Time-dependent quantal calculations for L=0 models of the electron-impact ionization of hydrogen near threshold

The electron-impact ionization cross section for hydrogen near threshold is calculated using both time-dependent wave-packet and time-dependent Green's-function methods. The time-dependent Green's-function method also allows the calculation of the elastic cross section. The need for absorbing potentials was removed by allowing our fast waves to leave our two-dimensional grid. Two different models are used for the Coulomb interaction between the electrons: a cusp model with v(r₁,r₂)=1/r> and a linear model with v(r₁,r₂)=1/(r₁+r₂), both with all angular momenta set to zero. Between 0.2 and 2.0 eV the cusp model cross section may exhibit an exponential suppression, while the linear model cross section follows a power-law behavior with an exponent of 1.1 with no noticeable oscillations. The results of the numerical experiments are compared with previous classical and quantal predictions extending back over 40 years to the pioneering work of Wannier.