Relativistic version of the boundary-layer method in the tunnel ionization of atoms by a constant uniform electric field

Abstract

Within the paraxial Fock-Leontovich approximation, the new method of calculation of the Dirac wave functions is developed for three-dimensional axially symmetrical problems which do not permit the complete separation of variables. By means of the elaborated quasiclassical method the relativistic wave functions for the H-like atom in the weak constant uniform electric field are constructed in the below-barrier and classically allowed ranges. General analytical expression for probability of ionization of the atom in an external electric field is obtained. The comparison of the found formulas with results known previously is carried out.