Time scaling with efficient time-propagation techniques for atoms and molecules in pulsed radiation fields

We present an ab initio approach to solve the time-dependent Schr\"odinger equation to treat electron and photon impact multiple ionization of atoms or molecules. It combines the already known time scaled coordinate method with a new high order time propagator based on a predictor-corrector scheme. In order to exploit in an optimal way the main advantage of the time scaled coordinate method namely that the scaled wave packet stays confined and evolves smoothly towards a stationary state the modulus square of which being directly proportional to the electron energy spectra in each ionization channel, we show that the scaled bound states should be subtracted from the total scaled wave packet. In addition, our detailed investigations suggest that multi-resolution techniques like for instance, wavelets are the most appropriate ones to represent spatially the scaled wave packet. The approach is illustrated in the case of the interaction of an one-dimensional model atom as well as atomic hydrogen with a strong oscillating field.