Exploring resonant positron annihilation on atomic electrons offers a promising method for detecting light dark sector particles that interact with e+e− pairs. However, to accurately estimate production rates, a thorough understanding of atomic electron momentum distributions is essential. We introduce a comprehensive approach using the Compton profile of target materials to accurately incorporate electron velocity effects into resonant annihilation cross-sections. We show that taking into account the finite motion of atomic electrons not only can improve the search for new physics, but can also allow to enhance the accuracy of hadronic cross-section measurements.