SINGLE COMPTON SCATTERING

   by 

   D.I. NAGIRNER (Astronomical Observatory, St.Petersburg University) 
   and  
   J. POUTANEN (Observatory and Astrophysics Laboratory, University of Helsinki) 


   Published in Astrophysics and Space Physics Reviews, Vol. 9, 1994
   (edited by R.A. Sunyaev) 

Abstract: 

 A review of  works on  single Compton
scattering is given. No  limitations on the energies of  photons and
electrons are assumed. The relativistic kinetic equation,  describing
the scattering of the polarized radiation by a non-degenerate
electron gas with  known distribution function, is formulated in 
linear approximation. The formulae for the mean values of the
Klein-Nishina cross-section and of the first and second degree of
frequency of the scattered photon are given.  Three types  of
averaging  are considered: over the scattering angle, over  electron
directions and over  electron energy distribution, which is assumed to
be the relativistic Maxwellian. Using these formulae, the balance of the
energy of the photon gas, the dispersion of the scattered photon
frequency and the radiation pressure are investigated.

The scattering matrix describing the interaction of photons with the
isotropic electron gas is obtained. It is shown that it consists of
five redistribution functions (RF) on  frequency, depending on the
scattering angle. The RF of intensity is studied in more detail. This
function is   averaged over directions with the weight factors 1 and
the cosine of the scattering angle.  Its connection with the mean
values is ascertained, and the moment equations of the zeroth  and first
orders are deduced.

The formulae for all  quantities considered are reduced to the forms
free of cancellation. In addition to the exact formulae, the asymptotic
expansions of the mean values and RF are obtained in three cases:
non-relativistic and ultrarelativistic electrons and the photons of
small energies. In particular, the limiting expressions for the RF of
intensity are found. Using these expressions, the well-known
Fokker-Planck differential (on frequency) kinetic equations  can be
easily deduced.