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

Nonlinear Compton scattering (NCS) and nonlinear Breit-Wheeler (NBW) process are strongly multi-photon and highly nonlinear processes. In ultra intense lasers (normalized field amplitude $a_0 \gg 1$), radiation formation length is much shorter than a period and single NCS/NBW cannot be described as scatterings of electrons dressing plane waves with $\gamma$ photons for what they feel is a local constant crossed field. However, present theories in constant crossed fields are hard to give some important quantum features due to divergence problems, such as number of laser photons involved, instantaneous angular distribution and detailed spectrum. As an alternative, present understanding of single NCS/NBW in ultra intense lasers includes several classical and semi-quantum ideas such as forward emission, recoil reaction and spectrum cutoff. We investigated multi-photon effects on NCS/NBW in ultra intense lasers by extracting the number of laser photons involved in a single process in ultra intense lasers from formulae of existing theories. New features of single NCS in ultra intense lasers including fixed emission angle to instantaneous electron momentum, instantaneous deflection of electron, and disappearance of spectrum cutoff are deduced. Similar features of single NBW in ultra intense lasers including non-vanishing emission angles to instantaneous $\gamma$ photon momentum, disappearance of spectrum cutoff and appearance of spectrum lower limit are also obtained. Simulations show that corresponding signals of multi-photon effects are significant on $10$PW scale and stronger lasers.