Carbon tubes or spheres synthesized by arc-discharge are usually mixed with other byproducts, prohibiting direct measurements of their physical properties by the well established optical techniques because a large quantity of pure specimen is required. Electron energy-loss spectroscopy (EELS) is a unique technique that can be applied to probe the electronic structure of a single carbon tube or sphere. In this paper, the classical dielectric response theory is applied to calculate the EELS spectra acquired from a graphitic carbon sphere at various impact parameters. Graphite is an anisotropic dielectric medium whose dielectric function is described by a tensor. A graphitic carbon sphere is composed of concentric graphitic shells whose dielectric tensor in the spherical geometry, under the local response approximation, is given by (Figure 1)
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS1431927600016779/resource/name/S1431927600016779_equ1.png?pub-status=live)
where
are the dielectric function of graphite for an electric field perpendicular and parallel, respectively, to the c axis. In the non-relativistic approximation, the surface excitation is calculated by [1]