Theory of Low Energy Electron Diffraction. II. OPW Method

The OPW method of the energy band calculation in solid state physics is applied to the theory of low energy electron diffraction. In the cases of “two-rod approximation” and the weak absorption, the amplitude reflection coefficient is derived on the basis of the dispersion surfaces with two branches for the normal incidence. In the case of the strong absorptions, considering the “two-dimensional OPW expansion” made by two-dimensional Bloch sum, the same fundamental equation as in I is obtained replacing the Fourier component of the crystal potential, V h - g ( z ) used in I , by an “effective potential” \(Ṽh,g(z){=}Vh-g(z)-Qh,g(z)+Rh,g(z)\), where - Q h , g ( z ) means the usual repulsive potential part which becomes maximum at the resonance condition K h r 2 =0, and R h , g ( z ) a complex potential proportional to K h r . When the atomic layers are not periodic, R h , g ( z ) has a imaginary part even in the case of no inelastic scatterings.