WKB method for the Dirac equation in a strong external field (Z > 137)

The WKB approximation for the Dirac equation in strong external fields is considered. Wave functions in the classically accessible and non-accessible regions and boundary conditions at the turning point are found. A one-dimensional case (kappa=0) and transition to the non-relativistic limit are specially discussed. The formulae for the widths of quasistationary states in the lower continuum and probabilities of finding and electron in the sub-barrier region are derived. The form of wave functions near the turning point where the quasiclassical approximation breakes is found. A problem of the WKB method accuracy, particularily for the Coulomb case, is discussed in detail. It is shown that, in the physical problems, the WKB method applicability region extends, as a rule, to the region of fairly small quantum numbers