  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.
