Tests of the semiclassical polarization approximation for electron scattering by helium and neon

We report calculations of the differential, integral, and momentum-transfer cross sections for elastic scattering for e-He collisions at 30-400 eV and e-Ne collisions at 50-400 eV. The calculations are based on static-exchange-plus- polarization-and-absorption model potentials. The static potentials are based on Hartree-Fock results, the exchange potentials are calculated with the semiclassical exchange approximation, and the absorption potentials are phenomenological ones previously adjusted to experimental total absorption cross sections. For polarization, we consider two approximations, both versions of the semiclassical polarization approximation of Valone and the authors. One of these, the low-energy semiclassical polarization approximation, is quite successful in all cases, although it does systematically overestimate the small-angle (10°) scattering by factors ranging from about 1.1 (at 30-100 eV) to 1.7 (at 400 eV) for He. (For Ne this model predicts the 10°scattering within 16% in all cases.) The integral elastic cross sections predicted by this model have a typical relative error of about 10% for both He and Ne. Another version of the model, the local-kinetic-energy semiclassical polarization approximation, is a little less successful. We also examined the differences between using perturbative and variational input for He and found that these differences are generally smaller than the differences between the low-energy and local-kinetic-energy models.