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Nonlinear Compton scattering (NCS) and nonlinear Breit-Wheeler (NBW) processare strongly multi-photon and highly nonlinear processes. In ultra intenselasers (normalized field amplitude $a_0 \gg 1$), radiation formation length ismuch shorter than a period and single NCS/NBW cannot be described asscatterings of electrons dressing plane waves with $\gamma$ photons for whatthey feel is a local constant crossed field. However, present theories inconstant crossed fields are hard to give some important quantum features due todivergence problems, such as number of laser photons involved, instantaneousangular distribution and detailed spectrum. As an alternative, presentunderstanding of single NCS/NBW in ultra intense lasers includes severalclassical and semi-quantum ideas such as forward emission, recoil reaction andspectrum cutoff. We investigated multi-photon effects on NCS/NBW in ultraintense lasers by extracting the number of laser photons involved in a singleprocess in ultra intense lasers from formulae of existing theories. Newfeatures of single NCS in ultra intense lasers including fixed emission angleto instantaneous electron momentum, instantaneous deflection of electron, anddisappearance of spectrum cutoff are deduced. Similar features of single NBW inultra intense lasers including non-vanishing emission angles to instantaneous$\gamma$ photon momentum, disappearance of spectrum cutoff and appearance ofspectrum lower limit are also obtained. Simulations show that correspondingsignals of multi-photon effects are significant on $10$PW scale and strongerlasers.

Multi-photon Effects in Single Nonlinear Compton Scattering and Single Nonlinear Breit-Wheeler Process in Ultra Intense Fields