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Journal of Physics B Atomic and Molecular Physics

Bound-free transitions in electromagnetic field of arbitrary intensity

N. K. Rahman, Farhad H. M. Faisal

Published Mar 1, 1973• 10 citations
Publisher

Abstract

A useful new method of calculation for bound-free transitions under the momentum translation approximation for multiphonon processes is outlined.
DOI
10.1088/0022-3700/6/3/024

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A general approximation method is developed for the treatment of bound quantum systems in the presence of an intense external electromagnetic field of long wavelength. The method is based upon a unitary transformation which approximately removes the electromagnetic field from the problem. The accuracy of the technique increases with the number of photons involved in any given process; and in the case of large photon number, the results have a simple, concise form resembling first-order perturbation theory. It is possible to handle intense-field problems with small numbers of photons also, but then the formalism takes on a complexity analogous to the corresponding perturbation expressions for the same number of photons. The theory is extended to the case where two electromagnetic field modes are present, one or both of which may be intense. Bound-bound transitions in a hydrogenlike atom are calculated as an illustration of the application of the method. One of the explicit nonlinear effects to appear is an intensity-dependent deviation of the transition probability behavior from In{I}^{n}In for nnn-photon transitions, where III is the field intensity. It is demonstrated that intensity effects are much more probable with bound electrons than with free electrons.
An approximation method is developed which yields very simple and general analytical results for electromagnetic bound-bound or bound-free transitions for any arbitrarily high order of interaction with the electromagnetic field. The approximation is perturbative in the sense that transition probabilities are proportional to the field intensity raised to the power NNN, where NNN is the order of the interaction. Limiting values of electromagnetic field strength are given within which the approximation is valid. These limits depend upon the binding potential which produces the bound states. A feature of the results is that they show the onset of high-order dominance effects which can occur at high-field intensities.