Pair production in a strong electric field with an account of the coulomb interaction

In the framework of the Dirac model of vacuum the creation of $e^{+}e^{-}$ pairs in a constant and uniform electric field with allowance Coulomb interaction between $e^{+}$ and $e^{-}$ is considered. The transmission coefficient via the energy gap deformed by external field and the electric fields of particles is calculated in the semiclassical approximation. The Sauter exponential factor is modified by the exactly calculated function $G(y)$ accounting Coulomb interaction of particles and changes in the shape of the potential barrier. When $y < 1$ the values of $G(y)$ exceeds unity, testifying the suppression of pair production in comparison with the predictions of Schwinger [1] and Ritus [2]. With further increase in the field strength, $y < 1 < 2$, $G(y)$ tends to zero and the probability of pair production has increased rapidly.