Detection schemes for quantum vacuum diffraction and birefringence

Motivated by recent experimental initiatives, such as at the
Helmholtz International Beamline for Extreme Fields (HIBEF)
at the European X-ray Free Electron Laser (XFEL), we calculate
the birefringent scattering of x-rays at the combined field of
two optical (or near-optical) lasers and compare various scenarios.
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In order to facilitate an experimental detection of quantum vacuum diffraction and
birefringence, special emphasis is placed on scenarios where the initial
and final x-ray photons differ not just in polarization, but also in
propagation direction (corresponding to scattering angles in the mrad regime)
and possibly energy.