Ionization of atoms in strong low-frequency electromagnetic field
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Ionization of Atoms in Strong LowFrequency Electromagnetic Field V. P. Krainov Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700 Russia email: [email protected] Received January 11, 2010
Abstract—The ionization of atoms in a lowfrequency linearly polarized electromagnetic field (the photon energy is much lower than the ionization potential of an atom) is considered under new conditions, in which the Coulomb interaction of an electron with the atomic core in the final state of the continuum cannot be considered in perturbation theory in the interaction of the electron with the electromagnetic field. The field is assumed to be much weaker that the atomic field. In these conditions, the classical motion of the electron in the final state of the continuum becomes chaotic (socalled dynamic chaos). Using the wellknown Chir ikov method of averaging over chaotic variations of the phase of motion, the problem can be reduced to non linear diffusion on the energy scale. We calculate the classical electron energy in the final state, which is aver aged over fast chaotic oscillations and takes into account both the Coulomb field and the electromagnetic field. This energy is used to calculate the probability of ionization from the ground state of the atom to a lowerlying state in the continuum using the Landau–Dykhne approximation (to exponential accuracy). This ionization probability noticeably depends on the field frequency. Upon a decrease in frequency, a tran sition to the wellknown tunnel ionization limit with a probability independent of the field frequency is con sidered. DOI: 10.1134/S1063776110080017
of a free electron in the field of a linearly polarized electromagnetic wave is given by
INTRODUCTION Let us first consider the wellknown results obtained by Keldysh for the probability of nonrelativ istic ionization of atoms by a lowfrequency linearly polarized electromagnetic field in the conditions in which the Coulomb field of the atomic core can be dis regarded in the final state of the continuous spectrum (i.e., the case of a shortrange potential). We will always assume that that the photon energy ω of this field is much smaller than ionization potential Ei of the atom. As a rule, henceforth, we will use the atomic system of units, in which the electron charge and mass, as well as the Planck constant, are equal to unity. In accordance of the general approach of the Landau– Dykhne approximation [2], we will calculate the ion ization probability to only an exponential accuracy, disregarding the preexponential factor. The low frequency of the electromagnetic field ensures the condition of adiabaticity of the field per turbation (i.e., applicability of the Landau–Dykhne approximation). The Stark shift of the initial state in the lowfrequency field can be disregarded; its value is close to the quadratic Stark shift in a static electric field that is much weaker than the atomic field and does not change the exponent in the ionization pr
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