Photon-stimulated production of electron-positron pairs in electric field

The rate of $e^+e^-$ pair creation by external electric field in the presence of an incident photon beam is calculated for the photon energy far below the threshold, $\omega \ll m$, and the field strength small as compared to the critical one, $e E \ll m^2$. We find the pair production rate using a recently developed method based on calculation of the process in a thermal bath with subsequent identification of the contribution of single-photon states. We demonstrate that a non-trivial dependence on the ratio of the small parameters, $\omega m/(e E)$, emerges in this approach from an essentially (semi)classical calculation.