Atoms as Electron Accelerators for Measuring the Cross Section of e^{+}e^{-}→Hadrons

The hadronic vacuum polarization contribution to (g-2)_{μ} can be determined via dispersive methods from e^{+}e^{-}→hadrons data. We propose a novel approach to measure the hadronic cross section σ_{had}(s) as an alternative to the initial-state radiation and energy scan techniques, which relies on positron annihilation off atomic electrons of a high Z target (^{238}U, Z=92). We show that by leveraging the relativistic electron velocities of the inner atomic shells, a high-intensity 12 GeV positron beam, such as the one foreseen at JLab, can allow measuring σ_{had}(s) with high statistical accuracy from the two-pion threshold up to above sqrt[s]∼1  GeV.