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We have solved the fully 3-dimensional time-dependent Schrodinger and Pauli equations for an electron bound in a Coulomb potential, interacting with a superintense electromagnetic (laser) field of high frequency. Adiabatic stabilization is observed at high intensities. Corrections to the dipole approximation modify the ionization probability only slightly, up to the maximum intensity considered (2.5. 1019 W The behaviour of atomic systems interacting with superintense laser fields has attracted considerable interest in recent years. For frequencies of the laser field which are low compared to the field-free ionization potential of the system, the ionization at high intensity is governed by a tunnelling mechanism [l, 21 and therefore keeps increasing with intensity. At high frequencies, on the other hand-and this is the case we are interested in here-adiabatic stabilization is predicted, that is, the ionization probability will decrease with increasing field intensity, while the ionization energy will also decrease in the field. This has been extensively discussed by Gavrila and coworkers [3] within the Floquet formalism, using the dipole approximation for the external strong laser field. Numerous other time-dependent 14-61 and Floquet [7] calculations have been performed.

A bound state and an autoionizing state of a complex atom, resonantly coupled by a multiphoton process in a strong laser field, can become degenerate at a certain laser frequency and intensity. These states are referred to as laser-induced degenerate states or LIDS. The ab initio, fully nonperturbative R-matrix Floquet method has been used to study the behaviour of LIDS coupled by three photons in argon. A simple single-photon model has been successfully applied to interpret the calculation and to predict a further degeneracy at a higher frequency and intensity.

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