Schwinger mechanism of electron-positron pair production by the field of optical and X-ray lasers in vacuum

The probability $W$ of $e^+e^-$-pair production in vacuum by an intense time-varying electric field created by optical or X-ray laser is calculated. Two characteristic regions $\gamma\ll 1$ and $\gamma\gg 1$ of adiabaticity parameter $\gamma$ are considered. With an increase in $\gamma$ and on passing from monochromatic radiation to a finite laser pulse, the probability $W$ increases sharply (for the same field intensity). The dependence of the probability $W$ and the electron and positron momentum spectrum on the pulse shape is discussed (the dynamic Schwinger effect).