Modern methods for calculations of photoionization and electron impact   ionization of two-electron atoms and molecules
  A review of some recently developed methods of calculating multiple differential cross-sections of photoionization and electron impactionization of atoms and molecules having two active electrons is presented. The methods imply original approaches to calculating three-particle Coulomb wave functions. The external complex scaling method and the formalism of the Schroedinger equation with a source in the right-hand side are considered. Efficiency of the time-dependent approaches to the scattering problem, such as the paraxial approximation and the time-dependent scaling, is demonstrated. An original numerical method elaborated by the authors for solving the 6D Schroedinger equation for an atom with two active electrons, based on the Chang-Fano transformation and the discrete variable representation, is formulated. Basing on numerical simulations, the threshold behavior of angular distributions of two-electron photoionization of the negative hydrogen ion and helium atom, and multiple differential cross-sections of electron impact ionization of hydrogen and nitrogen molecules are analyzed. It is demonstrated that the Wannier law for the angular distribution of double ionisation is not correct even at very small energies. 
Vladislav V. Serov, Vladimir L. Derbov, Tatiana A. Sergeeva, Sergue I.   Vinitsky
physics.atom-ph quant-ph