The WKB method for the Dirac equation with vector-scalar potentials in 2+1 and 3+1 dimensions

Abstract:
The recurrent scheme of deriving WKB-expansions for the Dirac equation with arbitrary central-symmetrical scalar and vector potential of a barrier type in two and three spatial dimensions is developed. The relativistic analog of the Bohr-Sommerfeld quantization condition and the general analytical expression for decay width of a quasistationary state are obtained. On the example of spherical model of the Stark effect the quasistationary spectrum of relativistic two- and three-dimensional hydrogen-like atoms (ions) in the external central-symmetrical field is found. Influences of the relativistic effects and spatial dimensionality on the position and width of quasistationary levels are investigated.