A new local exchange potential for low-energy electron scattering by atoms based on first principles

The authors derive a new expression for the exchange potential applicable to the elastic scattering of electrons by atoms. The derivation is based on a recent study by Fritsche and Gollisch (1982). Distinctly different from Slater-type X alpha potentials, the expression exhibits the correct long-range behaviour resulting from the electrostatic polarisation of the target atom in response to the incident electron. In order to facilitate a self-consistent calculation of the scattering potential (including the contributions of all target electrons and of the projectile as well) the authors derive a method which provides the localisation of the incident electron during the scattering process. The scattering potential obtained is parameter free and shows a noticeable energy dependence in the low-energy regime up to about 150 eV. Differential cross sections are calculated for Ne and Xe atoms and compared with recent experiments. Since the calculation includes relativistic effects, they obtain scattering-induced spin polarisation as well, yielding a relatively good description of the respective experiments by Klewer et al. (1979) and Berger et al. (1982).