Soft-photon emission in extreme-relativistic Compton scattering by K-shell electrons and connection to photoeffect

We have recently obtained cross-sections for Compton scattering by K-shell electrons at extreme-relativistic (ER) energies of the incoming photon. Our method is essentially analytical, and only at the end did it require a modest numerical computation. The results are valid for the Compton line of the scattered photon spectrum, but do not cover the infrared divergence at the soft-photon end of the spectrum. This case is treated in the present...