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We present experimental evidence confirming the existence of the theoretically proposed double-plasmon-excitation process in solid-state plasmas. Preliminary measurements of the relative probability of single-and double-plasmon excitation in aluminum show good agreement with theory.The mean free path for the second-order process of double-plasmon excitation in a free-electron gas has recently been calculated by Ashley and Ritchie. 1 Previous treatments of the interaction of fast electrons with a free-electron plasma ignored the possibility of spontaneous multiple-plasmon excitation and considered that only a single plasmon of energy H(*) p (oo p is the plasma frequency) is excited. Multiple-plasmon peaks have been observed in electron-energy-loss spectra from a wide range of materials, but these have always been entirely attributed to plural-scattering single-plasmon processes. These mask the multiple-plasmon single-scattering contributions which would occur at the same energy.As shown by Ashley and Ritchie, the mean free paths for the single-and double-plasmon processes are related bywhere k c is the cutoff wave number. It readily follows that a two-parameter Poisson distribution is now required to describe the zeroth, first, second, etc. plasmon-loss probabilities in the energy-loss spectrum. As a function of plasma thickness t these are given bywhere : *i • 1 + x a " 1 -In the expression for P 2 (t) the first term is due to single-plasmon double-scattering and the second due to double-plasmon single-scattering processes.Representing the free electrons in a thin crystal as a typical solid-state plasma and taking the value k c ~oo p /v ¥ (v ¥ being the Fermi velocity), Ashley and Ritchie find that, at a thickness equal to X 19 approximately 8% of the second plasmonloss intensity arises from the double-plasmon contribution. Thus at small thicknesses the influence of the double-plasmon term should be detectable experimentally.The present experiments involve the careful measurement of the zeroth, first, and second plasmon-peak intensities of the fast-electron energy-loss spectrum as a function of plasma thickness in the hope of identifying this doubleplasmon contribution to P 2 (t). The technique is an extension of that previously described 2 for the measurement of \ v An electron-microscope system with electronic recording and energy-analysis facilities 3 is used to examine wedge-shaped crystals of aluminum. The crystal is first oriented by means of a goniometer stage to an approximate "onebeam condition" in which no Bragg-diffracted beam is strongly excited. The resulting image of the crystal, with no objective aperture in place, is then scanned perpendicular to the edge of the wedge so that the number of transmitted electrons which have lost energy nH(x> p (n = 0,1, 2) is recorded as a function of crystal thickness. The energy window was chosen so as to include the full width of the plasmon-loss peaks as determined from an experimental differential energy spectrum from the same crystal. Figure 1 shows typical re...

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The retrieval of a unique crystal potential from the scattering matrix S in high-energy transmission electron diffraction is discussed. It is shown that, in general, data taken at a single orientation are not sufficient to determine all the elements of S. Additional measurements with tilted incident beam are required for the determination of the whole S matrix. An algorithm for the extraction of the crystal potential from the S matrix measured at a single energy and thickness is presented. The limiting case of thin crystals is discussed. Several examples with simulated data are considered.