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

Abstract

The spectrally resolved differential cross section of Compton scattering, $d\sigma /d{\omega }^{\prime }{|}_{{\omega }^{\prime }=const}$, rises from small towards larger laser intensity parameter $\xi$, reaches a maximum, and falls towards the asymptotic strong-field region. Expressed by invariant quantities: $d\sigma /du{|}_{u=const}$ rises from small towards larger values of $\xi$, reaches a maximum at ${\xi }_{max}=\frac{4}{9}\mathcal{K}u{m}^2/k\cdot p$, $\mathcal{K}=\mathcal{O}(1)$, and falls at $\xi >{\xi }_{max}$ like $\propto {\xi }^{-3/2}\exp \left(-\frac{2u{m}^2}{3\xi k\cdot p}\right)$ at $u\ge 1$. [The quantity $u$ is the Ritus variable related to the light-front momentum-fraction $s=(1+u)/u=k\cdot k^{\prime }/k\cdot p$ of the emitted photon (four-momentum $k^{\prime }$, frequency ${\omega }^{\prime }$), 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, ${\lim }_{\chi =\xi k\cdot p/m^2,\xi \to \infty }\mathbb{P}\propto \alpha {\chi }^{2/3}{m}^2/k\cdot p$, 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 $\xi \lesssim 4$. Laser bandwidth effects are quantified in the weak-field limit of the related trident pair production.

Comments: 12 pages, 8 figures