Inelastic neutron scattering from classical systems

Proceedings of the National Academy of Sciences, 2019

Proceedings of the National Academy of Sciences, 2018

Significance Despite the long history of neutron scattering studies on complex condensed matter systems, there is still a need for appropriate analysis concepts beyond the classical Van Hove theory, which is commonly used to interpret the experimental spectra in terms of trajectory-based dynamical models. The approach presented in this paper, which is based on quantum mechanical transition rather than on classical displacement probabilities, accounts by construction for the scattering kinematics and opens perspectives for the interpretation of quasielastic neutron scattering experiments from complex systems.

Simple Dense Fluids, 1968

ChemTexts, 2023

Neutron scattering is a very high-performance method for studying the structure and dynamics of condensed matter with similar approaches in wide ranges of space and time, matching dimensions in space from single atoms to macromolecules and in time from atomic vibrations over crystal phonons to low-lying transitions in the microwave range, and to motions of large molecular units. Concerning the number and depth of physical concepts, neutron scattering may be compared to modern nuclear magnetic resonance. Neutrons have contributed essential results to the understanding of atomic and molecular processes and are, in this respect, complementary to other materials science probes. Among others, three properties of thermal neutrons make them especially appropriate for such work: the neutron mass is similar to atomic masses, and both neutron energies and the wavelengths of the neutron material wave match typical values for condensed matter. A further important feature of neutron scattering, making it especially valuable in biochemistry and polymer sciences, is that hydrogen and deuterium atoms very significantly and specifically contribute to the signal in both diffraction and spectroscopy. Additionally, neutrons are scattered at the nuclei and directly reflect the nuclear structure and motions. Results from neutron scattering are of great general interest. This paper aims to provide an introduction for chemists on a level understandable also to students and researchers who are not going to become part of the neutron community and will not be involved in the experiments, but shall be able to understand the basic concepts of the method and its relevance to modern chemistry. The paper focuses on basic theory, typical experiments, and some examples demonstrating the applications. As for many modern experimental techniques, the interpretation of the results of neutron scattering is based on theoretical models and requires a significant mathematical overhead. Most results are only meaningful when compared with computer simulations. For understanding this, in this paper, the theory of scattering is developed, starting with intuitive models and presenting typical concepts such as the scattering triangle, energy and momentum transfer, and the relation of inelastic and elastic scattering to space- and time-dependent information. The interaction of neutrons with matter, scattering cross sections, beam attenuation, and coherent versus incoherent scattering are explained in detail. Two further typical concepts that are not generally familiar to scientists outside the community are the use of wave and particle equivalence, and of handling results as a scattering function that depends simultaneously on momentum and energy transfers. The possibility of obtaining neutron beams for scattering experiments at a few research centers around high-performance sources is explained, and experimentally relevant features of research reactors and spallation sources are mentioned. As neutron experiments always have to deal with small flux and extended beams and shielding, experimental conditions are very far away from laboratory methods where handling of samples and instruments is concerned. Experimental details are given for making experiments more understandable and familiarizing the reader with the method. Related to this are extended possibilities for handling samples in a large variety of different environments. In a further part of the manuscript, a variety of techniques and typical instruments are presented, together with some characteristic applications bringing alive the theory developed so far. This covers powder diffraction and structure of liquid water, triple-axis spectrometers and lattice phonons, backscattering spectrometry and rotational tunneling, time-of-flight spectrometry, and simultaneously probing the energy and shape of low lying vibrations and diffusion, filter spectrometer and vibrational spectroscopy without selection rules, small-angle neutron scattering and protein unfolding, as well as micelles, neutron spin echo spectroscopy, and polymer dynamics.

2020

We undertake herein to derive the Wigner-Wilkins [W-W] neutron/nucleus scattering kernel, a foundation stone in neutron thermalization theory, on the basis of a self-contained calculation in quantum mechanics. Indeed, a quantum-mechanical derivation of the W-W kernel is available in the literature, cited below, but it is, in our opinion, robbed of conviction by being couched in terms of an excessive generality. Here, by contrast, we proceed along a self-contained route relying on the Fermi pseudopotential and a first-order term in a time-dependent Born approximation series. Our calculations are fully explicit at every step and, in particular, we tackle in its every detail a final integration whose result is merely stated in the available literature. Furthermore, and perhaps the most important point of all, we demonstrate that the quantum-mechanical W-W kernel outcome is identical down to the last iota with its classical antecedent, classical not only by virtue of historical preceden...

Nowadays, the quasielastic neutron scattering (QENS) method is gaining increasingly more attention among the scientific community. In the past, QENS was an intensity limited technique, the time to record spectra with sufficient statistics was long, and consequently the total number of the experiments was small. The neutron scattering instrumentation at long existing world's leading neutron sources (in the first place: the Institut Laue-Langevin (ILL) in Grenoble, but also ISIS, UK; HMI, Germany; NIST CNR, USA and others) has been continuously improved. Furthermore, new powerful facilities, the nuclear reactor in München and the Spallation Neutron Source in USA came into operation, and other facilities will follow.

Zeitschrift für Physikalische Chemie, 2010

This tutorial introduction has been written for people who are not specialized in neutron scattering or in other scattering methods but who are interested and would like to get an impression and learn about the method of Quasielastic Neutron Scattering (QENS). The theoretical (scattering process) as well as the experimental basics (neutron sources, neutron scattering instruments, experimental periphery) are explained in a generally understandable way, with only the most essential formulas. QENS addresses the stochastic dynamics in condensed matter, and it is pointed out for which problems and for which systems in condensed matter research QENS is a powerful method. Thus sufficient information is provided to enable non-experts to think about their own QENS experiment and to understand related literature in this area of research.

The European Physical Journal A, 2006

With the use of theory developed earlier, bulk effects in ultracold neutron coherent inelastic scattering are considered both for solid and liquid target samples related to energy and momentum exchange with phonon and diffusion-like modes. For the neutron in a material trap, differential and integral probabilities for the energy transfer per bounce are presented in a simple analytic form which exhibits the parameter dependence. As an example, the theoretical values for the ultracold neutron loss rate from a storage bottle with Fomblin coated walls and stainless steel walls are evaluated. Possible contribution from incoherent inelastic scattering on hydrogen contamination is discussed.

Physica B+C

Recently a synthetic scattering law has been developed to describe the interaction of thermal neutrons with molecular gases. Although this function does not contain a detailed description of the atomic motions in the molecular unit (nor pair correlations), the main features of the molecular dynamics are retained through the introduction of effective quantities which are directly related to the basic properties of the system. In this work we present evaluations of inelasticity corrections using the synthetic model for both reactor and pulsed neutron diffraction experiments. Predictions are made of differential cross sections (self component) for light and heavy water and these are compared with available experimental results.

Physical review. B, Condensed matter, 1985

Motivated by the practical requirements of reactor-physics calculations as well as the necessity of applying inelasticity corrections to the observed spectrum in neutron-diffraction work on molecular gases and liquids, I have developed a synthetic scattering function T(Q, co;Eo) which allows a fast and reliable evaluation of cross sections. Unlike the dynamic structure factor (or scattering function) S(g,ro) in thermal neutron-scattering theory, T(Q, co;Eo) does not contain a detailed description of the atomic motions in the molecular units nor correlation between pairs, but rather it is intended to reproduce satisfactorily some integral properties of S(Q,co) (the self-component). However, the main characteristics of the molecular dynamics are retained through the introduction of an effective mass, and temperature and vibrational factors which depend on the incident neutron energy Eo. This is achieved by the use of the Krieger-Nelkin procedure for orientational averages and by the introduction of "switching functions" P (Eo) which define the variation with Eo of the above effective quantities. A very simple form is thus obtained for T(Q, co;Eo) which yields analytic expressions for the scattering kernel and the total cross section. To gauge the merits and limitations of this prescription I compared its predictions with experiments and other theories in the foIlowing cases involving hydrogen-containing molecules: (i) the total cross section of H20 and C6H6, ' (ii) the scattering cross sections (angular distributions) of H20 and D2O at several energies; and (iii) the average of the cosine of the scattering angle in H20. It is concluded from the comparisons that the model works in a very satisfactory way. It is anticipated that the present prescription could be a useful tool for the evaluation of departures from elasticity in time-of-flight experiments, where a wide range of neutron wavelengths may contribute at each channel in the observed diffraction spectrum.