Importance of the plasmon damping for the dynamical image forces

In the framework of the semiclassical approach the image force energy W(z) for incident or emitted charged particles moving in vacuum normal to the me tal surface is calculated taking into account the finite lifetime of plasmo ns in the metal. It is shown that the deep oscillations of W(z) induced by the creation of real plasmons are heavily damped by the dissipation factor, so that they may be not taken into account in the asymptotic region where the electrostatic dependence for W(z) is restored.