Vacuum pair-production in a classical electric field and an electromagnetic wave

•The electron–positron pair-production rate in an electric field and an electromagnetic wave.•The pair-production rate enhanced by the amplitude of the electromagnetic wave.•Its application for the superposition of the static electric field and laser beams.•Medium effects on the pair-production rate.•The enhancement of the pair-production rate by the self-focusing property of laser beams.

Using semiclassical WKB-methods, we calculate the rate of electron–positron pair-production from the vacuum in the presence of two external fields, a strong (space- or time-dependent) classical field and a monochromatic electromagnetic wave. We discuss the possible medium effects on the rate in the presence of thermal electrons, bosons, and neutral plasma of electrons and protons at a given temperature and chemical potential. Using our rate formula, we calculate the rate enhancement due to a laser beam, and discuss the possibility that a significant enhancement may appear in a plasma of electrons and protons with self-focusing properties.