  High energy positron annihilation is a viable mechanism to produce dark
photons ($A^\prime$). This reaction plays a significant role in beam-dump
experiments using experiments using multi-GeV electron-beams on thick targets
by enhancing the sensitivity to $A^\prime$ production. The positrons produced
by the electromagnetic shower can produce an $A^\prime$ via non-resonant ($e^+
+ e^- \to \gamma + A^\prime$) and resonant ($e^+ + e^- \to A^\prime$)
annihilation on atomic electrons. For visible decays, the contribution of
resonant annihilation results in a larger sensitivity with respect to limits
derived by the commonly used $A^\prime$-strahlung in certain kinematic regions.
When included in the evaluation of the E137 beam-dump experiment reach,
positron annihilation pushes the current limit on $\varepsilon$ downwards by a
factor of two in the range 33 MeV/c$^2<m_{A^\prime}<120$ MeV/c$^2$.
