  Compton scattering of low-frequency radiation by an isotropic distribution of
(i) mildly and (ii) ultra relativistic electrons is considered. It is shown
that the ensemble-averaged differential cross-section in this case is
noticeably different from the Rayleigh phase function. The scattering by an
ensemble of ultra-relativistic electrons obeys the law p=1-cos(alpha), where
alpha is the scattering angle; hence photons are preferentially scattered
backwards. This contrasts the forward scattering behaviour in the Klein-Nishina
regime. Analytical formulae describing first-order Klein-Nishina and
finite-electron-energy corrections to the simple relation above are given for
various energy distributions of electrons: monoenergetic,
relativistic-Maxwellian, and power-law. A similar formula is also given for the
mildly relativistic (with respect to the photon energy and electron
temperature) corrections to the Rayleigh angular function. One of
manifestations of the phenomenon under consideration is that hot plasma is more
reflective with respect to external low-frequency radiation than cold one,
which is important, in particular, for the photon exchange between cold
accretion disks and hot atmospheres (coronae or ADAF flows) in the vicinity of
relativistic compact objects; and for compact radiosources.
