eq. (4) in the case of resonant
scattering we approximate the integration over
Here, ![]() ![]() ![]() ![]() © European Southern Observatory (ESO) 2000 Online publication: May 3, 2000 ![]() |