Observation of the anisotropy of the inelastic scattering of fast electrons accompanied by the K-shell ionization of a carbon nanotube

The angular distribution of inelastically scattered electrons following the carbon K-shell ionization of a carbon nanotube (CNT) has been studied by using an energy-filtered transmission electron microscope. The energy-filtered scattering patterns of the CNT, whose cylindrical axis is oriented in the perpendicular direction with respect to the incident-electron beam, show anisotropic angular distributions caused by the p symmetry in the pi* and sigma* unoccupied states into which a K electron jumps, and the cylindrical shape of the CNT. Corresponding inelastic scattering cross sections, differential in solid angle, have been calculated within the first Born approximation by considering that each carbon atom has three, mutually orthogonal, unoccupied p orbitals, which are oriented in directions perpendicular or parallel to the tube surface. The observed angular patterns agree well with theoretical results, which are linear combinations of the differential cross sections accompanied by the transitions to pi* and sigma* states. A series of the fittings of the experimental patterns at successive values of energy loss provides magnitudes of the pi* and sigma* components, which can be called partial electron energy-loss spectra accompanied by the transitions to the pi* and sigma* states.