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

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 fi...

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Bibliographic Details
Published in:Optics and spectroscopy 2017, Vol.122 (1), p.120-127
Main Authors: Golovinskii, P. A., Preobrazhenskii, M. A.
Format: Article
Language:English
Subjects:
Electric field strength
Electric fields
Electric potential
Electron energy
Electron states
Elliptic functions
Lasers
Metal surfaces
Optical Devices
Optics
Perturbation theory
Photonics
Physics
Physics and Astronomy
Spectroscopy of Atoms and Molecules
Stark effect
Wave functions
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Summary: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.
ISSN:0030-400X
1562-6911
DOI:10.1134/S0030400X1701009X