Quasi-classical description of the stark effect for an electron in an image-potential state

Abstract

The quasi-classical approximation is used for establishing the positions of the classical turning points of an electron in an image-potential state exposed to an electric field of arbitrary strength perpendicular to the metal surface. It is demonstrated that the behavior of the system in electric fields of different directions is fundamentally different, which makes the dynamics of the low-dimensional system qualitatively different from that of its three-dimensional analog. The electric field strength leading to transition from the tunnel ionization regime to the regime of above-barrier decomposition is determined. The wavefunction of the bound electron state, which explicitly takes into account the influence of the electric field, is expressed in terms of elliptic integrals. The quantization condition is formulated, and the linear and quadratic in the field corrections to the electron energy are found. It is demonstrated that the difference between the linear Stark effect calculated by means of the perturbation theory and the quasi-classical energy shift in a weak field rapidly decreases with increasing quantum level number.