Note on Klein–Nishina effect in strong-field QED: the case of nonlinear Compton scattering

Abstract Suitably normalized differential probabilities of one-photon emission in external electromagnetic fields are compared to quantify the transit of nonlinear Compton scattering to linear Compton scattering, described by the Klein–Nishina formula, and to constant-crossed field treatment. The known Klein–Nishina suppression at large energies is further enforced by increasing field intensity. In view of the Ritus–Narozhny conjecture, we demonstrate that different paths in the field intensity versus energy plane toward large values of the quantum nonlinearity parameter $$\chi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>χ</mml:mi> </mml:math> facilitate significantly different asymptotic dependencies, both in the Klein–Nishina regime and the constant-crossed field regime and in between. Graphical abstract Differential perspective on the Klein-Nishina effect in strong-field QED: showing the smooth transition from the constant-crossed field (CCF) through the infinite plane-wave approximation (IPA) to the linear Klein-Nishina limit, highlighting the asymptotic behavior of the differential cross sections.