The Schwinger effect and possibilities for its observation using optical and X-ray lasers

The probability W of e ⁺ e ^? pair production from a vacuum in an intense variable electric field generated with powerful optical or X-ray lasers is calculated. Two characteristic ranges are considered: γ ? 1 and γ ? 1, where γ is the adiabaticity parameter. The probability W is shown to increase sharply with γ (at a fixed field strength F). The dependence of W and the momentum spectrum of electrons and positrons on the laser pulse shape is discussed in detail. Numerical calculations were performed for a laser pulse with a Gaussian envelope and for some pulsed fields.