<p>Due to Heisenberg’s uncertainty principle, atomic electrons localized around the nucleus exhibit a characteristic momentum distribution that, in elements with high atomic number, remains significant up to relativistic values. Consequently, in fixed-target experiments, atoms can effectively act as electron accelerators, increasing the centre-of-mass energy in collisions with beam particles. In this work, we leverage this effect to explore its potential for new physics searches. We consider positrons from beams of various energies annihilating with atomic electrons in a ⁷⁴W fixed target. We compute the production rates of new vector bosons and pseudoscalar particles as functions of their couplings and masses. We show that the electron-at-rest approximation significantly underestimates the mass reach for producing these new states compared to the results obtained by properly accounting for atomic electron momenta. In particular, we estimate the sensitivity for detecting these new particles using the positron beam at the Beam Test Facility linac at the Laboratori Nazionali di Frascati, the H4 beamline in the CERN North Area, and the proposed Continuous Electron Beam Accelerator Facility of Jefferson Laboratory.</p>