Compton effect as a Doppler effect

Abstract

An electromagnetic wave with the wavelength L, which has some energy, descends on an electron and makes it move in the same direction of propagation of the wave. The wave makes the moving electron oscillate with a lower frequency. A very much simple analysis shows that this moving oscillating electron radiates, in the direction making angle T with the direction of the incident wave, an electromagnetic wave which its wavelength is bigger by a factor proportional to L(1-cosT). 

(2) Compton effect as a Doppler effect (pdf)