Dispersion relations for plasmon excitations in nanostructures of different shapes and symmetries

We give a short overview of the dispersion relation for plasmon excitations in nanosystems of spherical (spheres, cavities and concentric spherical shells) and cylindrical (capillaries, wires and tubes) symmetries. We describe the interaction of external charged particles with the nanomaterials by using the dielectric response function. We apply the calculation to the case of electrons impacting nanosurfaces of Aluminum. We show how different is the response of the surface depending of its shape and configuration.