COMPTONIZATION OF GAMMA-RAYS BY COLD ELECTRONS

We develop an analytic method for calculating the emergent spectrum of gamma-rays and X-rays scattered in a homogeneous medium with low-temperature electrons. We take into account the Klein-Nishina corrections of the scattering cross section and absorption processes. We solve the wavelength relaxation and the spatial diffusion problems separately, and then calculate the emergent spectrum by convolving the evolution function of the spectrum in an infinite medium with the photon luminosity resulting from the spatial diffusion in a finite sphere. We compare the analytic results with that of Monte Carlo calculations and conclude that the analytic result is quite accurate.