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Re: [ccp4bb] Is anomalous signal a different wavelength? |
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CCP4bb navigationCCP4bb <-- 2007 <-- May 2007 <-- 31 May 2007Subject: Re: Is anomalous signal a different wavelength? From: Jacob Keller j-keller2 {- at -} MD {- dot -} NORTHWESTERN {- dot -} EDU Date: 2007-05-31 The reason I called the phenomenon "resonant scattering" is because that is the term used by "Elements of Modern X-ray Physics" by Jens Als-Nielsen, Des McMorrow. I prefer the term also because this scattering is, as somebody has said, no longer really "anomalous--" it fits well into x-ray physical theory. As for Compton scattering, I was under the impression that the event was a free electron being perturbed back and forth by an incoming EM wave, which changes its velocity, and like an free electron/positron bouncing around a synchrotron, the perturbed electron releases a photon, which emerges as a spherical wave. This spherical wave then is able to interact with all other spherical-wave photons emerging from analogous electrons elsewhere in the crystal. (Would this mean all of the constructively-interfering electron wave-functions would have to be in phase with each other, in the whole crystal? A conundrum...) Concerning resonant scattering, it seemed to me that the lower-level k- or l-edge (not free) electron was excited to a higher state, and another electron dropped down to fill its place. This process would on average take a finite amount of time, inducing an absolute phase shift in its emerging spherical wave, relative to the regular Compton-scattered wave. This phase shift is modelled by two vectors, real and imaginary, in complex space, which together represent the phase shift. No matter the phase of the protein wave, the length and direction of these vectors stays the same at a given wavelength. When the wavelength is shifted, say to the F' minimum (inflection), the average time required for the resonant scattering event changes, resulting in a different absolute phase shift which is little shifted from the Compton-scattered wave, although it might be even a few periods behind. I will try to look into this, and see if the observations and equations agree with what I am saying. All the best, Jacob Keller ps perhaps "anomalous" is better than "resonant," as it produces "MAD" and "SAD" and not "MRD" and "SRD"... ==============Original message text=============== On Thu, 31 May 2007 11:57:21 am CDT William Scott wrote: Dear Fellow Compatriots: A few pre-coffee random observations from the field offices of Dr. Cranky: 1. No mention of "Resonant Scattering in the index of JJ Sakurai Adv. Quantum Mechanics (1967, 1987 revision), which I used in (blush) 1989, although the phenomenon is discussed, with many exercises left to the reader. The index did, however, refer to the "retarded Green's function," which I find delightful in this context. 2. "Resonance scattering" does appear in JJ Sakurai, Modern Quantum Mechanics, which is a book he wrote a little bit later, and published in 1985 after he died. So I guess that dates the term as well as me. 3. "Anomalous scattering" in optics (i.e, the same phenomenon) describes the __inversion__ of the rainbow spectrum (dispersion) when white light propagates through a prism in which there are absorbers that absorb light near to the visible spectrum. This is accounted for with an imaginary component in the index of refraction. So violet is where you would normally expect to see red, and vice versa. 4. The QM analogue takes as its starting point the First Born approximation (I'm too tired to make a pun) in which a single photon scatters once elastically from a billiard ball point scattering center. You can then show that the diffraction pattern is the FT of the potential, and then get it into the form of electron density from there. Anomalous scattering dispersion and absorption effects are essentially grafted on as real and imaginary terms in the denominator of the scattering potential (see retarded Green's function, above). What comes out of that treatment is essentially identical to what you have in that equation in James that Blundell and Johnson use as a starting point for the derivation. The main point is it is phase shifting. The photon frequency is not changed. 5. Resonance scattering requires a different sort of potential in which you have what Sakurai calls a "quasi-bound state" with a soft barrier. The energy barrier has to be of the same order as the energy of the photon, so I think for X-rays this isn't a significant effect. Bill Scott ===========End of original message text=========== *********************************** Jacob Keller Northwestern University 6541 N. Francisco #3 Chicago IL 60645 (847)467-4049 j-keller2@northwestern.edu *********************************** CCP4bb navigationCCP4bb <-- 2007 <-- May 2007 <-- 31 May 2007 |
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