Electron emission characteristics in p-H(1s) collisions from numerical solutions of the time-dependent Schrodinger equation -: art. no. 012714

The numerical integration of the three-dimensional time-dependent Schrodinger equation that appears in the impact-parameter approximation is carried out using a Fourier collocation method that is based on a splitting technique for the time evolution operator. The final wave function is analyzed in momentum space using a histogram approach. Singly and doubly differential cross sections for ionization as a function of polar emission angle and energy are calculated near the maximum in the total cross section, i.e., at 50-60-keV impact energy. They compare well with recent experimental results for intermediate and high electron emission energies, while some discrepancies remain at low energies due to the neglect of residual Coulomb interactions in the ionized wave packet. In order to achieve convergence and to reproduce experimental results at electron energies below 20 eV one needs to extend the calculations to final internuclear separations beyond 30 a.u.