Production of dark sector particles via resonant positron annihilation on atomic electrons

Resonant positron annihilation on atomic electrons provides a powerful method to search for light new particles coupled to $e^{+}{e}^{-}$. Reliable estimates of production rates require a detailed characterization of electron momentum distributions. We describe a general method that harnesses the target material Compton profile to properly include electron velocity effects in resonant annihilation cross-sections. We additionally find that high $Z$ atoms can efficiently act as particle physics accelerators, providing a density of relativistic electrons that allows to extend by several times the experimental mass reach.