Atomic transitions in ultrastrong laser fields

We have calculated the ionization rate of hydrogen by an intense electromagnetic field in the dipole approximation and in an approximation in which this field dominates the electron-proton interaction in intermediate states. We find the transition rate behaves as $E^{-1\mathrm{}}$ for linearly polarized fields and $E^{-2\mathrm{}}\ln E$ for circularly polarized fields where $E$ is the amplitude of the electric field. We have also calculated the transition rate for excitation of the $2s$ state and a Raman photon. The result behaves as ($E^{-2\mathrm{}}W$) for small $W$ where $W$ is the energy of the Raman photon. We estimate that the method is a good one for electric field strengths of the order of 2×${10}^{11}$ V/cm or higher. This is larger than available currently.