Re: [ccp4bb] Is anomalous signal a different wavelength?
Especially, the crystallographers are interested in everything concerning resonance scattering, which is indeed a valid terminus technicus in natural sciences. The question of Jacob is very interesting. We have to distinguish between absorption cross section and scattering cross section and relate them, say, by Kramers Kronig. As I see it: The total scattering cross section of an electron depends on the eigenfrequency and the constant of friction of the electron bound to the nucleus. Near resonance the total scattering cross section increases dramatically and the proability to scatter an X-ray is much larger than remote from the edge. However, this scattering process is elastic: it means that the wavelength is NOT altered. However, a phase shift of the scattered photon occurs which is different from the 180 deg usually expected for Thompson scattering. We have to correct for this (Hönl-correction) and this gives us also the opportunity to determine phase. If really absorption occurs, of course we have fluorescence which has lost all the phase relation relative to the incident photon and is indeed not scattered in reflections anymore, EXCEPT when there are collective processes as for example observed in nuclear resonance scattering of Mössbauer radiation. Marius Dear Crystallographers, I have been wondering recently whether the anomalous component of a diffraction pattern is of a different wavelength from the regular diffraction pattern. It seems reasonable as resonant scattering seems to be akin to fluorescence, although as I understand it, is not exactly the same. Does anybody know here for sure, or at least where to look or whom to ask? All the best, Jacob Keller *** Jacob Keller Northwestern University 6541 N. Francisco #3 Chicago IL 60645 (847)467-4049 [EMAIL PROTECTED] *** PD Dr. habil. Marius Schmidt Physikdepartment E17 Technische Universitaet Muenchen James Franck Strasse 85747 Garching/Germany email: [EMAIL PROTECTED] http://users.physik.tu-muenchen.de/marius/ phone: +49-(0)89-2891-2550 fax: +49-(0)89-2891-2548
Re: [ccp4bb] Is anomalous signal a different wavelength?
Ethan A Merritt wrote: And please note that resonant scattering is not a standard term. Resonant Scattering is now the standard term accepted and used anywhere in the X-ray physics and crystallography literature, except in protein crystallography. It is the more adequate term since the X-ray phenomena under discussion involve resonant interactions of photons with matter and are actually not at all 'anomalous'. -- Marc SCHILTZ http://lcr.epfl.ch
Re: [ccp4bb] Is anomalous signal a different wavelength?
Dear All, While we are talking about X-ray scattering, I have another question. If an X-ray is elastically scattered from an electron at an angle theta, its energy is the same is the incoming X-ray. However, the momentum is not the same, as it now has a component in a perpendicular direction (see fig below). As I don't believe that the conservation of momentum really is violated, what is the source of the discrepancy? Contrast this with most textbook descriptions of Compton scattering, where the X-ray loses energy and the electron gains kinetic energy. best wishes James X-ray e- \ \ \ Dr. James Murray Biochemistry Building Department of Biological Sciences Imperial College London London, SW7 2AZ Tel: +44 (0)20 7594 5276
Re: [ccp4bb] Is anomalous signal a different wavelength?
I think it's to do with the Uncertainty Principle. You can't say for sure that a particular X-ray photon has gone off in that direction (if you could you would know both its position and momentum accurately which is not allowed). If you integrated the momentum over all possible outcomes I'm sure you would find that it's conserved (it has to be in an elastic collision). -- Ian -Original Message- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Murray, James W Sent: 31 May 2007 10:30 To: CCP4BB@JISCMAIL.AC.UK Subject: RE: [ccp4bb] Is anomalous signal a different wavelength? Dear All, While we are talking about X-ray scattering, I have another question. If an X-ray is elastically scattered from an electron at an angle theta, its energy is the same is the incoming X-ray. However, the momentum is not the same, as it now has a component in a perpendicular direction (see fig below). As I don't believe that the conservation of momentum really is violated, what is the source of the discrepancy? Contrast this with most textbook descriptions of Compton scattering, where the X-ray loses energy and the electron gains kinetic energy. best wishes James X-ray e- \ \ \ Dr. James Murray Biochemistry Building Department of Biological Sciences Imperial College London London, SW7 2AZ Tel: +44 (0)20 7594 5276 Disclaimer This communication is confidential and may contain privileged information intended solely for the named addressee(s). It may not be used or disclosed except for the purpose for which it has been sent. If you are not the intended recipient you must not review, use, disclose, copy, distribute or take any action in reliance upon it. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing [EMAIL PROTECTED] and destroy all copies of the message and any attached documents. Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain. Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof. Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674
Re: [ccp4bb] Is anomalous signal a different wavelength?
James, At least for diffraction experiments; the photon scatters off of the *crystal lattice*, not any individual electron, so you can conserve the momentum of the photons and the macroscopic crystal without the crystal recoiling too much. Best, Jon Murray, James W wrote: Dear All, While we are talking about X-ray scattering, I have another question. If an X-ray is elastically scattered from an electron at an angle theta, its energy is the same is the incoming X-ray. However, the momentum is not the same, as it now has a component in a perpendicular direction (see fig below). As I don't believe that the conservation of momentum really is violated, what is the source of the discrepancy? Contrast this with most textbook descriptions of Compton scattering, where the X-ray loses energy and the electron gains kinetic energy. best wishes James X-ray e- \ \ \ Dr. James Murray Biochemistry Building Department of Biological Sciences Imperial College London London, SW7 2AZ Tel: +44 (0)20 7594 5276
Re: [ccp4bb] Is anomalous signal a different wavelength?
On jeudi 31 mai 2007, Murray, James W wrote: While we are talking about X-ray scattering, I have another question. If an X-ray is elastically scattered from an electron at an angle theta, its energy is the same is the incoming X-ray. However, the momentum is not the same, as it now has a component in a perpendicular direction (see fig below). As I don't believe that the conservation of momentum really is violated, what is the source of the discrepancy? You cannot correctly describe photon-electron interactions using classical mechanics. One reason is that the energy (among over properties) of the electron is quantified, so the photon cannot transfer an arbitrary amount of energy/momentum to the electron. So you'd have to consider the interaction between the photon and everything it is bound with (atom, lattice..) Incidentally, I think the classical delta(lambda) formula for Compton scattering is computed for a _free_ electron. Vincent -- Vincent Favre-Nicolin Université Joseph Fourier
Re: [ccp4bb] Is anomalous signal a different wavelength?
On Thursday 31 May 2007 01:37, Marc SCHILTZ wrote: Ethan A Merritt wrote: And please note that resonant scattering is not a standard term. Resonant Scattering is now the standard term accepted and used anywhere in the X-ray physics and crystallography literature, except in protein crystallography. I stand corrected. Is there a IUPAC or other standard definition of the term? My attempts to find one via Google did not turn up anything definitive. The literature examples that I found use the term to refer to the experiment itself, or to the scattering process as a whole. However the original poster used the term in such a way that made it sound as if the resonant scattering was roughly a synonym for imaginary component of the scattering factor, which is not exactly the same thing. If we protein crystallographers are to begin using the term, we should first pin down what the definition is. It is the more adequate term since the X-ray phenomena under discussion involve resonant interactions of photons with matter and are actually not at all 'anomalous'. The 'anomalous' behaviour that gave rise to this label is the violation of the general principle that the strength of interaction between light and solid matter decreases as the wavelength decreases. At an absorption edge, the scattering curve is anomalous because the strength of the interaction is not monotone decreasing with photon energy. Instead it increases as you approach the edge from either direction. The term was inherited from the description of experiments with visible light that characterized the wavelength-dependence of a material's index of refraction. -- Ethan A Merritt Biomolecular Structure Center University of Washington, Seattle 98195-7742
Re: [ccp4bb] Is anomalous signal a different wavelength?
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
Re: [ccp4bb] Is anomalous signal a different wavelength?
Dear Crystallographers, 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 [EMAIL PROTECTED] ***
Re: [ccp4bb] Is anomalous signal a different wavelength?
Quoting Jacob Keller [EMAIL PROTECTED]: 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. Let the heroes speak: In 1994 D. H. Templeton wrote: The index of refraction of transparent materials for visible light generally increases as the wavelength decreases and this dispersion is said to be 'normal'. Near absorption bands there are intervals of wavelength where the slope of n versus \lambda is positive, and the dispersion is 'anomalous'. According to this convention and the relation between n and f', x-ray dispersion is anomalous only in those intervals where df'/d\lambda is negative. Yet 'anomalous dispersion' and 'anomalous scattering' have come to be used for the effects of absorption on x-ray optical properties at all wavelengths, or sometimes perhaps only for those related to the imaginary term f. These effects are significant for nearly all atoms at all wavelengths commonly used for diffraction experiments, and therefore 'anomalous' is somewhat inappropriate. I prefer 'dispersion' or 'resonant scattering'. (in 'Resonant Anomalous X-ray Scattering: Theory and Applications', G.Materlik, C.J.Sparks K.Fischer (eds.), Elsevier Science, Amsterdam: 1994) The editors (G.Materlik, C.J.Sparks K.Fischer) of that same book wrote in the preface: Since resonant interactions are characteristic of the interaction of photons with matter, we suggest that 'resonant' better describes the field than 'anomalous' scattering. But note that they used the pleonasm Resonant Anomalous X-ray Scattering as a title for their book ;-) More recent review articles use the term resonant scattering or resonant diffraction, e.g. Hodeau JL, Favre-Nicolin V, Bos S, Renevier H, Lorenzo E, Berar JF (2002). Resonant diffraction. Chem Rev. 101, 1843--1867. which includes a section on MAD phasing. Thus, resonant scattering and anomalous scattering are synonyms and it is almost a matter of taste which term one prefers. Both are perfectly acceptable. The x-ray physics and crystallography communities (except protein crystallography) have shifted from the usage of anomalous scattering to resonant scattering. But then, as you write, if we want to keep the MAD SAD SIRAS etc acronyms we are tied to anomalous. Marc Schiltz
Re: [ccp4bb] Is anomalous signal a different wavelength?
==Original message text=== On Wed, 30 May 2007 6:51:09 pm CDT Ethan Merritt wrote: On Wednesday 30 May 2007 16:24, Jacob Keller wrote: I have been wondering recently whether the anomalous component of a diffraction pattern is of a different wavelength from the regular diffraction pattern. The diffraction pattern satisfies Bragg's Law. If the input radiation is monochromatic, then the diffraction pattern shows a spot wherever that wavelength satisfies Bragg's Law for some set of planes in the crystal. In the presence of anomalous scattering, some of the incident radiation is absorbed rather than diffracted. The absorbed photon may then be re-emitted via X-ray fluorescence, as you mention. That emitted photon goes off in some random direction and does not contribute to the main Bragg diffraction pattern. In principle it could produce a diffraction pattern of its own as it travels through the rest of the crystal, but the diffraction pattern from a single photon will not be measurable in practice. Although I am no authority on this matter, the way I think of resonant scattering is scattering which is phase-shifted from the protein scattering by a certain absolute amount, due to a resonance event which takes a certain amount of time. Is this a correct model? If so, the question would be whether this resonance event saps energy from the incident light--then the emitted light from the heavy atoms would be of lesser energy. If this were true, then the heavy atoms would indeed be sending out a diffraction pattern of their own, which would be, I believe, at just slightly higher scattering angles and somewhat different Bragg conditions due to their lesser energy. Were you saying that there was some resonant scattering from the heavy atoms which was the same wavelength as the incident light, and some which was different? Thanks for your response, Jacob Keller *** Jacob Keller Northwestern University 6541 N. Francisco #3 Chicago IL 60645 (847)467-4049 [EMAIL PROTECTED] ***
