XVIth International Workshop on Quantum Systems in Chemistry and Physics 

Abstract 
Molecular dynamical simulations of helium atom interacting with the XUV field aimed at predicting partial ionization yields of helium ion in various electronic states 
Petra Ruth KapralovaZdanska^{1,2} and Jan Smydke^{1,2}
^{1} J. Heyrovsky Instritute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejskova 3, 182 23 Prague 8, Czech Republic
^{2} Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, Czech Republic 
This conference paper is devoted to the theoretical method which we developed for simulating ionization of the helium atom interacting with a strong electromagnetic field, with a view to later application to other atoms. It consists of two parts. The first part represents the solution of stationary Schroedinger equation for the complex scaled Hamiltonian of the helium atom. Here we focus on choosing the appropriate electronic basis set that allows for obtaining a large scale helium spectrum, which provides a sufficient density of the discretized continuum states, includes the doubly excited Rydberg states, etc. The spectrum is used in the second, dynamical part of the computational method as a part of the basis set for the timedependent wavefunction, see below. Timedependent coefficients of basis functions represent a source of information on the populations of various excited states of the helium atom. Partial sums of the populations of continuum states in each ionization threshold provide the required partial ionization yields associated with direct ionization. Except for the direct ionization, we calculate the ionization, which emerges from resonances that are populated in the process.
Details for the dynamical method are as follows: The interaction Hamiltonian is given in the classical dipole approximation. A typical pulse length is the order of fs to ps and a wavelength of 50 nm. The dynamical process is considered to be mostly adiabatic, in the sense that only one Floquet state is predominantly populated, namely, the one that corresponds to the initial electronic state of helium at zero field strength. Nevertheless, it is necessary to include nonadiabatic processes for calculating the populations of states with a long lifetime (whether they are lowlying continuum states, which are indeed rotated into the complex plane due to complex scaling, but their imaginary components are still small, or just the longlived resonances), where the adiabatic dynamics always inherently leads to their artificial deletion from the wavefunction at the end of the pulse, where the Floquet state goes back to the net initial state. Using the instantaneous Floquet states as a basis set for the timedependent wave function is still advantageous as it ensures an effective separation of the fast timedependence (due to field oscillation) and slow timedependence (due to intensity modulation). Floquet states themselves are given in the basis of the dressed states defined by the direct product of photon states and the field free states of the helium atom. 

