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.
*******************************************************
Dirk Kostrewa
Gene Center, A 5.07
Ludwig-Maximilians-University
Feodor-Lynen-Str. 25
81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
E-mail: [email protected]
*******************************************************
