A promising method for the detection of light particles interacting with $e^+e^-$ pairs comes from resonant positron annihilation on atomic electrons. A precise estimate of these production rates need the knowledge of the atomic electron momentum distribution. We propose to use the Compton profile of the target material to include atomic electron momentum effects into resonant annihilation cross-sections. Finally, we show the importance of atomic electron velocity for new physics searches and propose an accurate measurements of the hadronic cross section.