Anisotropy of the electron momentum density of graphite studied by $(\gamma ,e\gamma )$ and $\mathrm{}(e,2e)\mathrm{}$ spectroscopy

The electron momentum density (EMD) of two different modifications of graphite has been measured and the results of the measurements have been compared with theoretical calculations from three different theories: a full potential linear muffin-tin orbital, a modified augmented plane wave, and a pseudopotential calculation. Experimental results have been obtained by two different methods. The complete three-dimensional EMD is determined by inelastic photon-electron scattering, i.e., by the so-called $(\gamma ,e\gamma )$ experiment, and by electron-electron scattering, the $\mathrm{}(e,2e)\mathrm{}$ experiment, cuts in the spectral electron momentum density are studied. For the $(\gamma ,e\gamma )$ experiment 180 keV synchrotron radiation from the PETRA storage ring at the Deutsches Elektronen-Synchrotron has been used with coincident detection of the recoil electrons. The $\mathrm{}(e,2e)\mathrm{}$ experiments were carried out at the new $\mathrm{}(e,2e)\mathrm{}$ spectrometer at the Australian National University using 40 keV primary electron energy and simultaneous detection of the outgoing electrons in an equal energy sharing mode. As samples we have prepared approximately 20 nm thin self-supporting graphite foils either by thermal evaporation (TE) or by laser plasma ablation (LPA). They are thin enough to suppress in essence electron multiple scattering. Electron diffraction analysis revealed that the LPA foil contains graphitic basal planes with a random distribution of c axes, whereas the TE foil was strongly c-axis oriented in the sense that the basal planes were parallel to the foil surface. In the analysis of the results special attention was devoted to anisotropies in the EMD revealed by comparison of TE and LPA foils. The $\mathrm{}(e,2e)\mathrm{}$ measurements showed furthermore a strong orientation dependence of the intensity of $\pi$ and $\sigma$ states (here we have for comparison additionally measured highly oriented pyrolytic graphite). The EMD’s obtained by both techniques show anisotropies in the momentum distribution of graphite and are discussed in view of the theoretical results.