Electron capture by protons in helium and hydrogen atoms at intermediate energies

Cross sections for electron capture into each excited state of hydrogen up to $4f$ by proton impact on hydrogen and on helium in the energy range of 15-1000 keV have been calculated by means of the Born approximation (Bates's version). In addition we have used the method of close coupling to calculate the $2s$, $3s$, $2p$, $3p$, and $3d$ cross sections for the proton-helium process in the energy range of 30-300 keV. Evaluation of the two-center integrals occurring in the Born amplitude was facilitated by expanding the atomic wave functions in terms of Gaussian-type orbitals. At high energies the relative cross sections of the $\mathrm{nl}$ states (obtained from the Born approximation) for a given $l$ may be related to the importance of close encounters. For the close-coupling calculations we have included as many as eleven states in the multistate expansion of the total wave function. The effects of the intermediate states on the cross sections of the various excited states have been examined. The convergence of multistate cross sections to the two-state cross sections and to the Born cross sections is found to be slow, particularly for $p$ and $d$ states. Comparison of the 11-state close-coupling cross sections of the proton-helium process with experiment shows substantial agreement for the $2s$ and $2p$ states, and, at lower energies, for the $3s$, $3p$, and $3d$ states. At higher energies, however, differences between theory and experiment for the $3s$, $3p$, and $3d$ states somewhat exceed estimated experimental errors.