Hydrodynamic approximation for the nonlinear response of a metal surface

We present semiclassical and quantized hydrodynamic models to obtain the qu adratic electronic response of a plane-bounded electron gas. Explicit expre ssions for the dynamic image potential experienced by charged particles mov ing near a jellium surface are derived, up to third order in the projectile charge. These expressions are employed to compute the image potential at a ll distances outside the surface. Though nonlinear corrections are found to be more important far inside the solid than outside, our results indicate that the nonlinear image potential is enhanced with respect to the linear i mage potential by a factor that is for Al as large as similar to 1.15 near the surface in the case of a stationary particle (v --> 0) with positive un it charge e. [S0163-1829(99)08847-5].