Rise and fall of laser-intensity effects in spectrally resolved Compton process
The spectrally resolved differential cross section of Compton scattering, $d σ/ d ω' \vert_{ω' = const}$, rises from small towards larger laser intensity parameter $ξ$, reaches a maximum, and falls towards the asymptotic strong-field region. Expressed by invariant quantities: $d σ/du \vert_{u = const}$ rises from small towards larger values of $ξ$, reaches a maximum at $ξ_{max} = \frac49 {\cal K} u m^2 / k \cdot p$, ${\cal K} = {\cal O} (1)$, and falls at $ξ> ξ_{max}$ like $\propto ξ^{-3/2} \exp \left (- \frac{2 u m^2}{3 ξ\, k \cdot p} \right )$ at $u \ge 1$. [The quantity $u$ is the Ritus variable related to the light-front momentum-fraction $s = (1 + u)/u = k \cdot k' / k \cdot p$ of the emitted photon (four-momentum $k'$, frequency $ω'$), and $k \cdot p/m^2$ quantifies the invariant energy in the entrance channel of electron (four-momentum $p$, mass $m$) and laser (four-wave vector $k$).] Such a behavior of a differential observable is to be contrasted with the laser intensity dependence of the total probability, $\lim_{χ= ξk \cdot p/m^2, ξ\to \infty} \mathbb{P} \propto αχ^{2/3} m^2 / k \cdot p$, which is governed by the soft spectral part. We combine the hard-photon yield from Compton with the seeded Breit-Wheeler pair production in a folding model and obtain a rapidly increasing $e^+ e^-$ pair number at $ξ\lesssim 4$. Laser bandwidth effects are quantified in the weak-field limit of the related trident pair production.