SEMI-CLASSICAL PROPAGATION AND SPECTRAL ANALYSIS IN THE H- ION INTERACTING WITH A METALLIC SURFACE

Abstract

A semi-classical propagator method combined with harmonic inversion of short time signals is used to find the resonant states of an electron interacting with a hydrogen atom near a metallic surface. The atom-electron interaction corresponds to one electron in the presence of a neutral compact core, which can be described by a simple local potential proposed by Cohen. On the other hand, the electron-surface interaction is described by a model proposed by Jennings, the so-called Jelly Model, or by a more realistic local potential that takes into account the shell structure of the metal. A semi-classical propagator approach, proposed by Herman and Kluk, is used to calculate an approximation to the autocorrelation function A(t) = <ψt|ψ0> entirely in terms of classical trajectories. A filter-diagonalization method for harmonic inversion of the complex time signal A(t) is applied to extract the resonances. We verified that the spectral analysis of the signal obtained by semi-classical methods gives satisfactory numerical results for the position and width of the lowest lying resonances.