Predicted Radiation of Plasma Oscillations in Metal Films

Because of their highly collective nature it is predicted that plasma oscillations in a thin metal film should, under the proper circumstances, give off ultraviolet radiation. The plasma oscillations can be excited by fast electrons, incident normal to the film and inelastically scattered by it. Surface effects are essential, and of the special types of oscillations which can occur in a plane parallel slab of electron gas, only that involving motion normal to the slab can radiate. The yield is computed to be one photon for every one thousand electrons incident at 10 kev. The radiation is at the plasma frequency, ${\omega }_p$, or at 2100 A for a sodium film. Its identification should be facilitated by the characteristic $cos\theta$ dependence of the intensity, where $\theta$ is the angle between the foil normal and the direction of emission of the photon. Straight-forward computation yields a radiative mean life of ${{\omega }_p}^{-1\mathrm{}}\left(\frac{{\lambda }_p}{\pi \tau }\right)\times \left(\frac{cos\theta }{{sin}^2\theta }\right)$, which is generally shorter than that due to intrinsic interband damping, except at small angles. ${\lambda }_p$ is the photon wavelength and $\tau$ the film thickness. From the competition of the two decay modes it should be possible to determine the intrinsic damping rate, and hence the product of the optical constants $\mathrm{nk}$. The radiative lifetime is so short as to produce appreciable line-broadening, and thereby provide an independent check on the experiment. In the appendix the inelastic electron scattering coefficient is derived for the excitation in a thin film of the radiative-type plasma oscillations.