Total multiphoton-ionization rates for an extremely short-ranged potential

Abstract

The total ionization rate by a plane-wave field in the long-wavelength approximation from a three-dimensional \ensuremath{\delta}-function potential is reconsidered. Well into the above-threshold ionization regime, the Keldysh approximation turns out to yield virtually the exact ionization rate for circular polarization. For multiphoton orders in excess of n\ensuremath{\sim}10, lowest-order perturbation theory only holds for intensities much lower than those employed in current experiments. For moderate intensities, the total ionization rate is very well approximated by a slope of N+k with integer k\ensuremath{\ge}1. Within the range of most experimental interest where one or several channels are suppressed by the ponderomotive barrier, the slope is again near N and decreasing with increasing intensity.