Theoretical scattering amplitudes for the atomic scattering of low-energy electrons for use in surface crystallography by low-energy electron diffraction

As the use of low-energy electron diffraction (LEED) for surface structural analysis has increased, the need for accurate values of scattering amplitudes and cross sections in the angle and energy range of interest to those doing LEED work has also increased. Presently available tables of atomic scattering factors, which could serve as a standard starting point for more sophisticated LEED calculations, are unfortunately limited in angle and energy and do not include a number of elements of interest to the surface-science community. In order to calculate these scattering amplitudes as well as total elastic cross sections for atomic scattering of low-energy electrons, the Dirac equation was solved numerically. Various analytic and numerical forms for the atomic potential, including relativistic, self-consistent Hartree-Fock-Slater scattering potentials were used. The exchange of the incoming electron with the atomic electrons was neglected because this effect is negligible for atomic scattering in the ranges where this work is applicable. Care is taken to demonstrate the validity of this work for LEED calculations and the limits of its application. The complete set of data for relativisitic partial-wave phase shifts is available for H, He, Li, C, N, O, Ne, Na, Si, S, Ar, K, Ca, Sc, Cr, Fe, Co, Ni, Zn, Ge, Se, Kr, Rb, Y, Mo, Rh, Cd, Sn, Te, Xe, Cs, La, W, Ir, Hg, Pb, Po and Rn. The data covers the energy range from 15 to 305 eV in 10 eV increments. To ensure convergence of the series when calculating the atomic scattering factors and subsequently the total elastic cross section, the actual calculations were performed with 50 to 80 partial waves depending on the energy of the incident electron. Owing to space limitations the phase shifts as well as the complex atomic scattering factors and elastic cross sections are not presented in the paper. They are available from the authors on request.