Hi Jacob:

If you can find a copy of R. W. James, THE CRYSTALLINE STATE VOL II: THE OPTICAL PRINCIPLES OF THE DIFFRACTION OF X-RAYS. Hardcover – 1965, this gives a very good (albeit primarily classical) description.  Blundell and Johnson also has a good, slightly more modern, description, which I think is derived in part from James’s treatment. (Someone has swiped both books from me, so I can’t double-check.)  Having said that, I find an approach based on quantum scattering theory more intuitive.  Everything we normally deal with is elastic scattering within the first-order Born approximation, which means a single photon collides exactly once with a billiard ball-like spherically symmetric hard-sphere electron cloud, neither gaining nor losing energy.  Using the Poisson equation, you can then show that the electron density is the FT of the (completely real) potential.  To treat absorption within this framework, an imaginary term is added to the potential as a small perturbation.  

Briefly, in the first case, a photon elastically scatters, and in the second case, there is a probability of absorption. (An absorbed photon, absorbed in the conventional way , in which an electron is promoted to an excited state, will be re-emitted as a new photon having less energy, which is how we are able to do fluorescent XAFS to find the absorption edge when collecting data.)

Sorry, I will have to stop here to go teach something else I am equally unqualified to speak about — enzymology.  Hopefully this will be something to get a start with.

Bill










William G. Scott
Director, Program in Biochemistry and Molecular Biology
Professor, Department of Chemistry and Biochemistry
and The Center for the Molecular Biology of RNA
University of California at Santa Cruz
Santa Cruz, California 95064
USA

phone:  +1-831-459-5367 (office)

email:    [log in to unmask]

> On Mar 11, 2015, at 9:57 AM, Keller, Jacob <[log in to unmask]> wrote:
> 
> Dear Crystallographers,
> 
> I have had only a vague understanding of what specific things are happening with shell electrons at anomalous edges. Specifically, for example, to what energy of electron-transition does the x-ray k-edge correspond in terms of orbitals, and is that transition energy actually equal to the energy of the photon, suggesting that the photon is absorbed (or disappears?) in elevating the electron? I don't think we say it is absorbed, so how does the energy come back out, from the electron's falling back down, right? So then there's a new photon created, or the same one comes back out? Where was it? 
> 
> Further, I also have heard that the emerging anomalous/resonance photons are of the same wavelength as the incident radiation, but usually there is something lost in transitions (even non-fluorescence ones) I thought? Has it ever been definitively shown that the anomalous photons are of the same energy as the incident radiation?
> 
> In the case of L-edges, why are there three separate edges? Further, if the resonance occurs when the energies are equal, why does resonance occur at energies greater than the edge? I don't think this happens in other resonance phenomena, or does it? If projects a middle-C-tone into a piano, do all of the lower notes resonate as well, according to the Kramers-Kronig relation? I think it may actually happen in the mammalian cochlea's travelling wave, but is it completely general to resonance phenomena?
> 
> Just interested, and have wondered these things for a long time in the background of my mind...
> 
> Jacob Keller
> 
> 
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> Jacob Pearson Keller, PhD
> Looger Lab/HHMI Janelia Research Campus
> 19700 Helix Dr, Ashburn, VA 20147
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