Quasiclassical Theory of the Ionization of the Hydrogen-Like Atom by an External Electrostatic Field

Abstract

The recurrent scheme for finding the quasiclassical solutions of the one-dimensional equation obtained after separation of variables in the Schr\"odinger equation in the parabolic coordinates is elaborated. The method of quasiclassical localized states is developed for the Dirac equation with arbitrary axially symmetrical potential of barrier type which does not permit complete separation of variables. Using the proposed quasiclassical methods the non-relativistic and relativistic wavefunctions for hydrogen-like (H-like) atom in the external uniform electrostatic field of intensity F are constructed in classically forbidden and allowed regions. The general analytical expressions for leading term of the asymptotic (at small F) behaviour of ionization rate of H-like atom in the uniform electrostatic field are obtained for the non-relativistic and relativistic cases.