Although I agree with the main points that Bruce makes, I do want to comment on one piece: On Oct 6, 2010, at 7:03 AM, Bruce Ravel wrote:

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In no case can I understand a physical explanation for the the MS sigma^2 being smaller than for the SS.

Actually, there is a physical situation where something like that can occur, although it sounds like it's not the one that Han Sen has. Consider an absorbing atom rattling around in a relatively fixed cage or lattice. And then consider a linear (or near-linear) arrangement: S1 -- A -- S2 One multiple scattering path that can sometimes have a sizable contribution is A --> S1 --> S2 --> A. This path will have a sigma^2 that is a bit larger than the single-scattering path S1 --> S2 --> S1, because of the perpendicular component of the motion of A. But it's quite frequently the case that S1 --> S2 --> S1 is not modeled in a fit, because the S edge is not measured. On the other hand, the single scattering paths A --> S1 --> A and A --

S2 --> A ARE included in the fit. Those two have high sigma^2's, because A is rattling around a lot.

Under that circumstance, a multiple-scattering path included in the fit may indeed have a lower sigma^2 than the single-scattering paths included in the fit. The moral, of course, is that it's not hard to think physically about what sigma^2 means for a multiple scattering path. If one appears to have an "unphysically" small sigma2, then the explanation is probably one of the ones given by Bruce or Shelly. One more thought on this. How much does it change your fit, Han Sen, if you set the sigma^2 for the multiple-scattering path to some "reasonable" value. If the scientific information you want from your fit is not sensitive to exactly what sigma^2 the MS path gets, and is not significantly different when given a "reasonable" value than when allowed to find its "best-fit" value, then there's probably no need to resolve the issue. In my experience, this is often the case with low- amplitude MS paths: the fit is improved by their inclusion, but may not be particularly sensitive to the details of their path parameters. --Scott Calvin Sarah Lawrence College