The dynamics of the ionization of atoms exposed to strong low-frequency fields

We present a theoretical study of strong-low-frequency-field ionization of atoms in the intermediate regime where the Keldysh parameter is close to one. For that purpose we have developed a novel method based on an explicit algorithm for the propagation of the time-dependent Schroedinger equation which is known to be very stiff. This method overcomes the stiffness by taking into account the eigenfrequencies of the interacting system. With the help of this approach we are able in particular to investigate the ionization of the hydrogen atom by ultra-short (25 fs) 790 nm laser pulses at intensities 0.5-6 x 1014 W/cm2.