Savchenko Problem 14.5.22
Physics
Problem
What is the maximum energy that photons with energy E = 10 eV can acquire when scattering on an oncoming electron beam with energy E_e = 10^10 eV?Intuitive explanation
This is an inverse Compton scattering problem—a high-energy electron colliding head-on with a low-energy photon. The key insight is that in the lab frame, a head-on collision allows maximum momentum transfer from the electron to the photon. Rather than deriving the full relativistic formula, think of it this way: the photon's energy in the electron's rest frame is Doppler-boosted, then boosted back to the lab frame after scattering. The maximum gain occurs when the electron transfers as much kinetic energy as possible, which happens at a head-on collision where the photon scatters backward.
Intuitive explanation
This is an inverse Compton scattering problem—a high-energy electron colliding head-on with a low-energy photon. The key insight is that in the lab frame, a head-on collision allows maximum momentum transfer from the electron to the photon. Rather than deriving the full relativistic formula, think of it this way: the photon's energy in the electron's rest frame is Doppler-boosted, then boosted back to the lab frame after scattering. The maximum gain occurs when the electron transfers as much kinetic energy as possible, which happens at a head-on collision where the photon scatters backward.