Surface electron band structure and VLEED reflectivity for Al(111)
  The 2D layer Green function scattering method is used to calculate the energy of surface states and resonances at Gamma-bar for Al(111) for both below and above the vacuum level. The surface barrier potential is represented by an empirical form. The above vacuum level surface electron band structure for this surface has not been calculated before and it is important in understanding many surface phenomena. The geometric structure of the Al(111) surface is known from intensity analysis in low-energy electron diffraction at energies 60 -- 450 eV. The details of the surface barrier for Al(111) were obtained from a match with the below vacuum level experimental energy position of the first Rydberg surface resonance and the Shockley surface state at k_|| = 0 (Gamma-bar). The calculation was then extended to the above vacuum level case for 0 -- 27 eV with the inclusion of inelastic electron interactions. Tamm-type resonances at 6.9 eV and possibly also at 8.3 eV, a Shockley-type resonance at 14.0\pm0.5 eV and a series of Rydberg (image) resonances near 24 eV all above vacuum level are found at k_|| = 0. The same 2D layer Green function scattering method using the same input data was then used to calculate the intensity of the 00 beam for k_|| = 0 (normal incidence) in very low energy electron diffraction (VLEED) from this surface in the energy range 0 -- 65 eV. Features in the VLEED intensities are found due to the Shockley and Rydberg resonances. Experimental data from over 26 years ago found surface features near the energies found in this work. Beam intensities from low energy electron microscope (LEEM) measurements at normal incidence and new data from other surface spectroscopies could provide experimental confirmation of the resonances predicted in this work. 
M. N. Read