Hi John, Thanks for looking at this!
Clearly the coorrelations between S02, ThetaD and Ei make any assessment of possible problems with Ei problematic. Also, I don't know what the experimental resolution Gamma_expt is - probably some fraction of an eV, so Ei=Gamma_expt+Im delta Sigma implies a comparable but negative correction delta Sigma to the self-energy, which is evidence of excessive loss in the HL plasmon-pole self-energy for Cu.
I'd guess the monochromator resolution was around 0.75 to 1eV for the Cu measurement. And I agree that testing the effect of Ei v. S02 is very challenging, especially with finite monochromator resolution and finite thermal vibrations.
Moreover, although your fits are in R-space, inspection of the k-space data shows that contributions from distant MS paths are suppressed by the theory, also suggesting that FEFF's PP self-energy overestimates loss.
Yep, it looks to me that in both k- and R-space the shapes of the amplitudes for the best-fit result are slightly, but perceptively different from the data. At first look this is an exampalry "great fit". But looking more closely you can really see that reduced chi-square should be ~10, as the best-fit really is off from the data in ways that can't be easily explained as a wrong value for S02, sigma2, or Ei. I don't have a good explanation for the discrepcancy (and don't want to guarantee it's not a systematic error in the data -- but it sure doesn't seem to be). This results seem very similar to those of Bud Bridges several years ago. I think it's fair to say that neither you nor I disagreed with Bud at the time: we've known that reduced chi-square for fits to very good data is much too big for some time. It would be very nice if we could nail down the pieces that go into the EXAFS amplitudes better. It will be interesting to see if you come up with anything different. I'd love to hear about it! --Matt