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Charge-transfer (sublevel) cross sections for He~++H collisions have been calculated in the 20-eV -to -10-keV center-of-mass energy region. Both a time-independent quantum-mechanical closecoupling method (ZO -500 eV) and a semiclassical impact-parameter method (0.1 -10 keV) were used. The close-coupling formalism is developed in terms of a molecular-state description of the HeH + system and is extended to include both radial and rotational couplings. The potentials and radial and rotational couplings for the Zso. , Zpo. , 3do, and Zpm molecular states were computed by expressing the molecular orbitals as variationally determined linear combinations of Slater-type orbitals centered at the atoms. ' Common molecular-electron translation factors were introduced to ensure proper asymptotic behavior of the wave functions and were found to be crucial for agreement between calculated and experimental cross sections. The usual practice of compensating for the neglect of these factors by using couplings evaluated at an atomic origin rather than at the center of mass of the nuclei is analyzed. Quantum-mechanical and semiclassical results are compatible only if Coulomb trajectories instead of straight-line trajectories are used. In particular the sublevel cross section for He+(Zp+l ) production is found to be extremely sensitive to the trajectory. At all energies above 50 eV radial and rotational couplings are about equally important. Below 100 eV cross sections fall off rapidly, and radiative charge transfer becomes the dominant process below 25 eV.

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