Abstract
Within the framework of perturbation theory, the method of analytical continuation of transition matrix elements is proposed. The method is based on the Sturmian expansion of the transition matrix elements and the analytical continuation of the divergent part of the Sturmian transition matrix elements in the case of above-threshold ionization with one excess photon. Investigation of the ratio Q(N+1)/Q(N) with λ and comparison with experimental data proves the validity of perturbation theory up to I = 1013 W cm−2 for multiphoton ionization of atomic hydrogen in the ground state.
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