J. Mayers

Measurement of momentum distribution of light atoms and molecules in condensed matter systems using inelastic neutron scattering

Studies of single-particle momentum distributions in light atoms and molecules are reviewed with specific emphasis on experimental measurements using the deep inelastic neutron scattering technique at eV energies. The technique has undergone a remarkable development since the mid-1980s, when intense fluxes of epithermal neutrons were made available from pulsed neutron sources. These types of measurements provide a probe of the short-time dynamics of the recoiling atoms or molecules as well as information on the local structure of the materials. The paper introduces both the theoretical framework for the interpretation of deep inelastic neutron scattering experiments and thoroughly illustrates the physical principles underlying the impulse approximation from light atoms and molecules. The most relevant experimental studies performed on a variety of condensed matter systems in the last 20 years are reviewed. The experimental technique is critically presented in the context of a full list of published work. It is shown how, in some cases, these measurements can be used to extract directly the effective Born–Oppenheimer potential. A summary of the progress made to date in instrument development is also provided. Current data analysis and the interpretation of the results for a variety of physical systems is chosen to illustrate the scope and power of the method. The review ends with a brief consideration of likely developments in the foreseeable future. Particular discussion is given to the use of the VESUVIO spectrometer at ISIS. Contents PAGE 1. Introduction 378 2. Theoretical basis of measurements 381   2.1. The impulse approximation and the neutron Compton profile 381   2.2. Validity of the impulse approximation and corrections at finite q 384   2.3. Properties of the dynamic structure factor SIA (q ω) in the impulse approximation 389   2.4. Extracting the atomic momentum distribution from the neutron Compton profile 390   2.5. Determination of effective Born–Oppenheimer potentials 394 3. Theoretical momentum distributions of atoms 395   3.1. Maxwellian regime and atoms in harmonic solids 395   3.2. Quantum systems and weakly quantum systems 397   3.3. Fermi and Bose systems 398   3.4. Molecular systems 399   3.5. Polyatomic molecules 401 4. An exact calculation: liquid H2 and D2 403 5. Experimental technique 408   5.1. Direct and inverse geometry spectrometers for DINS measurements 408   5.2. The VESUVIO spectrometer 409   5.3. The resonance filter configuration 411   5.4. The resonance detector configuration 415   5.5. Extracting the neutron Compton profile from observations 417 6. Review of existing measurements 420   6.1. Liquid and solid 4He 420   6.2. Liquid and solid 3He 428   6.3. Liquid 4He–3He mixtures 431   6.4. Liquid para-H2, ortho-D2 and N2 436   6.5. Hydrogen sulphide 444   6.6. Water and ice 447   6.7. Single crystal measurements: the example of KDP (KH2PO4) 453 7. Conclusions and perspectives 457   7.1. Applications in physics 459   7.2. Applications in chemistry 460   7.3. Applications in biology 460   7.4. Technological applications 461 Acknowledgments 461 Appendix A: The intensity deficit problem 462 References 463

The Polaris powder diffractometer at ISIS

Abstract The Polaris instrument at the ISIS spallation neutron source operates as a medium resolution powder diffractometer. The high incident neutron flux enables datasets to be collected with comparatively short counting times or from extremely small sample volumes. Examples of recent experiments performed on Polaris, which exploit the high count rate and the particular advantages offered by fixed geometry diffraction measurements performed on a pulsed neutron source, are presented.

Direct observation of tunneling in KDP using Neutron Compton scattering.

Neutron Compton Scattering measurements presented here of the momentum distribution of hydrogen in

VESUVIO: a novel instrument for performing spectroscopic studies in condensed matter with eV neutrons at the ISIS facility

KH_2PO_4

The proton momentum distribution in water and ice

(KDP) just above and well below the ferroelectric transition temperature show clearly that the proton is coherent over both sites in the in the high temperature phase, a result that invalidates the commonly accepted order-disorder picture of the transition. The Born-Oppenheimer potential for the hydrogen, extracted directly from data for the first time, is consistent with neutron diffraction data, and the vibrational spectrum is in substantial agreement with infrared absorption measurements. The measurements are sensitive enough to detect the effect of surrounding ligands on the hydrogen bond, and can be used to study the systematic effect of the variation of these ligands in other hydrogen bonded systems.

The VESUVIO electron volt neutron spectrometer

The VESUVIO project aims to provide unique prototype instrumentation at the ISIS-pulsed neutron source and to establish a routine experimental and theoretical program in neutron scattering spectroscopy at eV energies. This instrumentation will be specifically designed for high momentum, , and energy transfer inelastic neutron scattering studies of microscopic dynamical processes in materials and will represent a unique facility for EU researchers. It will allow to derive single-particle kinetic energies and single-particle momentum distributions, n(p), providing additional and/or complementary information to other neutron inelastic spectroscopic techniques.

The measurement of anomalous neutron inelastic cross-sections at electronvolt energy transfers

Deep Inelastic Neutron Scattering (Neutron Compton Scattering), is used to measure the momentum distribution of the protons in water from temperatures slightly below freezing to the supercritical phase. The momentum distribution is determined almost entirely by quantum localization effects, and hence is a sensitive probe of the local environment of the proton. The distribution shows dramatic changes as the hydrogen bond network becomes more disordered. Within a single particle interpretation, the proton moves from an essentially harmonic well in ice to a slightly anharmonic well in room temperature water, to a deeply anharmonic potential in the supercritical phase that is best described by a double well potential with a separation of the wells along the bond axis of about 0.3 Angstrom. Confining the supercritical water in the interstices of a C60 powder enhances this anharmonicity and enhances the localization of the protons. The changes in the distribution are consistent with gas phase formation at the hydrophobic boundaries and inconsistent with the formation of ice there.

Single particle dynamics in fluid and solid hydrogen sulphide: An inelastic neutron scattering study

This paper describes the VESUVIO electron volt neutron spectrometer at the ISIS pulsed neutron source and its data analysis routines. VESUVIO is used primarily for the measurement of proton momentum distributions in condensed matter systems, but can also be used to measure the kinetic energies of heavier masses and bulk in-situ sample compositions. A series of VESUVIO runs on the same zirconium hydride sample over the past two years show that (1) kinetic energies of protons can be measured to an absolute accuracy of ?1%. (2) Measurements of the proton momentum distribution n(p) are highly reproducible from run to run. This shows that small changes in kinetic energy and the detailed shape of n(p) with parameters such as temperature, pressure and sample composition can be reliably extracted from VESUVIO data. (3) The impulse approximation (IA) is well satisfied on VESUVIO. (4) The small deviations from the IA due to the finite momentum transfer of measurement are well understood. (5) There is an anomaly in the magnitude of the inelastic neutron cross-section of the protons in zirconium hydride, with an observed reduction of 10% ? 0.3% from that given in standard tables. This anomaly is independent of energy transfer to within experimental error. Future instrument developments are discussed. These would allow the measurement of n(p) in other light atoms, D, 3He, 4He, Li, C and O and measurement of eV electronic and magnetic excitations.

The anisotropy of the proton momentum distribution in KHCO3: A deep inelastic neutron scattering study

It has been proposed that short-lived quantum entanglement of protons in condensed matter systems would result in anomalous inelastic scattering cross-sections at electronvolt energy transfers. This proposal seems to be confirmed by neutron measurements on the VESUVIO spectrometer at ISIS and by measurements using other techniques. However, there have been a number of published suggestions of ways in which the observed effects on VESUVIO could be introduced by assumptions used in the data analysis. In this paper it is shown using experimental data and Monte Carlo simulations that these suggestions cannot explain the observed cross-section anomalies. The other assumptions of the data analysis are also examined. It is shown that the assumption of a Gaussian peak shape for the neutron Compton profile can introduce significant errors into the determination of cross-section ratios, but also cannot explain the observed anomalies.

Temperature measurement by neutron resonance radiography

Inelastic neutron scattering experiments were performed at intermediate and high momentum transfer, up to 88.2 A−1, to study the temperature dependence of single hydrogen mean kinetic energy in polycrystalline and liquid hydrogen sulphide (H2S), in the temperature range 16–206 K. Values of the hydrogen mean kinetic energy were extracted, within the impulse approximation, by fitting to the high momentum transfer data a model response function, obtained from a momentum distribution which is the orientational average of a multivariate Gaussian function. The extracted kinetic energies are compared with a harmonic model for the vibrational and roto-translational dynamics. The model makes use of the hydrogen-projected density of states worked out from intermediate momentum transfer data, as well as of optical frequencies determined from Raman and infrared (IR) spectroscopy. A fairly good agreement is obtained in the whole temperature range, while noticeably lower values for the kinetic energy are found if a sin...