Optical Properties of Small Metal Spheres: Surface Effects

It has been assumed that the optical properties of small spheres can be understood by means of a Drude dielectric function that incorporates a boundary scattering rate $\frac{1}{{\tau }_s}\simeq \frac{v_{\mathrm{F}}}{R}$, where $v_{\mathrm{F}}$ is the Fermi velocity and $R$ is the sphere radius. An effective scattering rate $\frac{1}{{\tau }_s}=f\frac{v_{\mathrm{F}}}{R}$ is calculated and $f$ is evaluated as a function of photon frequency. The largest contribution to $f$ is due to the electron density profile of the sphere rather than the boundary scattering that is reduced an order of magnitude by electron screening.