The cross section ${\sigma }_1(\epsilon ;E)$ has been calculated for the direct impact ionization of hydrogen atoms by protons, ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to 2{\mathrm{H}}^{+}+e^{-}$, for low relative collision energies $E$ between 100 and 500 eV, and all electron energies $\epsilon$ 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 ${\sigma }_1(\epsilon ;E)$ show the expected steep falloff with increasing $\epsilon$ and decreasing $E$, owing to the increasing inefficiency of momentum and energy transfer from the heavy particles to the electron under such changes; ${\sigma }_1$ decreases by about two orders of magnitude from $E=500\mathrm{} \mathrm{eV}$ to $E=100\mathrm{}$ eV, and by four orders of magnitude from $\epsilon =0\mathrm{}$ a.u. to $\epsilon =1.0\mathrm{}$ 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 $1s{\sigma }_u\left(2p{\sigma }_u\right)$ molecular electronic state is about 500 times greater than that for ionizing a $1s{\sigma }_g$ molecular electron, the main source of transitions being the Coriolis coupling operator.

• Received 2 March 1973

DOI:https://doi.org/10.1103/PhysRevA.8.1316