[Ifeffit] imaginary energy correction

[Bruce Ravel]

On Wednesday 18 February 2004 09:34 pm, Stanislav Stoupin wrote:
> Hello all,
>
> I would appreciate if somebody could explain the meaning of imaginary
> energy correction (Ei parameter).
> So far I have not found any description of the parameter. If anyone knows
> of any example on how to use it, please let me know.

Stanislav,

There are a lot of things that lead to broadening of the XAS
spectrum.  Among them are :

 * The energy resolution of the monochromator
 * The size of the entrance slits + the divergence of the beam
 * The mean free path of the photoelectron (i.e. the exp(-2R/lambda(E))
   term), which includes such physics as the core hole lifetime, the
   plasmon excitation, and so on

In an ideal situation, the mono resolution would be small compared to
the core-hole lifetime and so could be ignored.  The entrance slits
would be set to optimize the resolution, i.e. to make the effect of
the beam divergence small compared to the core-hole lifetime.

In that situation, only the lamdba(E) term would contribute to the
broadening of the spectrum.  lambda(E) is one of the things that we
rely upon Feff to compute for us (along with the photoelectron
scattering amplitude and phase shift).  Again in the ideal world, Feff
would compute that correctly within our experimental uncertainties.

If all of those things are true, then there is no need for an
imaginary energy.  Or. more specifically, if you allow an imaginary
energy to float in a fit, it will be consistent with zero.

Alas, in the world that I live in, I cannot rely on all of that.  I
occassionally do something (accident, sleepiness, whatever) in my
experimental set up that affects the resolution.  And Feff does not
always compute lambda(E) reliably.  Indeed, the folks who write Feff
have been working hard of late to improve the loss terms in the
calculation.

Consequently, it is sometimes prudent to consider an imaginary energy
in a fit.  So, what does that term mean?  Well, in the formalism used
by Feff and Ifeffit, the broadening terms are expressed in energy
units.  And it's imaginary because its a loss term.  Hence the name.
Because the term in the exafs equation that contains lambda has an R
dependence, it effects the data differently than the amplitude terms,
S02 and N.  Upon examining your data and the statistical results of
the fits, you may be able to tell the difference between an amplitude
effect and a lambda effect.

Finally, I'll direct you to a past discussion on the ifeffit mailing
list.  In November of 2002 there was an extensive discussion about the
correlations between S02, sigma^2, and the imaginary energy.  Go here:

  http://millenia.cars.aps.anl.gov/pipermail/ifeffit/2002-November/

and look for the threads labeled "Debye factor and S02 correlation"

Hope that helps,
B

  
  

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