On 12/03/2015 13:11, Keller, Jacob wrote:
If projects a middle-C-tone into a piano, do all of the lower notes resonate as
well, according to the Kramers-Kronig relation?
If you press the right pedal the harmonics of the note you play will
resonate. My piano teachers never mentioned to me the Kramers-Kronig relation
but that's a long time ago, perhaps they do these days.
Right, I always understood that it was just the harmonics which would resonate.
But according to Kramers-Kronig, wouldn't there be resonance on all strings,
just as there's anomalous scattering at all higher energies above the edge?
Each string of lower frequency would be analogous to an anomalous scatterer
with an edge at a lower energy than the incident radiation. Hmm, maybe it
really does happen?
Yes, it really does happen. Get your toddler to bang on the piano while
you hold down a note.
A different question: do the real and imaginary components of anomalous
scattering arise from different processes, or are they simply a way to
represent the phase of the anomalous scattering?
All the best,
Jacob
________________________________________
From: CCP4 bulletin board [CCP4BB@JISCMAIL.AC.UK] on behalf of Keller, Jacob
[kell...@janelia.hhmi.org]
Sent: Wednesday, March 11, 2015 6:57 PM
To: CCP4BB@JISCMAIL.AC.UK
Subject: [ccp4bb] Basic Anomalous Scattering Theory
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
email: kell...@janelia.hhmi.org
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