Abstract
The Sturmian expansions of the multiphoton transition matrix elements diverge in the case of above-threshold ionisation (ATI). To get convergent expressions the analytical continuation methods can be used. The method proposed is based on the analytical continuation of the radial transition matrix elements developed earlier by the author for the two-photon ATI and is proved to be valid for numbers of photons up to nine with one additional photon involved. Transition rates for the ATI of atomic hydrogen in the ground state with one extra photon by linearly polarised light are calculated. Ionisation rates are evaluated for numbers of photons up to nine in the whole energy range where ionisation by one additional photon is possible. For the ratio of five-photon and four-photon ionisation cross sections a good agreement with experiment is obtained.
Published Version
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