[Ifeffit] Cumulant expansion fittings

[Matt Newville]

Hi Marco, John,

Thanks for the responses -- I think we're all in agreement, at least
mostly.  That is, I don't disagree with anything that Marco or John
has said, and don't disagree with anything in the Fornasini paper or
with Marco's attachment.   My only complaint is there is the potential
to cause confusion in the notation and terminology.

For example, by setting
      <delta u_par> == 0
because any small change in average displacement along the line
between lattice points would be taken up by L,
one gets
     <R> ~= L + <delta u_perp^2>/2L.
But then one then has to have the correct value for L at all
measurements.    This also might also lead one to conclude that only
displacements perpendicular to L affect the XAFS.   I suspect that
some people are actually confused by this, which is why sigma_perp^2
and sigma_par^2 show up now and then in the literature.

Of course, as Marco hinted at (by saying this is all in the literature
and pre-dates EXAFS),
     <R> ~= L + <delta u_perp^2>/2L
is really a way to convert diffraction results for L and <u^2> into
the interesting quantity <R>, to which diffraction is not very
sensitive.  On the other hand, the relation shows that, though EXAFS
will give you <R>, it will not give you L.

--Matt