A simple semiclassical model is proposed for the calculation of the polarization potential at short range where the impacting electron penetrates the electron cloud of the target atom. The new method is applied to the scattering of electrons and positrons from He atoms at energies between 0.1 and 50 eV. The model is described in detail and is shown to produce a local effective potential which is computationally very easy to devise. Calculations for electron scattering are carried out for the elastic integral cross sections and for angular distributions of electrons at several collision energies and compared both with experiments and with more sophisticated calculations. The agreement of the present results with experiments is invariably very good. Further test calculations for the positron scattering processes also agree very well with the available experiments and with other theoretical predictions.