Soft photon approximation in a laser field: applications
arXiv:2607.11160
The paper develops compact analytical formulas for soft‑photon emission in strong plane‑wave laser fields and applies them to single, double, and multi‑photon nonlinear Compton scattering, showing high accuracy and providing a Mathematica implementation.
Abstract
We apply the soft photon approximation to QED processes in a strong plane-wave laser field. New compact expressions for the emission factors are presented, which simplify the generalization to multiple soft photon emission. The method is applied to nonlinear single, double, and -photon Compton scattering. For single Compton scattering, we show that the soft photon approximation reproduces the exact spectrum with accuracy , significantly outperforming the classical radiation theory. For double Compton scattering, we derive analytical expressions for the differential probability in two kinematic regimes: when both photons are soft, and when one photon is soft while the other has arbitrary energy. We present a compact analytical expression for the amplitude of -photon emission within the soft photon approximation. A numerical implementation in Wolfram Mathematica for single and double Compton scattering is provided.
21 pages,10 figures