[Ifeffit] Right way of choosing E0 in Athena

[Matt Newville]

Hi Vadim,

> 1. Many experts advise to do multiple k-weight fitting to deal with
> correlated variables. Should one always use multiple k-weights, or is it
> better to switch to one kw value once the correlations are taken care of –
> to refine the remaining variables? Does it make any difference?

I wouldn't say that multiple k-weights "take care of correlations", as the
correlations are generally unavoidable, and don't always drop by very
much when using multiple k-weights either.  As an example, I just tried
kweight=2 v. kweight = 1,2,3 on a test case, and saw Correl(S02, sigma2)
drop from 0.90 to 0.88, and Correl(DelR,E0) drop from 0.87 to 0.80.  The
correlations are smaller, but hardly gone.

But I still recommend using multiple k-weights most of the time because
it seems to improve the stability and reliability of the fit results
(that is, it's
harder for a small change in fit parameters to give a different result).  That
is, I use it unless the performance hit is unacceptable.

> 2. When modeling the Debye-Waller factors for multiple-scattering paths, is
> it possible to express them in terms of the sigma^2's of single-scattering
> paths that correspond to the atoms involved in the multiple scattering
> events; i.e. for a core—atomA—atomB—core path, can sigma^2 be obtained by
> some combination of core—atomA and core—atomB sigmas? It seems intuitively
> that they should be related, and also that the amplitudes of multiple
> scattering paths should be more sensitive to disorder. Does this make any
> sense?

In general, there is not a simple relation between the sigma2 for single-
and multiple-scattering paths.  As Anatoly points out, for some collinear
paths there are some fairly simple approximations that seem to work.
Other than that,  it is often safe to assume that a sigma2 for a MS path
will be larger than that of a SS path that is one of its legs. ;).

There are other approaches to _calculating_ sigma2 for single- and
multiple-scattering paths.   From what I can tell, these tend to be
computationally intensive, highly system-dependent, and difficult to
reduce to a set of parameters that can be refined to match data.

--Matt