Excitation and charge transfer inHe++H collisions. A study of the origin dependence of calculated cross sections

A treatment of the ${\mathrm{He}}^{+}$ -H collision is presented in an impact-parameter formalism for collision energies 0.5 - 30 keV. The origin dependence of the calculated total cross sections is studied in detail. It is shown that the branching ratio between reactions ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ and ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{He}\left(1s2p\right)+{\mathrm{H}}^{+}$ oscillates as a function of the origin of electronic coordinates chosen in the calculation. This oscillation is strong enough so that at nuclear velocity 0.5 a.u., either both reactions are competitive or one of them can have a cross section twice as large as that of the other. Likewise the cross section for the reaction $\mathrm{He}\left(1\mathrm{}{s}^2\right)+{\mathrm{H}}^{+}\to {\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ can either be negligible or comparable to those of the other reactions. We study the oscillatory behavior of the charge-exchange-transition probability as a function of $\frac{1}{v}$. We show the similarity, for high velocity, between non-resonant and resonant charge-exchange processes, the origin of the damping factor, and the influence of the rotational coupling on the transition probabilities as functions of $\frac{1}{v}$. A connection between Lichten's and Demkov's models is established.