Quantum-Mechanical Calculation of Inelastic Cross Sections for1S1→2S3Excitation Collisions of Ground-State He Atoms withHe+Ions

Quantum-mechanical, three-state, close-coupling calculations of the inelastic cross sections for $1{}_{}{}^1{}_{}{}^{}S\to 2{}_{}{}^3{}_{}{}^{}S$ excitation of ground-state He atoms in collision with ${\mathrm{He}}^{+}$ ions have been carried out for energies between 25 and 50 eV (c.m.). Differential, partially integrated (over small angles), and total inelastic cross sections were obtained. The calculations were performed using linear combinations of three single-configuration, valence-bond-type electronic wave functions as the basis of a diabatic representation. The diabatic coupling in the vicinity of the well-established ${}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ curve crossing at $R\simeq 1.5a_0$ was found to be small, and it was verified by comparison with the close-coupling results that the Stueckelburg-Landau-Zener (SLZ) theory was applicable. Several SLZ model calculations were performed using the best available adiabatic potential curves and modeling the crossing region. The resulting differential and partially integrated (over small angles) cross sections were found to be in good qualitative agreement with the measurements. In particular, the strange hump apparent in the small-angle cross sections versus energy curve, which was first found by Utterback, and recently confirmed by MacVicar-Whelan and Borst, was reproduced in our calculations. The interesting nature of the small-angle scattering is discussed, and the sensitivity of the cross section to details of the potential curves near the crossing is examined in detail.