[Ifeffit] schemes for delr and sigma2 for multiple scattering paths

[Bruce Ravel]

On Friday 08 October 2010 09:30:14 am Jatinkumar Rana wrote:
> In EXAFS, the oscillations are due to the intereference between the 
> outgoing photo electron from absorbing atom and incoming backscattered 
> photoelectron from the scatterer. Depending upon, how much they are out 
> of phase w.r.t each other we get oscillations in EXAFS curve. These 
> oscillations are nothing but the variation in the absobtion coefficient 
> of sample as the energy of incident photon is varied.
> 
> I wonder, how, the intereference between the photo electrons is related 
> to absorbtion coefficient of sample ??
> 
> because, It = I0 * exp (-ut)

As always, it is important to consider the physical meaning of the
terms we use.  \mu is the absorption coefficient, i.e. the thing that
goes up at the edge and up and down throughout the EXAFS.

Another way to say this is that \mu is some kind of measure of the
amplitude of the unoccupied (recall that electrons are fermions -- if
an electron already occupies a particular statem, the photoelectron
cannot transition into that state) portion of the density of states
projected onto the final state angular momentum.  That's a mouthful.
In short, for a K edge, we measure the unoccupied portion of the p
band.

That portion of the density of states is not flat.  It has structure
-- peaks and troughs.  A peak is place where there is higher state
density and vice versa for a trough.  Consequently, if the incident
photon has the amount of energy needed to raise the photoelectron to
an energy at which there is a peak in the density of states, then it
is relatively more likely to be absorbed than for a photon with an
energy that takes the photoelectron to a trough.  The wiggles in the
XAS follow the ups and downs of the density of states.

Now suppose that one were interested in calculating an XAS spectrum.
Well, there are many theoretical frameworks for making such a
calculation.  Feff (and, as a consequence, Ifeffit and Artemis) use an
approach called "real space multiple scattering".  In this approach we
need to know two things -- the function that describes how an electron
travels between points in space and the function that describes how an
electron scatters off of an atom.  Putting these two functions
together, we can now describe how an electon leaves the point in space
occupied by the absorbing atom, travels to a neighbor, scatters off
that neighbor, and continues traveling.

We are interested in computing the absorption at a particular atom.
The photoelecton starts in the deep core of the absorber and is
promoted to a higher lying state OF THE ABSORBER.  Thus, the thing
that is relevant is to compute the density of states OF THE ABSORBER.
In the RSMS approach, the density of states is computed from the
overlap of the wavefunctions of the outwardly propagating
photoelectron with the functions of the various scattered waves.
The part of the overlap that is relevant to computing the density AT
THE ABSORBER is the bit that happens at the position OF THE ABSORBER.

So, the interaction in question is "a deep core electron is promoted
to an occupied state of the absorber".  The computational tool used to
compute that interaction is RSMS.  Happily, the parameters of the RSMS
approach (R, sigma^2, N) map readily onto the things that we want to
know when we do an XAS experiment.

Here are all the details, as implemented in Feff:

  http://rmp.aps.org/abstract/RMP/v72/i3/p621_1

It's a dense read but it's also an excellent and very rewarding paper.

B



-- 

 Bruce Ravel  ------------------------------------ bravel at bnl.gov

 National Institute of Standards and Technology
 Synchrotron Methods Group at NSLS --- Beamlines U7A, X24A, X23A2
 Building 535A
 Upton NY, 11973

 My homepage:    http://xafs.org/BruceRavel
 EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/