Collective Oscillations in a Dense Electron Gas Containing a Fixed Point Charge

The collective excitations of a dense electron gas containing a fixed point charge with neutralizing positive background are investigated. A dielectric formulation, evaluated in a self-consistent-field approximation, yields a single-particle Schrödinger equation describing the collective modes. This equation has solutions belonging to the continuous spectrum (free plasmons) and to the discrete spectrum (bound plasmons). A cross section is derived for scattering of free plasmons by the point charge. The bound plasmon, representing a density wave trapped at the impurity site, has no counterpart in the uniform gas; it exists only for negative impurity charge and has an excitation frequency lying in the range $\frac{{\omega }_p}{\sqrt{2}}\le \omega <{\omega }_p$, where ${\omega }_p$ is the plasma frequency. The bound plasmon appears to be a reasonably well-defined excitation with a lifetime ∼${10}^{-15\mathrm{}}$ sec in metals. A simple hydrodynamical model provides further physical insight. The experimental detection of bound and free plasmons in metals and the relationship between surface plasmons, experimentally observed in many metals, and the predicted bound plasmon are discussed.