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I'm confused by why the scattering trajectory of a photoelectron that has already been excited by an x-ray has an effect on the absorption coefficient i.e. the likelihood to absorb said x-ray.

In the case where it's jumping some number of discrete energy levels, I understand the probabilistic nature of the absorption, but in the continuum, I don't see how the scattering processes can determine the probability of absorption after the fact. It seems to me like probing the future for appropriate final states.

Bear in mind, I'm thinking of this in terms of Fermi's golden rule, i.e. the transition probability between core states and whatever scattered states there are (??)

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  • $\begingroup$ Consider to spell out acronyms. $\endgroup$ – Qmechanic Sep 23 '17 at 9:47
  • $\begingroup$ Thank you for the comment. In my case, should I spell them out in the title, or in the question itself? $\endgroup$ – Jon Snow Sep 24 '17 at 22:45
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EXAFS :== extended X-ray absorption fine structure. At some Xray energies, almost all absorption is due to photoelectric effect, an (inner) electron being promoted to a higher energy state, often escaping the atom entirely.

The 'scattered state' that contains the outgoing photoelectron has to overlap the core state. That is where the matrix element comes from, that determines the rate of photoelectric absorption of an X-ray. The key here, is that the outgoing states are perturbed by the cores of any neighboring atoms, which are significant parts of the Hamiltonian of that outgoing electron.

It is the extended electron wave, in all its not-exactly-a-point-particle extent, which carries away the X-ray's quantum of energy, and not just a small local orbital (like a bound electron in the 1S shell).

The result is that some energies and directions are unlikely (because the outgoing electron wave backscatters), which means the matrix element is small, because of those other, distant, atoms.

EXAFS with polarized X-rays (synchrotron radiation) can give directional information on crystalline samples with orientation, because of the different neighbor positions as a function of the crystal orientation with respect to the outgoing-electron direction. With liquids or polycrystalline samples, an average over many directions is seen instead.

And with a dilute gas of atoms, a 'pure' absorption of the Xrays by a free atom is observed. The cases are all different, because the outgoing electrons are waves that may overlap multiple neighbors. The absorption depends on those outgoing-electron wavefunctions, so it is modulated by the absorbing atom's neighbors.

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  • $\begingroup$ Thank you for the explanation, thoroughly appreciate it! However, when you say that the scattered state of the outgoing photoelectron has to overlap the core state, you mean that in the spatial extent only, correct? Otherwise, if it should overlap in time as well, then it seems impossible, as time passes in between. This is what I was getting hung up on, hopefully my train of thought is understandable. $\endgroup$ – Jon Snow Sep 25 '17 at 5:18

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