Boundary-layer method in the theory of tunnel ionization of an atom by constant uniform electric field

Abstract

Within the paraxial Fock-Leontovich approximation the three-dimensional version of the WKB method is developed for the Schrodinger equation with an arbitrary axially symmetrical potential of barrier type which does not permit the complete separation of variables. By means of the elaborated recurrent scheme of WKB expansions the wave functions in the problem of an atom in a constant uniform electric field are constructed in the classically forbidden and allowed regions. This has allowed for the first time to calculate the first two terms of the asymptotic (at small intensity of electric field) behavior of probability of tunneling ionization of an arbitrary atom (not H-like one) in a constant uniform electric field, taking into account the centrifugal energy.