Precision measurement of Compton scattering in silicon with a skipper CCD for dark matter detection

Experiments aiming to directly detect dark matter through particle recoils can achieve energy thresholds of $\mathcal{O}(10\text{ }\text{ }\mathrm{eV})$. In this regime, ionization signals from small-angle Compton scatters of environmental $\ensuremath{\gamma}$ rays constitute a significant background. Monte Carlo simulations used to build background models have not been experimentally validated at these low energies. We report a precision measurement of Compton scattering on silicon atomic shell electrons down to 23 eV. A skipper charge-coupled device with single-electron resolution, developed for the DAMIC-M experiment, was exposed to a $^{241}\text{Am}$ $\ensuremath{\gamma}$-ray source over several months. Features associated with the silicon K-, ${\mathrm{L}}_{1}$-, and ${\mathrm{L}}_{2,3}$-shells are clearly identified, and scattering on valence electrons is detected for the first time below 100 eV. We find that the relativistic impulse approximation for Compton scattering, which is implemented in Monte Carlo simulations commonly used by direct detection experiments, does not reproduce the measured spectrum below 0.5 keV. The data are in better agreement with ab initio calculations originally developed for x-ray absorption spectroscopy.