We briefly review some technical aspects of our Sturmian basis calculations of rates for high-order multiphoton processes occurring in atomic hydrogen initially in its ground state. The processes under study include ionization, Raman scattering, and harmonic generation. We present results that illustrate the efficacy of the method and that also highlight some of the interesting physics of multiphoton processes. In particular, we show nonperturbative rates for harmonic generation by 1064-nm light and for ionization by light of wavelengths 532, 608, 616, and 1064 nm, with laser intensities in the range 1012–1014 W/cm2. We discuss in some detail the role of intermediate resonances in ionization processes. Some of these resonances strongly enhance the rates; others do not. The influential resonances can be characterized by the orbital angular quantum number of the corresponding intermediate states. At long wavelengths and moderate intensities, perturbation theory grossly overestimates the ionization rates. Consequently, at long wavelengths the peak intensity that atoms can experience in short pulses before undergoing ionization is far higher than would be anticipated on the basis of perturbation theory.
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