WKB - type approximations in the theory of vacuum particle creation in   strong fields
  Within the theory of vacuum creation of an $e^{+}e^{-}$ - plasma in the strong electric fields acting in the focal spot of counter-propagating laser beams we compare predictions on the basis of different WKB-type approximations with results obtained in the framework of a strict kinetic approach. Such a comparison demonstrates a considerable divergence results. We analyse some reasoning for this observation and conclude that WKB-type approximations have an insufficient foundation for QED in strong nonstationary fields. The results obtained in this work on the basis of the kinetic approach are most optimistic for the observation of an $e^{+}e^{-}$ - plasma in the range of optical and x-ray laser facilities. We discuss also the influence of unphysical features of non-adiabatic field models on the reliability of predictions of the kinetic theory. 
S.A. Smolyansky, V.V. Dmitriev, A.D. Panferov, A.V. Prozorkevich, D.   Blaschke, L. Juchnowski
physics.plasm-ph hep-ph quant-ph