Direct and charge-exchange excitation processes inH+−H(1s)collisions at 1 to 7 keV

We have computed direct and charge-exchange cross sections for ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(\mathrm{nl}\right)\mathrm{}$ collisions, for projectile energies 1-7 keV, using the close-coupling method with $\mathrm{H}_2^{}{}_{}{}^{+}$ molecular states modified by electron translation factors (ETF's); switching functions recently derived analytically for exact $\mathrm{H}_2^{}{}_{}{}^{+}$ states were used to construct ETF corrections. Basis sets with up to 10 molecular states were used in systematic calculations, and good convergence is found for all atomic cross sections with $n\le 2$. Results have been compared with other theoretical calculations [especially that of Crothers and Hughes (1978-1979)] and with recent experiments. Where differences between our results and those of Crothers and Hughes are found, our results agree more closely with experiment. The most notable case is the $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ charge-exchange (and direct) cross sections, where our results show no minimum whatever near $E=2-4\mathrm{}$ keV, in agreement with experiments of Morgan et al. (1980) and Hill et al. (1979), but in strong disagreement with the calculations of Crothers and Hughes and 1969 experiments of Bayfield. In one case discrepancies between our results and those of Crothers and Hughes can be shown to arise from their treatment of ETF effects (using a different switching function for the $2p{\sigma }_u$ state)—i.e., they obtain a much larger population of the $4f{\sigma }_u$ state than is found here. We have also carried out selected studies with larger basis sets (up to $16u$ states) to examine the behavior of cross sections for excitation to atomic levels with $n\ge 3$. These studies strongly suggest that a "ladder-climbing" sequence of excitations via upper levels is the dominant process by which ionization occurs in ${\mathrm{H}}^{+}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions at these energies.