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**Atoms and molecules exposed to intense laser fields: **

The numerical treatment of atoms or molecules exposed to intense fields (comparable to the Coulombic binding forces within these systems) remains a great challenge to theory. On the other hand, this research area is not only of interest for atomic and molecular physics, but also for example for astrophysics (strong magnetic fields in, e.g., white dwarfs), laser physics (intense, short pulses), scanning tunneling microscopy (strong electric fields due to short distances), or single-molecule conduction (how does an electric current flows through an atom or molecule).

#### Perturbative multiphoton regime:

In the case of not too high intensities but high photon frequencies, the interaction of a laser with an atom or molecule can be described within lowest-order perturbation theory. However, already on this level of approximation an in principle infinite sum over all field-free states of the atom or molecule is required. This includes also the corresponding electronic (ionization) or vibrational (dissociation) continua. Special techniques have to be developed and coded that allow for such a summation. Presently, we are using two different techniques (the discretization approach and the complex-scaling method) to achieve this goal.

#### Quasi-static regime:

In the case of higher intensities but low frequencies the interaction of a laser with atoms or molecules may be approximately described within the so-called quasi-static approximation. The laser field is then described as a slowly varying electric field. Simple expressions for predicting the corresponding ionization rates were predicted long time ago, and they are usually used when interpreting experiments. However, the reliability of these expressions has not yet been carefully investigated. The experimental verification is difficult, since the knowledge about the laser-pulse parameters is usually too unprecise. A theoretical check is difficult, since fully three-dimensional ab initio calculations were for a long time only feasible for atomic hydrogen, but the simplified expressions were derived for this system. Thus atomic hydrogen is not a good test candidate. We have developed a code that allows such an ab initio calculation for diatomic two-electron systems like molecular hydrogen. This lead to the discovery of interesting phenomena (bond softening and enhanced ionization) that were predicted to occur only in molecular ions with an odd number of electrons. We have shown that these phenomena occur also for neutral molecules, but for different reasons than for the ions. Presently, we are working on extending our calculations to laser pulses (instead of considering static fields).

#### Non-perturbative regime:

With the new laser sources intensity and frequency regimes can be reached that do not allow the approximative treatments discussed above (perturbation theory or quasi-static approximation). In this case a full time-dependent treatment is required. This is computationally extremely demanding. Two different approaches to this problem are presently under development for molecular systems. The grid-method expands the time-dependent wave function on a discretized many-dimensional grid and solves the resulting discretized equations. Based on our (good) experience with atomic systems, we are working on an expansion in field-free eigenstates.