Velocity-dependent screening in metals

We propose a model to calculate in a quantum-mechanical way the screening and energy loss of swift ions in metals. The model is based on an extension of the Friedel sum rule to finite velocities, which allows us to describe the scattering and nonlinear screening of electrons in the field of the moving ion. The scattering process is formulated according to the partial-wave expansion, assuming an effective scattering potential that is adjusted in a self-consistent way using the phase-shift sum rule. We consider in particular the limits of low and high velocities-where the results of this model agree with those obtained using the density-functional and perturbation theories. We apply the method to the calculation of the mean energy loss (stopping power) on the whole range of velocities. [S1050-2947(97)04812-9].