Abstract
We study the $2\rightarrow1$ process of electron-positron pair annihilation to a single photon in a plane-wave background. The probability of the process in a pulsed plane wave is presented, and a locally constant field approximation is derived and benchmarked against exact results. The stricter kinematics of annihilation (compared to the $1\rightarrow2$ processes usually studied) leads to a stronger dependence on the incoming particle states. We demonstrate this by studying the effect that initial state wavepackets have on the annihilation probability. The effect of annihilation in a distribution of particles is studied by incorporating the process into Monte Carlo simulations.
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