Plane-wave-factor, molecular-state treatment of electron transfer in collisions ofHe2+ions with H atoms

Total cross sections are reported for electron transfer into the individual states $2s$, $2p_0$, and $2p_1$, and into all bound states of ${\mathrm{He}}^{+}$ in collisions of 1- to 70-keV ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ ions with H atoms. Following Bates and McCarroll, plane-wave factors have been fully incorporated in a coupled-molecular-state approximation. All velocity-dependent matrix elements have been evaluated as power series in the nuclear velocity. The bases used include up to 10 states $1s\sigma , 2s\sigma , \dots , 3d\delta$, of the frozen He${\mathrm{H}}^{2+}$ molecule. Convergence of cross sections with respect to the size of the bound-state basis was studied: fewer basis functions are needed than when plane-wave factors are omitted. To test the convergence of the latter results with respect to the size of the bound-state basis, the two potentially important states $5g\sigma$ and $5g\pi$ have been added to the previously used 20-state ($1s\sigma , 2s\sigma , \dots , 4f\varphi$) basis, and were found to affect the cross section for transfer into all states by at most 6%. For transfer into all states, results with and without plane-wave factors converge at low energies, agreeing to within 5% at 1 keV. The agreement of the plane-wave-factor results with the experimental data for transfer into all states is excellent at ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ energies down to 8 keV, but poor at the lower energies, where the coupled-state results are believed to be more fully converged. For capture into the $2s$ state, the plane-wave-factor results lie above the upper bound of the experimental values by 25% at 20 keV.