A Calculation of the Differential Cross Section for Compton Scattering in Tree-Level Quantum Electrodynamics

The differential cross section for unpolarised Compton scattering is calculated with respect to both t and cos θ. |M(e−γ → e−γ)|2 is evaluated to first order in αem using perturbative QED. The Klein-Nishina formula is derived using two different approaches, working both from the centre of mass and lab frames. Plots of dσ dt and dσ d cos θ resemble classical Thomson scattering at low s. At higher energy dσ d cos θ is largest at θ = 0, decreasing rapidly towards π. The overall cross section decreases as s increases.