Perturbative calculation of the ac Stark effect by the complex rotation method

We have calculated the high-order ac Stark effect for the ground state of atomic hydrogen by applying Rayleigh-Schrödinger perturbation theory to a complex-rotated Hamiltonian. We present results for the level-shift and multiphoton-ionization rate, which include effects of above-threshold ionization. Our results indicate that the field intensities at which high-order contributions become dominant can be as low as 1011 W/cm2, much lower than is commonly expected. A systematic treatment of the frequency dependence of the perturbation coefficients in the vicinity of multiphoton resonances and ionization thresholds is provided by reference to the analytical properties of the Coulomb Greens function.