Elastic scattering of electrons by a cut-off Coulomb potential at low energies

Elatic scattering of electrons by the cut-off Coulomb potential U/sub c/(r) [U/sub c/(r) = 0 for r > r/sub c/ and U/sub c/(r) = -1/r + 1/r/sub c/ for r <= r/sub c/] is investigated in terms of both classical and quantum mechanical (partial wave) methods in the energy range 0 <= epsilon < approx. 1/r/sub c/ for free electrons. Scattering in this energy region displays a number of particular characteristics, such as backscattering at certain energies and resonance. Classical methods do not yield satisfactory results for epsilon < approx. 1/r/sub c/. The principle cause of discrepancies between classical and quantum mechanical results is discussed. It is concluded that neither classical norquasi-classical methods as well as that of Born are appropriate in the energy range considered. Therefore, it is essential to utilize the partial wave method which does not require cumbersome calculations