Fast-electron scattering by bispherical surface-plasmon modes

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Abstract
We have determined the surface-plasmon modes of interacting spherical particles as a function of the particle radii, the separation R, and the dielectric constant of the surrounding medium. The coupling between the two particles produces a shift of all surface-plasmon eigenfrequencies leading, in the case of Al particles embedded in Al oxide, to a bispherical plasmon mode in the 3–4-eV range. Using a second-quantization description of the surface plasmons, the loss probability for fast electrons scattered inelastically by spheres of equal or different radii is obtained. Application to Al particles surrounded by Al oxide yields results that are compared with the experimental data obtained by Batson using scanning transmission electron microscopy. The theoretical results allow us to explain the existence of the experimentally observed modes, as well as the dependence of the loss function on the electron trajectory.