  Low-energy Compton scattering is an important background for sub-GeV dark
matter direct-detection and other experiments. Current Compton scattering
calculations typically rely on assumptions that are not valid in the low-energy
region of interest, beneath ~ 50 eV. Here we relate the low-energy Compton
scattering differential cross section to the dielectric response of the
material. Our new approach can be used for a wide range of materials and
includes all-electron, band structure, and collective effects, which can be
particularly relevant at low energies. We demonstrate the strength of our
approach in several solid-state systems, in particular Si, Ge, GaAs, and SiC,
which are relevant for current and proposed experiments searching for dark
matter, neutrinos, and millicharged particles.
