Linear density response at the metal surface in the hydrodynamic approximation

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Abstract
The density response of a jellium surface to external charge and potential perturbations is derived within the hydrodynamic approximation. Retardation effects, damping, and spatial dispersion are included. Results agree with those of Schaich, and in the non‐retarded limit with correct results of Das Sarma and Quinn. The density–potential reponse function, which gives information on inelastic scattering experiment, is explicitly given in the two‐step density model. Dispersion of the surface modes are also discussed in this model.