Multiple Photon Production by Electron Pair Annihilation in Flight

Starting with the Feynman-Dyson $S$ matrix, we have computed the two leading terms in the high-energy expansion of the cross section for multiple photon production by electron pair annihilation in flight. In the extreme relativistic limit, when $\ln \left(\frac{E_{+}}{m}\right)\gg 1$, where $E_{+}$ is the positron energy in the laboratory system, our result reduces to that previously obtained by Gupta.