By J.M. Blakely (Eds.)
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0 ) ( + ) (105) : <>( + ) = P «#>(-) = R - < ( + ) + + ) 50 J. A. , D . W . JEPSEN, A N D F. J O N A where a ( + ) is the incident beam, which is known. Next the wave field propagating in the backward direction (αί ) is calculated to first order from ( 0) 0 _) : <#>(-) = (106) R-4°>( + ) + P-etfX-) where a ^ — ) is now the outgoing wave field at the top layer calculated to first order. The forward and backward components of the wave field have now been calculated everywhere to zero and first order respectively (a to zero order is assumed to be zero).
This is most fortunate, as hopefully the extra computational time inherent in multiple-scattering analysis can be partly made up by not having to examine a large number of beams over a large energy range. The only approximation so far developed that preserves the accuracy of an exact calculation while materially reducing the computation time is the so-called renormalized forward scattering (RFS) approximation due to Pendry (1971b,c). This approximation is limited to the interlayer scattering problem only, while the intralayer scattering is calculated exactly (as previously discussed).
Equation (66) can be set up on a computer, for a crystal five to nine layers thick, to give a fairly accurate calculation of LEED intensities (Laramore et al, 1971; Laramore and Duke, 1972). Instead of calculating expressions of the form given in Eq. (67) for G when i Φ j to get the scattering from layer i to layer j , we could calculate the beams produced in the crystal by the scattering in layer i using Eq. (68) and consider them as input waves to layer j using Eq. (62). Since the calculation is nearly the same for different layers j , this can improve calculational speed.
Surface Physics of Materials by J.M. Blakely (Eds.)