Lateral motion of electrons in the tunneling ionization process

Abstract We report a study of the distribution of electron coordinates at the moment of the tunnel exit in the process of strong field ionization. One can get an insight into the physical observables characterizing electron at the moment of ionization using approximate approaches such as the Strong Field Approximation (SFA). Our study is based solely on the analysis of the solution to the time-dependent Schrödinger equation (TDSE), and thus can be considered as a completely ab initio approach, allowing to extract information about electron’s characteristics at the moment of ionization by analyzing suitably designed correlation functions obtainable from the TDSE. This approach allows to unambiguously single out the part of the wave-function describing the ionized electron wave-packet from the solution of the TDSE for the atomic system in the laser field, and achieve a clear separation of direct and rescattering trajectories without resorting to classical or semi-classical methods. We find that for the short-range Yukawa potential, the distribution of the lateral coordinate at the time of ionization agrees well with the predictions based on SFA. However, for the hydrogen atom, the lateral coordinate distribution is significantly modified. We show that this modification is due primarily to the Coulomb rescattering effects occurring toward the end of the laser cycle. This highlights the significant contribution of Coulomb rescattering to the time evolution of the electron wave-packet following strong field ionization.