Independent-particle-model study of the elastic scattering of low-energy electrons by positive ions

The elastic scattering by positive ions of electrons with energies below 2 Ry was investigated theoretically using the independent-particle-model (IPM) potentials of Green, Sellin, and Zachor to represent the electron-ion interaction. Parameters were determined from minimization of the total energy of the bound system consisting of the electron plus target ion, or in some cases from fits to the single-electron eigenvalues of this same system. Potentials of the former type are generally the stronger of the two. The IPM phase shifts versus energy are qualitatively similar to, but usually larger than, those obtained using Hartree-Fock-Slater potentials. For energies below 1 Ry there is excellent agreement between the differential cross sections for ${\mathrm{Na}}^{+}$ obtained from the IPM and those computed from semiempirical quantum-defect methods. For this same ion the IPM differential cross sections likewise resemble those computed from Hartree-Fock potentials and lie between the Hartree-Fock results obtained with and without local exchange contributions. Phase shifts are computed using the independent-particle model for all positive ions of nitrogen and oxygen, species of atmospheric interest.