High-energy approximation for exchange scattering and application to 1 1S → 2 3S excitation of He by electron impact

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Abstract
A high‐energy approximation is derived for the second order term in the T matrix for exchange scattering of electrons by atoms or molecules. A limiting selection rule for exchange scattering at high incident energies is obtained, which states that second‐order contributions are important in forward scattering if the initial and final states of the target system have the same orbital term symbol. Calculations on the zero angle differential cross section, approximated by the cross section at zero momentum change, of the 1 1S→2 3S excitation in He by electron impact are carried out over an energy range 100–500 eV using the present approximation. Reasonable agreement with the experimental data of Skerbele, Harshbarger, and Lassettre [J. Chem. Phys. 58, 4285 (1973)] is obtained, indicating that second‐order contributions are sufficient to account for the differences between Born‐Oppenheimer calculations and the experimental data. The present calculation also shows that, for this transition in He, a minimum exists in the zero angle differential cross section vs incident energy curve. The existence of the minimum has been verified experimentally by Klump and Lassettre.