ИСТИНА

The strong field approximation is derived through the introduction of an ansatz. This approach allows one to develop a gauge independent Born series in the Coulomb potential and provides a tractable way of evaluating high order contributions. Different families of ansatz are discussed in details. The accuracy of the strong field approximation in the long wavelength regime is studied by comparing it to the numerical solution of the time-dependent Schroedinger equation in the case of the interaction of atomic hydrogen with a short laser pulse.