# [Ifeffit] sigma^2 values for multiple scattering paths

Scott Calvin dr.scott.calvin at gmail.com
Wed Oct 6 11:39:49 CDT 2010

```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:

> .
>
> 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

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