Convergence of Rayleigh-Schrödinger perturbation theory in calculations of multiphoton processes

We have calculated the high-order ac Stark shift, multiphoton ionization rates, and nonlinear susceptibilities for high harmonic generation for the hydrogen atom in a radiation field. The calculations are done in the framework of Rayleigh-Schrödinger perturbation theory applied to a complex-rotated Hamiltonian. Our intention is to investigate the limitations of perturbation theory in calculations of multiphoton processes. Comparisons are made with results from nonperturbative calculations. For some frequencies the results of lowest-order perturbation theory are found to disagree with nonperturbative calculations even at moderate to low intensities (I ˜ 1011 Wcm-2) and in the absence of resonances. We find that the high-order perturbation expansion converges only in a very limited range of intensities, so that perturbation theory is not a reliable predictor of the behavior of hydrogen atoms in radiation fields with intensities greater than ˜ 1012 Wcm-2.