DIFFUSION-APPROXIMATION IN COMPTONIZATION PROCESS OF HARD X-RAY PASSING THROUGH A COLD-PLASMA - A GENERALIZED KOMPANEETS EQUATION

The down-Comptonization scattering of hard x-ray radiation passing thr ough an optically thick 'cold' plasma is an important radiative transf er process in x-ray astronomy as well as in radiation physics. In this paper, an extended Kompaneets equation which is valid both for up-Com ptonization (hnuBAR much less than kT(e)) and down-Comptonization (hnu BAR much less than kT(e)) is derived. The numerical solutions of this resultant equation in the down-Comptonization process (i.e. in the cas e hnuBAR much greater than kT(e), which we are interested in) are pres ented, e.g. the shift of the emission-line centroid and the asymmetry of the line-profile, and the steeplization of an initial contiuum spec trum with a power-law form I(nu) approximately nu(-alpha). The potenti al applications of this improved equation in astrophysics and radiatio n physics are emphasized.