Impact Ionization in the Proton—H-Atom System. V. Final-Cross-Section Calculations

The cross section σ₁(ε;E) has been calculated for the direct impact ionization of hydrogen atoms by protons, H⁺+H(1s)→2H⁺+e^-, for low relative collision energies E between 100 and 500 eV, and all electron energies ε for which it is significant. Fundamental theory and most electronic matrix-element calculations were presented in earlier papers of the series. In the present paper we complete the electronic matrix-element calculations (in particular, the "optimization" of Coriolis or angular coupling matrix elements for ionizing transitions, through introduction of an angular velocity electron-translation factor); and we perform the final integrations over classical trajectories and impact parameters to obtain the cross sections. The cross sections σ₁(ε;E) show the expected steep falloff with increasing ε and decreasing E, owing to the increasing inefficiency of momentum and energy transfer from the heavy particles to the electron under such changes; σ₁ decreases by about two orders of magnitude from E=500 eV to $E=100$ eV, and by four orders of magnitude from ε=0 a.u. to ε=1.0 a.u. A strong dependence of cross section on isotopic mass at fixed E is also predicted thereby. Finally, the most significant conclusion is that the cross section for ionization from the 1sσᵤ(2pσᵤ) molecular electronic state is about 500 times greater than that for ionizing a 1sσg molecular electron, the main source of transitions being the Coriolis coupling operator.