I think Scott is right that the original meaning of "effective" was that the scattering amplitude is not for point scattering of a plane wave, as was used in earlier work (say, Sayers, et al 1971). Feff3 (circa 1990) didn't to do multiple scattering, but did put in curved wave effects. http://leonardo.phys.washington.edu/feff/Docs/feff3.html But once you move away from the point scattering of plane waves, "effective" can fold everything else in. So now "effective" does include mapping the MS paths to a SS formalism does make more "effective" (less native point-scattering of plane waves). The fast, clever matrix representation for MS paths of Rehr and Albers was incredibly important for making the calculations actually useful. I believe others (Schaich? Gurman?) were calculating MS on triangles and 4-legged focused paths somewhat before Rehr, but that it was slow and hard to generalize. Feff5 generalized this for all orders. --Matt