[Ifeffit] Debye factor and S02 correlation

[John J. Rehr]

Matt's test of fitting the inelastic losses using So2 and an effective mean free
path (via a constant imaginary shift Ei in the net lifetime width in FEFFIT)
is quite interesting. In particular the results are consistent with our current
understanding of the physics, namely that the inelastic losses are generally
overestimated by the plasmon-pole self energy. Thus one expects Ei to be
negative to compensate for errors in this self-energy model. Also it's
particularly encouraging that one can fit *both Ei and So2*. I'm not
too worried by the evident correlation between these parameters since
they both smoothly affect the overall amplitude; what matters is the
value of Ei when So2 is about 0.9.

Matt wrote:

>This seems like a fine approach to me, and it could be automated,
>at least somewhat.  Feffit/Ifeffit have Ei as a path parameter,
>so setting So2 to 0.9 and floating Ei is possible right now.
>Using Ei instead of So2 has a couple possible benefits:
>  1.  Not completed correlated with N (though see below!)
>  2.  Can accomodate measurement resolution issues.
>  3.  Might be a little easier conceptually on the new people.
>
>For one variation on the canonical 'Cu 10K first shell fit',
>with sigma2 varying as well, I get these values:
>    So2              Ei            chi_square  r-factor
>  0.93(0.03)      0.00(fix)          119.      0.0017
>  1.00(fix)       0.55(0.25)         128.      0.0018
>  0.95(fix)       0.14(0.24)         120.      0.0017
>  0.90(fix)       -.29(0.23)         116.      0.0016
>  0.85(fix)       -.75(0.23)         116.      0.0016
>
>  0.87(0.14)      -.58(1.27)         116.      0.0016
>
>The last one had both So2 and ei (and sigma2!!) floating. The
>correlation between them was 0.98, higher than that between So2
>and sigma2, which was a mere(!) 0.94.  So it looks like, for this
>data, So2 really does want to be ~0.90 +/ 0.05, and Ei wants to
>be 0.00 +/- 0.25.

  As I read the numbers for the minimum chi_square, I would say
that the results suggest Ei = -.52 +/- .3  I don't believe the
error bar on So2 of +/- .14. Probably +/- .05 is more like it,
so the error bar on Ei will be much smaller than 1.27.

  Also, I think if you look at plots of the fits, they look better with
a slightly negative Ei. We would very much like to see more evidence
for the inadequacy of the plasmon pole self energy.

  Thus I would encourage more fits to include E_i as a fitting parameter,
with So2 kept under control (e.g. fixed or floating in a range
0.9 +/- .05, assuming edje jump is well defined).

  J. Rehr