Particle production in a varying electric field

The spectral density of particles created from the vacuum in a slowly varying electric field E(t) is calculated. A formula is also obtained for the rate of pair production which generalizes the well known Schwinger formula. It is shown that if m2/Vertical BareEVertical Bar>>1, the field can be assumed constant only for Vertical BarE/EVertical Bar<<m(Vertical BareEVertical Bar/m2)/sup 3/2/. The results obtained are used to take into account the back reaction of the created particles. It is shown that an exponentially decreasing electric field creates particles from the vacuum with a thermal spectrum if the residual effect of the field on the created particles can be neglected