The effect of a resonant electric field on a one-dimensional classical hydrogen atom

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Abstract
The authors study the classical motion of an electron moving in a Coulomb potential and a resonant and near-resonant electric field, but constrain the electron to move only in the direction of the field. This simple model of an excited hydrogen atom in a microwave field is simpler to understand than the three-dimensional system, yet retains some essential dynamical features. They show how the Coulomb singularity can be removed by regularisation in order to produce a Hamiltonian suited to efficient numerical computations. They obtain accurate estimates of the field strengths at which ionisation occurs and show that for resonant fields this is well estimated by the second-order resonance-overlap criterion. They show that the frequency dependence of the ionisation probability is similar to that of the classical three-dimensional system and show how its behaviour depends upon particular stable periodic orbits which persist for quite strong fields. They discuss the relevance of this model to the three-dimensional case and to quantal calculations.