Sampling of angular distribution in Compton scattering

We develop an algorithm, based on the acceptance-rejection method, with a simple envelope rejection function for sampling the angular distribution in Compton scattering from Klein-Nishina differential scattering cross section. The algorithm enhances the sampling efficiency for high-energy photons increasingly with increasing photon energies, The sampling efficiency is 79.6, 89.5, 92.3, 95.9, 96.6% for photon energies 1, 5, 10, 50, 100 MeV respectively. We compare the speed of our algorithm with some methods currently used and find that our method is faster than the others in most cases.