Coupling effects in the excitations by an external electron beam near close particles

The energy-loss experienced by swift scanning transmisson electron microscopy electrons is calculated for a target constituted by two spherical particles in the framework of dielectric theory, using bispherical coordinates. Deviations from the behavior of the isolated sphere are investigated. The coupling between close particles and its effects on the energy-loss spectrum is found to depend significantly on the electron trajectory and target situation (particle size and interparticle distance). Excitations above the planar surface plasmon energy are found to be the dominant contribution to the loss spectrum for trajectories between the two spheres, while low-energy excitations, under those of the isolated sphere, appear for trajectories out of that region. The different possibilities are analyzed and compared with experimental results for aluminum particles and provisions of recent effective medium theories. The inelastic part of the induced electric field around the spheres is also studied showing a very important localization of the excitation in the space between both particles, even for trajectories outside that region. The expressions obtained are available for any local dielectric function.