Linear Response of a Metal to an External Charge Distribution

The linear response of a metal to an external-charge distribution is computed in the random-phase approximation (RPA). The surface is assumed to be perfectly reflecting and the boundary-value problem is solved by a symmetric continuation of the metal. The linear response of the metal to an external point charge is found to be described by a function $\ensuremath{\nu}$ which depends only on the properties of the surface and the metal. From $\ensuremath{\nu}$, we compute a surface function $S$ which fully describes the electrical properties outside the metal. Graphs of $S$ as a function of the parallel momentum $K$ are given for the quantum-mechanical RPA and for the quasiclassical RPA which is obtained by neglecting interference effects. The potential and normal fields outside the metal are well approximated by the analytic expressions which are obtained when $S(K)$ is replaced by ${e}^{\ensuremath{-}\ensuremath{\lambda}K}$, where $\ensuremath{\lambda}$ has the physical meaning of a screening length.