User:Dougsim/sandbox

Derivation of the scattering formula


Consider a photon $γ$  with wavelength $λ$ colliding with an electron $e$ in an atom, which is treated as being at rest. The collision causes the electron to recoil, and a new photon $γ$'  with wavelength $λ$'   emerges at angle $θ$  from the photon's incoming path. Let $e$' denote the electron after the collision. Compton allowed for the possibility that the interaction would sometimes accelerate the electron to speeds sufficiently close to the velocity of light as to require the application of Einstein's special relativity theory to properly describe its energy and momentum.