Analytic expressions for the inelastic scattering and energy loss of electron and proton beams in carbon nanotubes

We have determined “effective” Bethe coefficients and the mean excitation energy of stopping theory (I-value) for bulk-like samples of single- and multi-walled carbon nanotubes (SWCNTs, MWCNTs) based on a sum-rule constrained optical-data model energy loss function with improved asymptotic properties. Noticeable differences between MWCNTs, SCWNTs, and the three allotropes of carbon (diamond, graphite, glassy carbon) are found. Using Bethe’s asymptotic approximation, the inelastic scattering cross section, the electronic stopping power, and the average energy transfer to target electrons are calculated analytically over a broad energy range for electron and proton beams using realistic excitation parameters.