Semiclassical matrix elements, essential-states models and perturbation theory of above-threshold ionisation

Abstract
The authors make a quantitative comparison of semiclassical matrix elements for dipole transitions in atomic hydrogen with the known exact expressions. They propose a refinement of some semiclassical formulae. They are then used to estimate the discrepancy between the low-laser-intensity limit of essential states models of above-threshold ionisation and the perturbation theory. For optical photons this discrepancy need not be significant.

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