Rise and fall of laser-intensity effects in spectrally resolved Compton process

The laser intensity dependence of nonlinear Compton scattering is discussed in some detail. For sufficiently hard photons with energy ω', the spectrally resolved differential cross section dσ/dω'|ω'=const, rises from small toward larger laser intensity parameter ξ, reaches a maximum, and falls toward the asymptotic strong-field region. Such a rise and fall of a differential observable is to be contrasted with the monotonously increasing laser intensity dependence of the total probability, which is governed by the soft spectral part. We combine that hard-photon yield from Compton scattering with the seeded Breit–Wheeler pair production in a folding model and obtain a rapidly increasing e+e− pair number at ξ ≲ 4. Laser bandwidth effects are quantified in the weak-field limit of the related trident pair production.