[Ifeffit] Third cumulant in DWF

[Matt Newville]

Hi Yuan, (Bruce, Matthew),

Yes, the correction described by Tranquada and Ingalls is explicitly
included in ifeffit's fits.

There are a couple different effects going on.  Short of doing actual
integrals over g(R), we try to take all the effects into account.
The cumulant expansion models the effects of varying R in the sin(2kR)
 (actually exp( i2kR)) but does not model the effect of changing R in
   a) the exp(-2R/lambda) term, and
   b) the 1/R^2 term
in the EXAFS equation.

The b) term is what Tranquada and Ingalls discuss, and the correction
they have is applied.

The effect from the lambda term is handled separately, and more simply
by working in the complex plane.
the terms    exp[i2kR] exp[-2R/lambda]    becomes  exp[i2pR]  where p
is the complex photoelectron wavenumber, p = k + i/lambda.

The cumulant expansion is then done over exp[i2pR], and the subtle
effect of deltaR on the amplitude and sigma^2 on the phase are
automatically accounted for.

All of these effects are small, but for highly disordered systems,
they are noticeable.
.
Hope that helps,

--Matt

PS:  One thing we don't correctly account for is the effect of the R
dependence of the scattering amplitudes and phase-shifts themselves.

On Mon, Apr 4, 2011 at 5:01 PM, Ping, Yuan <ping2 at llnl.gov> wrote:
> So the term is included? Please see the attached paper. I meant the Coj(k)
> in Eq. (5).
>
> Thanks.
> Yuan
>
>
> On 4/4/11 2:33 PM, "Bruce Ravel" <bravel at bnl.gov> wrote:
>
>> On Monday, April 04, 2011 05:25:39 pm Ping, Yuan wrote:
>>> Does the math expression in IFEFFIT include the term -4k*sigma2*(1/labmda
>>> +1/R) in the phase? If yes, the 1st cumulant is sigma1= R+dR. If no,
>>> sigma1= R+dR+2*sigma2*(1/labmda +1/R). It this correct?
>>
>> When Ifeffit evaluates the exafs equation, it includes lamdba from the
>> Feff calculation.
>>
>> B
>
>
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