Electron-impact double ionization of a model helium atom

Single- and double-ionization processes in electron scattering from a model helium atom are calculated by a direct solution of the time-dependent Schrodinger equation on a 3D lattice. The Coulomb interaction between the electrons is described by v(r(1),r(2)) = 1/r(>) and all angular momenta are set to zero. The initial state is a product of the ground state of the model helium atom on a 2D lattice with a wave packet for the free electron. At times following the collision and for incident electron energies around 200 eV, the probability density associated with double ionization is found to be quite small when compared to other scattering processes. Projections onto 1D continuum states an employed to calculate single- and double-ionization cross sections. Although absolute cross sections for the model cannot be compared to experiments on helium due to the neglect of higher partial waves, the ratio of double to single ionization for the model is found to be 1% or less, in fair agreement with experiment, [S1050-2947(99)03806-8].