Dirk Kostrewa wrote:
> yes, this is certainly true for real fluorescence effects. But the 
> anomalous scattering can be best thought of as a resonance phenomenon 
> without any frequency change, and as such, it has a distinct phase 
> relationship to the elastically scattered photon and does have an 
> effect on the intensities (which, I think, was the background of the 
> original question?). But for the lighter atoms in biological 
> macromolecules, where in a typical experiment the measurement 
> frequency is far away from any resonance frequency, this effect can be 
> neglected.
>
> This leads me to my follow-up question to the experts: why is the 
> resonance effect "anomalous scattering" measured by a fluorescence 
> scan that should have all the effects mentioned by James? Don't we get 
> as a result a mixture of signals from resonance (i.e. anomalous) and 
> from absorption-emission (i.e. fluorescence) effects?
>

 Fluorescent photon emission happens well after the incident photon has 
"passed", so anomalous scattering is only indirectly related to 
fluorescence.  The relationship is that absorption induces a phase shift 
in scattering (this is the anomalous scattering effect), but it also 
induces an electronic transition in the atom, leaving a "core hole" or 
vacant orbital near the nucleus.  The filling of this core hole will 
generate a fluorescent photon (some fixed fraction of the time), and 
this allows us to equate the intensity of observed fluorescence to the 
number of core holes produced and therefore to the absorption cross 
section of the atom.  In actual fact, the "MAD scan" we do before a 
MAD/SAD experiment is not a "fluorescence spectrum", but rather an 
absorption spectrum using fluorescence as a tally.  A fluorescence 
spectrum would have the energy of the fluorescent photon on the x-axis. 
(Bob Sweet has corrected me several times for getting that wrong).

As for the connection between absorption and anomalous scattering, I 
tend to think of this in the classical picture.  Scattering lags the 
incident beam by 90 degrees because a simple harmonic oscillator driven 
at frequencies much higher than resonance lags behind the force upon 
it.  An oscillator driven at resonance will move 180 degrees 
out-of-phase with the driving force.  You can verify this yourself by 
playing with a weight tied to the end of a rubber band.  Another way to 
think about it is that absorption must create a wave that is 180 degrees 
out of phase with the incident beam because it reduces the intensity of 
the incident beam.  The details of the physics are much more complicated 
than this, but this is how I like to remember it. 

So, as you approach a resonance, some of the electrons in the atom will 
start "absorbing" (resonating) and therefore move out-of-phase with the 
other electrons in the atom (and indeed the other electrons in the 
crystal).  It is this "out of sync" behavior that reduces the effective 
occupancy of the atom and also creates an "imaginary" component to the 
scattering.  This "imaginary electron density" is hard to accept if you 
have never taken complex algebra, but the easy way to think about it is 
to remember than multiplying a complex number by sqrt(-1) changes its 
phase by 90 degrees.  So the "imaginary component" is really just a 
mathematical way to represent electrons that are out-of-sync with the 
majority of electrons in the crystal.  Yes, the majority, because a pure 
selenium crystal has no anomalous scattering (since no atoms lag any 
other atoms).  The "imaginary component" is what leads to the breakdown 
of Friedel's law (which states that the Fourier transform of a 
real-valued function is centrosymmetric).  But all this is really just a 
fancy way of saying that some of the electrons are out of phase with the 
rest.

Hope this makes sense.

-James Holton
MAD Scientist

> Best regards,
>
> Dirk.
>
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> Dirk Kostrewa
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