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The particle creation by the so-called peak electric field is considered. The latter field is a combination of two exponential parts, one exponentially increasing and another exponentially decreasing. We find exact solutions of the Dirac equation with the field under consideration with appropriate asymptotic conditions and calculate all the characteristics of particle creation effect, in particular, differential mean numbers of created particle, total number of created particles, and thedoi:10.1140/epjc/s10052-016-4289-0 fatcat:xthg22zahjb57cguhr6xrztkfa