Neutron spin echo

Last updated November 07, 2024

Neutron spin echo spectroscopy is an inelastic neutron scattering technique invented by Ferenc Mezei in the 1970s and developed in collaboration with John Hayter.^[1] In recognition of his work and in other areas, Mezei was awarded the first Walter Haelg Prize in 1999.

In magnetic resonance, a spin echo is the refocusing of spin magnetisation by a pulse of resonant electromagnetic radiation. The spin echo spectrometer possesses an extremely high energy resolution (roughly one part in 100,000). Additionally, it measures the density-density correlation (or intermediate scattering function) F(Q,t) as a function of momentum transfer Q and time. Other neutron scattering techniques measure the dynamic structure factor S(Q,ω), which can be converted to F(Q,t) by a Fourier transform, which may be difficult in practice. For weak inelastic features S(Q,ω) is better suited, however, for (slow) relaxations the natural representation is given by F(Q,t). Because of its extraordinary high effective energy resolution compared to other neutron scattering techniques, NSE is an ideal method to observe^[2] overdamped internal dynamic modes (relaxations) and other diffusive processes in materials such as a polymer blends, alkane chains, or microemulsions. The extraordinary power of NSE spectrometry^[3] was further demonstrated recently^[4]^[5] by the direct observation of coupled internal protein dynamics in the proteins NHERF1 and Taq polymerase and the adherens junction,^[6] allowing the direct visualization of protein nanomachinery in motion.^[7] Several elementary reviews of the technique exist.^[8]^[9]^[10]^[11]^[12]

How it works

Neutron spin echo is a time-of-flight technique. Concerning the neutron spins it has a strong analogy to the so-called Hahn echo,^[13] well known in the field of NMR. In both cases the loss of polarization (magnetization) due to dephasing of the spins in time is restored by an effective time reversal operation, that leads to a restitution of polarization (rephasing). In NMR the dephasing happens due to variation in the local fields at positions of the nuclei, in NSE the dephasing is due to different neutron velocities in the incoming neutron beam. The Larmor precession of the neutron spin in a preparation zone with a magnetic field before the sample encodes the individual velocities of neutrons in the beam into precession angles. Close to the sample the time reversal is effected by a so-called flipper. A symmetric decoding zone follows such that at its end the precession angle accumulated in the preparation zone is exactly compensated (provided the sample did not change the neutron velocity, i.e. elastic scattering), all spins rephase to form the "spin-echo". Ideally the full polarization is restored. This effect does not depend on the velocity/energy/wavelength of the incoming neutron. If the scattering at the sample is not elastic but changes the neutron velocity, the rephasing will become incomplete and a loss of final polarization results, which depends on the distribution of differences in the time, which the neutrons need to fly through the symmetric first (coding) and second (decoding)precession zones. The time differences occur due to a velocity change acquired by non-elastic scattering at the sample. The distribution of these time differences is proportional (in the linearization approximation which is appropriate for quasi-elastic high resolution spectroscopy) to the spectral part of the scattering function S(Q,ω). The effect on the measured beam polarization is proportional to the cos-Fourier transform of the spectral function, the intermediate scattering function F(Q,t). The time parameter depends on the neutron wavelength and the factor connecting precession angle with (reciprocal) velocity, which can e.g. be controlled by setting a certain magnetic field in the preparation and decoding zones. Scans of t may then be performed by varying the magnetic field.

It is important to note: that all the spin manipulations are just a means to detect velocity changes of the neutron, which influence—for technical reasons—in terms of a Fourier transform of the spectral function in the measured intensity. The velocity changes of the neutrons convey the physical information which is available by using NSE, i.e.

$I(Q,t)\propto S(Q)+\int \cos(\omega t)\,S(Q,\omega )\,dt$ where $\omega \propto \Delta v$ and $t\propto B\times \lambda ^{3}$ .

B denotes the precession field strength, λ the (average) neutron wavelength and Δv the neutron velocity change upon scattering at the sample.

The main reason for using NSE is that by the above means it can reach Fourier times of up to many 100ns, which corresponds to energy resolutions in the neV range. The closest approach to this resolution by a spectroscopic neutron instrument type, namely the backscattering spectrometer (BSS), is in the range of 0.5 to 1 μeV. The spin-echo trick allows to use an intense beam of neutrons with a wavelength distribution of 10% or more and at the same time to be sensitive to velocity changes in the range of less than 10⁻⁴.

Note: the above explanations assumes the generic NSE configuration—as first utilized by the IN11 instrument at the Institut Laue–Langevin (ILL)--. Other approaches are possible like the resonance spin echo, NRSE with concentrated a DC field and a RF field in the flippers at the end of preparation and decoding zones which then are without magnetic field (zero field). In principle these approaches are equivalent concerning the connection of the final intensity signal with the intermediate scattering function. Due to technical difficulties until now they have not reached the same level of performance than the generic (IN11) NSE types.^{[ citation needed ]}

What it can measure

In soft matter research the structure of macromolecular objects is often investigated by small angle neutron scattering, SANS. The exchange of hydrogen with deuterium in some of the molecules creates scattering contrast between even equal chemical species. The SANS diffraction pattern—if interpreted in real space—corresponds to a snapshot picture of the molecular arrangement. Neutron spin echo instruments can analyze the inelastic broadening of the SANS intensity and thereby analyze the motion of the macromolecular objects.^[14] A coarse analogy would be a photo with a certain opening time instead of the SANS like snapshot. So we can analyze the change of the arrangement of the molecules as function of time. The opening time corresponds to the Fourier time which depends on the setting of the NSE spectrometer, it is proportional to the magnetic field (integral) and to the third power of the neutron wavelength. Values up to several hundreds of nanoseconds are available. Note that the spatial resolution of the scattering experiment is in the nanometer range, which means that a time range of e.g. 100 ns corresponds to effective molecular motion velocities of 1 nm/100 ns = 1 cm/s. This may be compared to the typical neutron velocity of 200..1000 m/s used in these type of experiments.

Spin-incoherent scattering (from protons)

Many inelastic studies that use normal time-of-flight (TOF) or backscattering spectrometers rely on the huge incoherent neutron scattering cross section of protons. The scattering signal is dominated by the corresponding contribution, which represents the (average) self-correlation function (in time) of the protons.

For NSE spin incoherent scattering has the disadvantage that it flips the neutron spins during scattering with a probability of 2/3. Thus converting 2/3 of the scattering intensity into "non-polarized" background and putting a factor of −1/3 in front of the cos-Fourier integral contribution pertaining the incoherent intensity. This signal subtracts from the coherent echo signal. The result may be a complicated combination which cannot be decomposed if only NSE is employed. However, in pure cases, i.e. when there is an overwhelming intensity contribution due to protons, NSE can be used to measure their incoherent spectrum.

The intensity situation of NSE—for e.g. soft-matter samples—is the same as in small angle neutron scattering (SANS). Molecular objects with coherent scattering contrast at low momentum transfer (Q) show coherent scattering at considerably higher intensity than the incoherent background scattering. This effect weakens as Q becomes larger. For systems containing hydrogen, contrast requires the presence of some protons, which necessarily adds some amount of incoherent contribution to the scattering intensity. In addition even deuterons add a weak spin-incoherent scattering intensity. In SANS these Q-independent intensities are typically considered as background and subtracted. In NSE experiments they are present and may become a more significant admixture as Q increases.

Fully protonated samples allow successful incoherent measurements but at intensities of the order of the SANS background level.^[15] Note: This interference with the spin manipulation of the NSE technique occurs only with spin-incoherent scattering. Isotopic incoherent scattering yields a "normal" NSE signal.

Existing spectrometers

IN11 (ILL, Grenoble, France)

IN15 (ILL, Grenoble, France)

NL2a J-NSE "PHOENIX" (JCNS, Juelich, Germany, hosted by FRM II Munich, Munich, Germany)

NL5-S RESEDA (FRM II Munich, Munich, Germany)

V5/SPAN (Hahn-Meitner Institut, Berlin, Germany)

C2-3-1 iNSE (JRR-3, Tokai, Japan)

BL06 VIN-ROSE (MLF, J-PARC, Tokai, Japan)

BL-15 NSE (SNS, ORNL, Oak Ridge, USA)

NG5-NSE (NCNR, NIST, Gaithersburg, USA)

Related Research Articles

Infrared spectroscopy is the measurement of the interaction of infrared radiation with matter by absorption, emission, or reflection. It is used to study and identify chemical substances or functional groups in solid, liquid, or gaseous forms. It can be used to characterize new materials or identify and verify known and unknown samples. The method or technique of infrared spectroscopy is conducted with an instrument called an infrared spectrometer which produces an infrared spectrum. An IR spectrum can be visualized in a graph of infrared light absorbance on the vertical axis vs. frequency, wavenumber or wavelength on the horizontal axis. Typical units of wavenumber used in IR spectra are reciprocal centimeters, with the symbol cm⁻¹. Units of IR wavelength are commonly given in micrometers, symbol μm, which are related to the wavenumber in a reciprocal way. A common laboratory instrument that uses this technique is a Fourier transform infrared (FTIR) spectrometer. Two-dimensional IR is also possible as discussed below.

Spectroscopy is the field of study that measures and interprets electromagnetic spectrum. In narrower contexts, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum.

Fourier-transform spectroscopy is a measurement technique whereby spectra are collected based on measurements of the coherence of a radiative source, using time-domain or space-domain measurements of the radiation, electromagnetic or not. It can be applied to a variety of types of spectroscopy including optical spectroscopy, infrared spectroscopy, nuclear magnetic resonance (NMR) and magnetic resonance spectroscopic imaging (MRSI), mass spectrometry and electron spin resonance spectroscopy.

Raman spectroscopy is a spectroscopic technique typically used to determine vibrational modes of molecules, although rotational and other low-frequency modes of systems may also be observed. Raman spectroscopy is commonly used in chemistry to provide a structural fingerprint by which molecules can be identified.

Small-angle neutron scattering (SANS) is an experimental technique that uses elastic neutron scattering at small scattering angles to investigate the structure of various substances at a mesoscopic scale of about 1–100 nm.

Biological small-angle scattering is a small-angle scattering method for structure analysis of biological materials. Small-angle scattering is used to study the structure of a variety of objects such as solutions of biological macromolecules, nanocomposites, alloys, and synthetic polymers. Small-angle X-ray scattering (SAXS) and small-angle neutron scattering (SANS) are the two complementary techniques known jointly as small-angle scattering (SAS). SAS is an analogous method to X-ray and neutron diffraction, wide angle X-ray scattering, as well as to static light scattering. In contrast to other X-ray and neutron scattering methods, SAS yields information on the sizes and shapes of both crystalline and non-crystalline particles. When used to study biological materials, which are very often in aqueous solution, the scattering pattern is orientation averaged.

Neutron scattering, the irregular dispersal of free neutrons by matter, can refer to either the naturally occurring physical process itself or to the man-made experimental techniques that use the natural process for investigating materials. The natural/physical phenomenon is of elemental importance in nuclear engineering and the nuclear sciences. Regarding the experimental technique, understanding and manipulating neutron scattering is fundamental to the applications used in crystallography, physics, physical chemistry, biophysics, and materials research.

Muon spin spectroscopy, also known as μSR, is an experimental technique based on the implantation of spin-polarized muons in matter and on the detection of the influence of the atomic, molecular or crystalline surroundings on their spin motion. The motion of the muon spin is due to the magnetic field experienced by the particle and may provide information on its local environment in a very similar way to other magnetic resonance techniques, such as electron spin resonance and, more closely, nuclear magnetic resonance (NMR).

In cell biology, adherens junctions are protein complexes that occur at cell–cell junctions and cell–matrix junctions in epithelial and endothelial tissues, usually more basal than tight junctions. An adherens junction is defined as a cell junction whose cytoplasmic face is linked to the actin cytoskeleton. They can appear as bands encircling the cell or as spots of attachment to the extracellular matrix.

In magnetic resonance, a spin echo or Hahn echo is the refocusing of spin magnetisation by a pulse of resonant electromagnetic radiation. Modern nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) make use of this effect.

Fourier-transform infrared spectroscopy (FTIR) is a technique used to obtain an infrared spectrum of absorption or emission of a solid, liquid, or gas. An FTIR spectrometer simultaneously collects high-resolution spectral data over a wide spectral range. This confers a significant advantage over a dispersive spectrometer, which measures intensity over a narrow range of wavelengths at a time.

Angle-resolved low-coherence interferometry (a/LCI) is an emerging biomedical imaging technology which uses the properties of scattered light to measure the average size of cell structures, including cell nuclei. The technology shows promise as a clinical tool for in situ detection of dysplastic, or precancerous tissue.

In molecular biology, proteins are generally thought to adopt unique structures determined by their amino acid sequences. However, proteins are not strictly static objects, but rather populate ensembles of conformations. Transitions between these states occur on a variety of length scales and time scales , and have been linked to functionally relevant phenomena such as allosteric signaling and enzyme catalysis.

In condensed matter physics, the dynamic structure factor is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization of the structure factor that considers correlations in both space and time. Experimentally, it can be accessed most directly by inelastic neutron scattering or X-ray Raman scattering.

Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are disturbed by a weak oscillating magnetic field and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. High-resolution nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crystalline materials. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging (MRI). The original application of NMR to condensed matter physics is nowadays mostly devoted to strongly correlated electron systems. It reveals large many-body couplings by fast broadband detection and should not be confused with solid state NMR, which aims at removing the effect of the same couplings by Magic Angle Spinning techniques.

Pulsed electron paramagnetic resonance (EPR) is an electron paramagnetic resonance technique that involves the alignment of the net magnetization vector of the electron spins in a constant magnetic field. This alignment is perturbed by applying a short oscillating field, usually a microwave pulse. One can then measure the emitted microwave signal which is created by the sample magnetization. Fourier transformation of the microwave signal yields an EPR spectrum in the frequency domain. With a vast variety of pulse sequences it is possible to gain extensive knowledge on structural and dynamical properties of paramagnetic compounds. Pulsed EPR techniques such as electron spin echo envelope modulation (ESEEM) or pulsed electron nuclear double resonance (ENDOR) can reveal the interactions of the electron spin with its surrounding nuclear spins.

Incoherent broad band cavity enhanced absorption spectroscopy (IBBCEAS), sometimes called broadband cavity enhanced extinction spectroscopy (IBBCEES), measures the transmission of light intensity through a stable optical cavity consisting of high reflectance mirrors (typically R>99.9%). The technique is realized using incoherent sources of radiation e.g. Xenon arc lamps, LEDs or supercontinuum (SC) lasers, hence the name.

Helium-3 surface spin echo (HeSE) is an inelastic scattering technique in surface science that has been used to measure microscopic dynamics at well-defined surfaces in ultra-high vacuum. The information available from HeSE complements and extends that available from other inelastic scattering techniques such as neutron spin echo and traditional helium-4 atom scattering (HAS).

<span class="mw-page-title-main">Nano-FTIR</span> Infrared microscopy technique

Nano-FTIR is a scanning probe technique that utilizes as a combination of two techniques: Fourier transform infrared spectroscopy (FTIR) and scattering-type scanning near-field optical microscopy (s-SNOM). As s-SNOM, nano-FTIR is based on atomic-force microscopy (AFM), where a sharp tip is illuminated by an external light source and the tip-scattered light is detected as a function of tip position. A typical nano-FTIR setup thus consists of an atomic force microscope, a broadband infrared light source used for tip illumination, and a Michelson interferometer acting as Fourier-transform spectrometer. In nano-FTIR, the sample stage is placed in one of the interferometer arms, which allows for recording both amplitude and phase of the detected light. Scanning the tip allows for performing hyperspectral imaging with nanoscale spatial resolution determined by the tip apex size. The use of broadband infrared sources enables the acquisition of continuous spectra, which is a distinctive feature of nano-FTIR compared to s-SNOM. Nano-FTIR is capable of performing infrared (IR) spectroscopy of materials in ultrasmall quantities and with nanoscale spatial resolution. The detection of a single molecular complex and the sensitivity to a single monolayer has been shown. Recording infrared spectra as a function of position can be used for nanoscale mapping of the sample chemical composition, performing a local ultrafast IR spectroscopy and analyzing the nanoscale intermolecular coupling, among others. A spatial resolution of 10 nm to 20 nm is routinely achieved.

.

References

↑ Mezei, F., ed. (1980). Neutron Spin Echo. Lecture Notes in Physics Vol. 128. Berlin, Heidelberg, New York: Springer.
↑ B. Farago (2006). "Neutron spin echo study of well organized soft matter systems". Physica B. 385–386: 688–691. Bibcode:2006PhyB..385..688F. doi:10.1016/j.physb.2006.05.292.
↑ Callaway, D. J.; Farago, B; Bu, Z (2013). "Nanoscale protein dynamics: A new frontier for neutron spin echo spectroscopy". The European Physical Journal E. 36 (7): 76. doi:10.1140/epje/i2013-13076-1. PMID 23884624. S2CID 10246098.
↑ B. Farago, Li J, Cornilescu G, Callaway DJE, Bu Z (November 2010). "Activation of Nanoscale Allosteric Protein Domain Motion Revealed by Neutron Spin Echo Spectroscopy". Biophysical Journal . 99 (10): 3473–3482. Bibcode:2010BpJ....99.3473F. doi:10.1016/j.bpj.2010.09.058. PMC 2980739 . PMID 21081097.{{cite journal}}: CS1 maint: multiple names: authors list (link)
↑ Bu Z, Biehl R, Monkenbusch M, Richter D, Callaway DJE (2005). "Coupled protein domain motion in Taq polymerase revealed by neutron spin-echo spectroscopy". Proc Natl Acad Sci USA . 102 (49): 17646–17651. Bibcode:2005PNAS..10217646B. doi: 10.1073/pnas.0503388102 . PMC 1345721 . PMID 16306270.{{cite journal}}: CS1 maint: multiple names: authors list (link)
↑ Farago B, Nicholl ID, Wang S, Cheng X, Callaway DJ, Bu Z (March 30, 2021). "Activated nanoscale actin-binding domain motion in the catenin-cadherin complex revealed by neutron spin echo spectroscopy". Proc Natl Acad Sci USA. 118 (13): e2025012118. Bibcode:2021PNAS..11825012F. doi: 10.1073/pnas.2025012118 . PMC 8020631 . PMID 33753508.
↑ Callaway DJ, Nicholl ID, Shi B, Reyes G, Farago B, Bu Z (2024). "Nanoscale dynamics of the cadherin-catenin complex bound to vinculin revealed by neutron spin echo spectroscopy". Proceedings of the National Academy of Sciences of the United States of America. 129 (39). doi: 10.1073/pnas.2408459121 . PMC 11441495 . PMID 39298480.
↑ L. Kay Nicholson (1981). "The neutron spin-echo spectrometer: A new high resolution technique in neutron scattering". Contemp. Phys. 22 (4): 451–475. Bibcode:1981ConPh..22..451N. doi:10.1080/00107518108231544.
↑ Higgins JS, Benoit HC (1997). Polymers and neutron scattering. Oxford Series on Neutron Scattering in Condensed Matter (Book 8). Clarendon Press. ISBN 978-0198500636.
↑ Callaway DJ, Bu Z (2017). "Visualizing the nanoscale: protein internal dynamics and neutron spin echo spectroscopy". Curr. Opin. Struct. Biol. 42: 1–5. doi:10.1016/j.sbi.2016.10.001. PMC 5374024 . PMID 27756047.
↑ Richter D (2006). "Neutron spin echo for the exploration of large scale macromolecular dynamics". J. Phys. Soc. Jpn. 75 (11): 110041–11004112. Bibcode:2006JPSJ...75k1004R. doi:10.1143/JPSJ.75.111004.
↑ Jacrot, B (1976). "The study of biological structures by neutron scattering from solution". Reports on Progress in Physics. 39 (10): 911–53. Bibcode:1976RPPh...39..911J. doi:10.1088/0034-4885/39/10/001. S2CID 250751286.
↑ E.L. Hahn (1950). "Spin Echoes". Physical Review. 80 (4): 580. Bibcode:1950PhRv...80..580H. doi:10.1103/PhysRev.80.580.
↑ M. Monkenbusch & D. Richter (2007). "High resolution neutron spectroscopy - a tool for the investigation of dynamics of polymers and soft matter". Comptes Rendus Physique. 8 (7–8): 845–864. Bibcode:2007CRPhy...8..845M. doi:10.1016/j.crhy.2007.10.001.
↑ A. Wischnewski and M. Monkenbusch and L. Willner and D. Richter and G. Kali (2003). "Direct observation of the transition from free to constrained single-segment motion in entangled polymer melts". Physical Review Letters. 90 (5): 058302. Bibcode:2003PhRvL..90e8302W. doi:10.1103/PhysRevLett.90.058302. PMID 12633402.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[1] Mezei, F., ed. (1980). Neutron Spin Echo. Lecture Notes in Physics Vol. 128. Berlin, Heidelberg, New York: Springer.

[2] B. Farago (2006). "Neutron spin echo study of well organized soft matter systems". Physica B. 385–386: 688–691. Bibcode:2006PhyB..385..688F. doi:10.1016/j.physb.2006.05.292.

[3] Callaway, D. J.; Farago, B; Bu, Z (2013). "Nanoscale protein dynamics: A new frontier for neutron spin echo spectroscopy". The European Physical Journal E. 36 (7): 76. doi:10.1140/epje/i2013-13076-1. PMID 23884624. S2CID 10246098.

[pmid21081097-4] B. Farago, Li J, Cornilescu G, Callaway DJE, Bu Z (November 2010). "Activation of Nanoscale Allosteric Protein Domain Motion Revealed by Neutron Spin Echo Spectroscopy". Biophysical Journal . 99 (10): 3473–3482. Bibcode:2010BpJ....99.3473F. doi:10.1016/j.bpj.2010.09.058. PMC 2980739 . PMID 21081097.{{cite journal}}: CS1 maint: multiple names: authors list (link)

[5] Bu Z, Biehl R, Monkenbusch M, Richter D, Callaway DJE (2005). "Coupled protein domain motion in Taq polymerase revealed by neutron spin-echo spectroscopy". Proc Natl Acad Sci USA . 102 (49): 17646–17651. Bibcode:2005PNAS..10217646B. doi: 10.1073/pnas.0503388102 . PMC 1345721 . PMID 16306270.{{cite journal}}: CS1 maint: multiple names: authors list (link)

[pmid33753508-6] Farago B, Nicholl ID, Wang S, Cheng X, Callaway DJ, Bu Z (March 30, 2021). "Activated nanoscale actin-binding domain motion in the catenin-cadherin complex revealed by neutron spin echo spectroscopy". Proc Natl Acad Sci USA. 118 (13): e2025012118. Bibcode:2021PNAS..11825012F. doi: 10.1073/pnas.2025012118 . PMC 8020631 . PMID 33753508.

[7] Callaway DJ, Nicholl ID, Shi B, Reyes G, Farago B, Bu Z (2024). "Nanoscale dynamics of the cadherin-catenin complex bound to vinculin revealed by neutron spin echo spectroscopy". Proceedings of the National Academy of Sciences of the United States of America. 129 (39). doi: 10.1073/pnas.2408459121 . PMC 11441495 . PMID 39298480.

[nicholson-8] L. Kay Nicholson (1981). "The neutron spin-echo spectrometer: A new high resolution technique in neutron scattering". Contemp. Phys. 22 (4): 451–475. Bibcode:1981ConPh..22..451N. doi:10.1080/00107518108231544.

[higgins-9] Higgins JS, Benoit HC (1997). Polymers and neutron scattering. Oxford Series on Neutron Scattering in Condensed Matter (Book 8). Clarendon Press. ISBN 978-0198500636.

[current-10] Callaway DJ, Bu Z (2017). "Visualizing the nanoscale: protein internal dynamics and neutron spin echo spectroscopy". Curr. Opin. Struct. Biol. 42: 1–5. doi:10.1016/j.sbi.2016.10.001. PMC 5374024 . PMID 27756047.

[richter-11] Richter D (2006). "Neutron spin echo for the exploration of large scale macromolecular dynamics". J. Phys. Soc. Jpn. 75 (11): 110041–11004112. Bibcode:2006JPSJ...75k1004R. doi:10.1143/JPSJ.75.111004.

[Jacrot-12] Jacrot, B (1976). "The study of biological structures by neutron scattering from solution". Reports on Progress in Physics. 39 (10): 911–53. Bibcode:1976RPPh...39..911J. doi:10.1088/0034-4885/39/10/001. S2CID 250751286.

[13] E.L. Hahn (1950). "Spin Echoes". Physical Review. 80 (4): 580. Bibcode:1950PhRv...80..580H. doi:10.1103/PhysRev.80.580.

[14] M. Monkenbusch & D. Richter (2007). "High resolution neutron spectroscopy - a tool for the investigation of dynamics of polymers and soft matter". Comptes Rendus Physique. 8 (7–8): 845–864. Bibcode:2007CRPhy...8..845M. doi:10.1016/j.crhy.2007.10.001.

[15] A. Wischnewski and M. Monkenbusch and L. Willner and D. Richter and G. Kali (2003). "Direct observation of the transition from free to constrained single-segment motion in entangled polymer melts". Physical Review Letters. 90 (5): 058302. Bibcode:2003PhRvL..90e8302W. doi:10.1103/PhysRevLett.90.058302. PMID 12633402.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]