A model for the velocity-dependent screening

A general expression, that relates the scattering amplitude to the integrated induced charge generated by a penetrating charged particle in an ideal electron gas, is used supposing a convenient spherical symmetry of the screened scattering potential. Based on this expression the velocity-dependent screening parameter of a Yukawa potential is determined, applying the constraint of complete screening, in first-order Born approximation for the scattering. The zero-temperature and Boltzmann limits for the environment are discussed. Via the common partial-wave representation for the scattering amplitude a velocity-dependent Friedel-like sum of phase shifts is deduced.