George Reiter

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

Direct observation of tunneling in KDP using Neutron Compton scattering.

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

The vibrational proton potential in bulk liquid water and ice

KH_2PO_4

Proton quantum coherence observed in water confined in silica nanopores

(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 proton momentum distribution in water and ice

We present an empirical flexible and polarizable water model which gives an improved description of the position, momentum, and dynamical (spectroscopic) distributions of H nuclei in water. We use path integral molecular dynamics techniques in order to obtain momentum and position distributions and an approximate solution to the Schrodinger equation to obtain the infrared (IR) spectrum. We show that when the calculated distributions are compared to experiment the existing empirical models tend to overestimate the stiffness of the H nuclei involved in H bonds. Also, these models vastly underestimate the enormous increase in the integrated IR intensity observed in the bulk over the gas-phase value. We demonstrate that the over-rigidity of the OH stretch and the underestimation of intensity are connected to the failure of existing models to reproduce the correct monomer polarizability surface. A new model, TTM4-F, is parametrized against electronic structure results in order to better reproduce the polarizability surface. It is found that TTM4-F gives a superior description of the observed spectroscopy, showing both the correct redshift and a much improved intensity. TTM4-F also has a somewhat improved dielectric constant and OH distribution function. It also gives an improved match to the experimental momentum distribution, although some discrepancies remain.

The VESUVIO electron volt neutron spectrometer

Deep inelastic neutron scattering measurements of water confined in nanoporous xerogel powders, with average pore diameters of 24 and 82 A, have been carried out for pore fillings ranging from 76% to nearly full coverage. DINS measurements provide direct information on the momentum distribution n(p) of protons, probing the local structure of the molecular system. The observed scattering is interpreted within the framework of the impulse approximation and the longitudinal momentum distribution determined using a model independent approach. The results show that the proton momentum distribution is highly non-Gaussian. A bimodal distribution appears in the 24 A pore, indicating coherent motion of the proton over distances d of approximately 0.3 A. The proton mean kinetic energy W of the confined water molecule is determined from the second moment of n(p). The W values, higher than in bulk water, are ascribed to changes of the proton dynamics induced by the interaction between interfacial water and the confining surface.

Origin of the intensity deficit in neutron Compton scattering

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.

Deuteron momentum distribution in KD2PO4

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.

Vortex avalanches with robust statistics observed in superconducting niobium

Neutron Compton scattering measurements in a variety of materials have shown a relative deficit in the total signal from hydrogen compared to deuterium and heavier ions. We show here that a breakdown in the Born-Oppenheimer approximation in the final states of the scattering process leads to such a deficit and may be responsible for the effect.

The proton momentum distribution in strongly H-bonded phases of water: a critical test of electrostatic models.

The momentum distribution in KD2PO4 (DKDP) has been measured using neutron Compton scattering above and below the weakly first-order paraelectric–ferroelectric phase transition (T=229 K). There is very little difference between the two distributions, and no sign of the coherence over two locations for the proton observed in the paraelectric phase, as in KH2PO4 (KDP). We conclude that the tunnel splitting must be much less than 20 meV. The width of the distribution indicates that the effective potential for DKDP is significantly softer than that for KDP. As electronic structure calculations indicate that the stiffness of the potential increases with the size of the coherent region locally undergoing soft mode fluctuations, we conclude that there is a mass-dependent quantum coherence length in both systems.