Abstract
A non-perturbative method is used to obtain an analytic expression for the rate of multiphoton ionization of hydrogenic atoms as a function of the incident radiation. The result shows that at low intensities the ionization rate is similar to that obtained in the usual perturbative calculations. With increasing intensities, however, the perturbative result is violated and the ionization rate is found to depend not only on the Nth power of intensity but on higher powers as well.