Localized Modes of Excitation of an Electron Gas in the Vicinity of an Impurity in Metals

Modes of vibration of an electron gas in a uniform background of positive charge containing a fixed point charge are investigated. A hydrodynamic model is used in which the electrons are treated as a Fermi fluid. It is found that a localized excitation of electron gas may exist near a positive impurity. Such a local excitation can be detected in characteristic energy losses of fast electrons.