Quantum Field Theory and the Standard Model by Schwartz M.D. z-lib.org · Problem 2.5
Lorentz invariance and second quantization — Schwartz M.D. z-lib.org
Physics — QFT · compton-scattering
Problem
Compton scattering. Suppose we scatter an X-ray off an electron in a crystal, but we cannot measure the electron's momentum, just the reflected X-ray momentum.
(a) Why is it OK to treat the electrons as free?
(b) Calculate the frequency dependence of the reflected X-ray on the scattering angle. Draw a rough plot.
(c) What happens to the distribution as you take the electron mass to zero?
(d) If you did not believe in quantized photon momenta, what kind of distribution might you have expected? [Hint: see [Compton, 1923].]