Low density approximation of electron-positron pair production in strong field

Electron-positron pair production in time-dependent homogenous strong external electric field is investigated．For turning points of scattering potential, low-density approximation (LDA) arising from quantum Vlasov equation is proven to be equivalent to semi-classical WKB (Wentzel-Kramers-Brillouin) method．Typical examples are used to confirmed numerically the equivalency of these two methods．When there are too many turning points, WKB integrals become tedious, then LDA is a more convenient calculation technique．Our work by the combination of quantum kinetic process with quantum tunneling process will facilitate understanding of electron-positron pair production in the vacuum under strong fields．