PERTURBATIVE APPROACH TO HIGH-ENERGY-ELECTRON SURFACE-RESONANCE SCATTERING

Recently, an exact expression has been developed to determine the elas tic reflection coefficient for the phenomenon of surface resonance in reflection high-energy-electron diffraction [S. L. Dudarev and M. J. W helan, Phys. Rev. Lett. 72, 1032 (1994)]. Following this proposal, dia grammatic techniques are used to obtain a series expansion for the res onant reflection coefficient with respect to an array of noninteractin g Breit-Wigner scatterers. Application to the (111) surface of platinu m within the weak-potential scattering regime reveals, within the unce rtainty of the scattering parameters, that only the lowest-order resul t is required. This disputes the contention (in this case) that the Br eit-Wigner scattering law is violated. From an analysis of the converg ence properties of the series, it is found that this is due primarily to incoherent resonant scattering within the bulk between the (111) pl anes. In turn, its origin is the off-Bragg scattering condition associ ated with weak-potential scattering. On the other hand, for the case o f strong-potential scattering in which the Bragg condition is satisfie d, the perturbation series breaks down and the exact solution is neede d. We then develop a renormalized perturbation expansion with respect to the Breit-Wigner scattering vertex in the intermediate regime, wher e there is still strong-potential scattering. Correspondingly, a more general convergence criterion is determined. We conclude by showing th at the developed perturbation expansion and convergence criterion reta in their form for an arbitrary number of interacting resonant modes.