X-ray excitation of surface plasmons in metallic spheres

The cross section for excitation of surface plasmons by x rays is calculated for a free-electron gas confined to a small spherical region and surrounded by a medium having constant dielectric permittivity ${\epsilon }_0$. The free-electron gas is described in the hydrodynamical approximation, and first-order perturbation theory is used to calculate the transition probability for inelastic scatter. The analogous cross section for volume-plasmon excitation by x rays is also calculated using the hydrodynamical model, and it is compared with a result obtained by Ohmura and Matsudaira using the random-phase approximation. The ratio of cross sections for surface-plasmon and volume-plasmon excitation is also determined.