Plasmon Excitation by Charged Particles Outside a Metal Film

A detailed study is given of the interaction between a metal film and a charged particle outside the film. It is shown in particular that a point charge $\mathrm{Ze}$ moving with a given initial velocity $u$ in a direction parallel to the film excites surface plasmons in the film as a result of which a reaction force acts on the moving charge. Provided $u$ is much larger than the Fermi velocity of the metal, and assuming specular reflection for scattering of the metal electrons at film boundaries, the force is given approximately by $\left[\frac{{\mathrm{}\left(\mathrm{Ze}\right)\mathrm{}}^2}{{\left(2\mathrm{}{z}_0\right)}^2}\right]{\left(\frac{1}{8}\pi \right)}^{\frac{1}{2}}{\alpha }^{\frac{3}{2}}{e}^{-\alpha }; \alpha =\frac{\sqrt{2}{\omega }_p{z}_0}{u},$ for $\frac{{\omega }_{p}d}{u}\gg 1$ and $\alpha \gg 1$, and $\left[\frac{{\mathrm{}\left(\mathrm{Ze}\right)\mathrm{}}^2}{{\left(2\mathrm{}{z}_0\right)}^2}\right]{\left(\frac{1}{2}\pi \right)}^{\frac{1}{2}}{\beta }^{\frac{3}{2}}{e}^{-\beta }; \beta =d\frac{{{\omega }_p}^2{z}_0}{u},$ for $\frac{{\omega }_{p}d}{u}\ll 1$ and $\beta \gg 1$, where $z_0$ is the distance between the moving charge and the film, ${\omega }_p$ the volume plasmon frequency, and $d$ the thickness of the film. A brief discussion is also given of the case of diffuse reflection.