Sturmian expansion of Green’s function and its application to multiphoton ionization of hydrogen

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Abstract
We report a study of the Sturmian expansion of Green’s function and its convergence properties in the complex energy plane. We take as a model for our study multiphoton ionization of hydrogen. Convergence difficulties arise from the fact that the stationary wave of the outgoing photoelectron contains both outgoing and ingoing parts, whereas the Sturmian functions have outgoing wave character and so do not provide an expansion of the ingoing part of the photoelectron wave. We show how this difficulty can be overcome. We have tested the method for N-photon ionization of hydrogen when (N-1)-photon ionization is possible, with N=2–5, and for three-photon ionization when ordinary photoionization is possible.