Relativistic Green's-function electron-diffraction theory

Abstract

A relativistic electron-diffraction theory is presented, which solves the Dirac equation by the Green's-function method and incorporates spin polarization. For muffin-tin potentials, the reflection coefficient of a beam scattered elastically from either unpolarized or polarized incident electrons is very similar to that of its nonrelativistic counterpart. The atomic properties are included in the relativistic phase shifts. The geometric structure constants are related to the nonrelativistic structure constants. The polarization of the scattered electrons is analyzed by the density matrix. The relation between this theory and the nonrelativistic one is discussed. The exact reflection coefficient is suitable for the calculation of diffraction intensities of low-energy incident electrons from heavy-atomic-crystal surfaces. A pseudokinematic theory, which may be useful for incident energies up to several keV, is obtained by taking the first-order approximation.