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Soft photon approximation in a laser field: Applications

Peter A. Krachkov* and Simon V. Sorokin†

  • *Contact author: P.A.Krachkov@inp.nsk.su
  • †Contact author: S.Sorokin1@g.nsu.ru
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Phys. Rev. D 114, 056028 – Published 29 September, 2026

DOI: https://doi.org/10.1103/nb7r-qhkb

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 N-photon Compton scattering. For single Compton scattering, we show that the soft photon approximation reproduces the exact spectrum with accuracy O(ω/ϵ), 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 N-photon emission within the soft photon approximation. A numerical implementation in wolfram mathematica for single and double Compton scattering is provided.

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Soft photon approximation in a laser field

P. A. Krachkov
Phys. Rev. D 109, 076002 (2024)

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Phys. Rev. D 114, 056028– Published 29 September, 2026
  • Received 14 July 2026
  • Accepted 8 September 2026
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