Re: CORRECTIONS imaginary shift enquiry

["John J. Rehr" <jjr@leonardo.phys.washington.edu>]

Dear David and other Feffusers,

> I find that the increase in peak width does not reflect my perception of 
> what 0.5eV broadening means (this is my error, I know). Previously sharp 
> peaks in the XANES become much broader, and peaks merge seemingly beyond 
> the 0.5eV parameter. I know this is an amateurish description of the 
> fitting process, but I'm just trying to get my point across simply. I would 
> have expected a Gaussian Full Width Half Maximum type broadening process, 
> but my data does not reflect this.
> 
> If some kind soul could provide me with a description of how 
> (mathematically) the imaginary shift is broadening the spectra, it would 
> really help my peak fitting process a lot.

  If the XAS were a step function, then the imaginary part of the
Green's function G energy denominator omega - E + i  Gam  gives
rise to lorentizian broadening at each energy, i.e.,
(-1/pi) Im G = Gam/[(omega-E)^2 + Gam^2]. That is, adding an imaginary
part is equivalent to lorentzian broadening.

  However, in general the XAS is not a simple step function, so the
apparent broadening at the edge to take into account the energy dependence
of the matrix elements and the density of states and the thermal and
lifetime broadening of the fermi function at threshold.  This 
complicates the math, obviating a "simple" description that works in all
cases. One sees the biggest deviations in cases where there is a big
white line for example.

  The details of how broadening is accounted for in FEFF are given in

"Theory of solid state contributions to the x-ray elastic scattering
amplitude," by A. L.  Ankudinov, and J. J. Rehr, Phys. Rev. B,
{\bf62}, 2437 (2000)

This paper treats both XAS and spectroscopies like DAFS, DANES, etc.
where broadening at the edge has to be done carefully.

  Sincerely, 
  John Rehr