It is shown that in the presence of Bose-Einstein condensation (BEC) in any N particle system, the N particle Schrodinger wave functions of thermally occupied states are the sum of a 'localized' component and a 'delocalized' component, identical to the ground state wave function. It is shown that if N is sufficiently large, this implies that all physical properties of the system are the sum of two independent contributions from these two components. These results are used here to provide quantitative explanations of fundamental properties of BE condensed liquid He-4, unexplained even qualitatively by existing theory; why BE condensed liquid He-4 is the only known physical system in which pair correlations between atomic positions reduce as it is cooled, why it is the only known liquid with sharp peaks in its dynamic structure factor, why the liquid expands with cooling and how the condensate fraction is related to the super-fluid fraction. It is shown that these results also provide a relatively simple, physically transparent and quantitative explanation from first principles of macroscopic quantum effects. A new algorithm is given for the calculation of the time development of the macroscopic density of any BE condensed liquid or gas at any temperature. Unlike the Gross-Pitaevskii equation, this algorithm is valid for both strongly and weakly interacting systems. It is used here to show that macroscopic quantum interference fringes, observed between overlapping clouds of BE condensed atoms, are a necessary consequence of BEC and the N particle Schrodinger equation for the atoms in the clouds. It follows that the widely held view that these fringes are created by measurement is unnecessary. New, experimentally testable predictions are made of how the visibility of these fringes will vary with temperature.

Deep inelastic neutron scattering provides a means of directly and accurately measuring the momentum distribution of protons in water, which is determined primarily by the proton ground-state wave function. We find that in water confined on scales of 20 \AA{}, this wave function responds to the details of the confinement, corresponds to a strongly anharmonic local potential, shows evidence in some cases of coherent delocalization in double wells, and involves changes in zero-point kinetic energy of the protons from $\ensuremath{-}$40 to +120 meV difference from that of bulk water at room temperature. This behavior appears to be a generic feature of nanoscale confinement. It is exhibited here in 16 \AA{} inner diameter carbon nanotubes, two different hydrated proton exchange membranes (PEMs), Nafion 1120 and Dow 858, and has been seen earlier in xerogel and 14 \AA{} diameter carbon nanotubes. The proton conductivity in the PEM samples correlates with the degree of coherent delocalization of the proton.

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.

Dreismann, Gray and Blach (DGB) have claimed that neutron scattering from molecular hydrogen at energy transfers E sufficiently large to break the H-H bond, gives E ∼3% larger than predicted by conventional quantum theory. DGB presented this claim as the first experimental evidence for energetic consequences of decoherence of quantum entangled particles due to interactions with the environment. It is shown here this claim is entirely spurious. DGB obtained disagreement with conventional theory by changing the geometrical description of the Vesuvio instrument at ISIS, they used to collect their data. Instead of using the default scattering angles obtained from neutron diffraction, DGB used scattering angles obtained using a steel rule and protractor. DGB then manufactured apparent but in fact completely spurious evidence for quantum decoherence effects from the large measurement errors in the scattering angles they used. These give shifts to both higher and lower E than predicted by conventional quantum theory. DGB simply ignored detectors giving shifts to lower values of E. DGB also ignored previously published H2 data that clearly contradict their claim.

We present momentum widths and mean kinetic energies of lithium and fluorine in 7LiF, as determined simultaneously from deep inelastic neutron scattering (DINS) measurements. Experimental data across a temperature range from 4 to 300 K are presented, and these results compared to those calculated using a quasi-harmonic density-functional approach. In all cases, measured momentum widths are seen to be within approximately 5% of those calculated, despite the very low scattering cross sections of both 7Li and 19F. This is the first determination and comparison with theory of such simultaneous measurements for nuclei of mass > 4 amu, and demonstrates the implementation of the DINS method in its current form as a mass-selective neutron spectroscopy.

In the present study we report neutron spectroscopic measurements on polycrystalline lithium imide, namely, incoherent inelastic neutron scattering at 20 K, and neutron Compton scattering from 10 K up to room temperature. From the former technique the H-projected density of phonon states up to 100 meV is derived, while the latter works out the spherically averaged single-particle (i.e., H, Li, and N) momentum distributions and, from this, the mean kinetic energies. Only for H at the lowest investigated temperature, non-gaussian components of its momentum distribution are detected. However, these components do not seem directly connected to the system anharmonicity, being fully compatible with the simple N-H bond anisotropy. Neutron data are also complemented by ab initio lattice dynamics simulations, both harmonic and, at room temperature, carried out in the framework of the so-called "quantum colored noise thermostat" method. The single-particle mean kinetic energies in lithium imide as a function of temperature show a quite peculiar behavior at the moment not reproduced by ab initio lattice dynamics methods, at least as far as H and Li are concerned. As matter of fact, neither their low temperature values nor their temperature trends can be precisely explained in terms of standard phonon calculations.

In this study we utilize neutron Compton scattering (NCS) to determine differences in nuclear momentum distributions in NaH, both as bulk material and encapsulated as nanoscale particles (from 20 to 50 nm in diameter) within an amorphous silica-gel matrix (SiGNaH). In addition, elemental Na dispersed in such a matrix is also studied (SiGNa). Data treatment and fitting of experimental spectra yields comparison of the nuclear Compton profiles and radial momentum distributions for the proton in both bulk NaH and nanoscale SiGNaH, with resultant proton kinetic energies being in agreement with previous inelastic neutron studies of bulk NaH. Slight differences in proton radial momentum distributions for bulk and nanoscale systems are witnessed and discussed. The technique of stoichiometric-fixing is applied to the backscattering spectra of each system in order to examine changes in the Na profile width, and NCS is shown to be sensitive to the chemical environment change of this heavier nucleus. Examination of the Si and O profile widths in the gel samples also supports this method.

The procedure for calibrating the VESUVIO eV neutron spectrometer at the ISIS neutron source is described. VESUVIO is used primarily to measure the momentum distribution n(p) of atoms, by inelastic scattering of very high energy (5–150eV) neutrons. The results of the calibrations show that measurements of n(p) in atoms with masses lower than 16amu can be measured with a resolution width ∼25% of the intrinsic peak widths in the current instrument configuration. Some suggestions as to how the instrument resolution could be significantly improved are made.

The paper by Chatzidimitriou-Dreismann, Gray and Blach in the title reports measurements on gaseous hydrogen, performed on the VESUVIO electron volt neutron spectrometer at the ISIS neutron source. It was claimed in this paper that the VESUVIO measurements show that, if the energy transfer is sufficiently large that the bond in the H2 molecule is broken, then a larger energy transfer than that predicted by conventional neutron scattering theory occurs. It was also claimed that this is the first evidence for an increase in the energies of the proton and its environment due to quantum disentanglement. It is shown here that this evidence is almost certainly a spurious consequence of errors in the data analysis of Chatzidimitriou-Dreismann et al. When the standard VESUVIO instrument programs are used to analyse the same data on gaseous hydrogen the results obtained are in very good agreement with conventional theory.

Deep Inelastic Neutron Scattering provides a means of directly and accurately measuring the momentum distribution of protons in water, which is determined primarily by the protons ground state wavefunction. We find that in water confined on scales of 20A, this wave function responds to the details of the confinement, corresponds to a strongly anharmonic local potential, shows evidence in some cases of coherent delocalization in double wells, and involves changes in zero point kinetic energy of the protons from -40 to +120 meV difference from that of bulk water at room temperature. This behavior appears to be a generic feature of nanoscale confinement. It is exhibited here in 16A inner diameter carbon nanotubes, two different hydrated proton exchange membranes(PEMs), Nafion 1120 and Dow 858, and has been seen earlier in xerogel and 14A diameter carbon nanotubes. The proton conductivity in the PEM samples correlates with the degree of coherent delocalization of the proton.

The measured changes in the zero-point kinetic energy of the protons are entirely responsible for the binding energy of water molecules to A phase DNA at the concentration of 6  water molecules/base pair. The changes in kinetic energy can be expected to be a significant contribution to the energy balance in intracellular biological processes and the properties of nano-confined water. The shape of the momentum distribution in the dehydrated A phase is consistent with coherent delocalization of some of the protons in a double well potential, with a separation of the wells of 0.2 Å.

The paper in the title [1] reports measurements of neutron scattering from hydrogen in the 1-100 eV range of energy transfers, using the direct geometry MARI spectrometer at ISIS. Stock et al claim that their measurements have better or comparable energy resolution to those on the inverse geometry VESUVIO spectrometer at ISIS. Most importantly the main conclusions of ref [1] are not valid unless this claim is true: in particular the conclusion that anomalous neutron cross sections measured on VESUVIO [2] are "the result of experimental issues using indirect geometry spectrometers". We present here overwhelming evidence that the energy resolution of the measurements in ref [1] is much coarser than on VESUVIO. It follows that the conclusions of Stock et al are unfounded. In reality the measurements of reference [1] serve mainly to demonstrate that at eV neutron energies, direct geometry chopper spectrometers have greatly inferior energy resolution to inverse geometry spectrometers based on resonance foil methods.

Measurements of the proton momentum distribution n(p) in water from ambient conditions to above the supercritical point are compared with theoretical calculations based on a recently developed polarizable water model. The n(p) along the H-bond direction is narrower in the dense phases, and approaches that of the isolated molecule in the more dilute phases. The theoretical model, which includes only electrostatic interactions, is unable to explain the softening of the local potential experienced by the proton in the dense phases, but it accurately predicts the n(p) for the dilute phases.

Recoil effects have been observed for neutron and electron scatterings, and in photoemission. In all cases highly oriented pyrolytic graphite was used as a testing material and dependencies of recoil effects on the crystal orientation were found but these results have, so far, not been compared. We show that the same theory can describe the results of all three experiments in a quantitative way.

The momentum distribution in KD(2)PO(4) (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 KH(2)PO(4) (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.

Single-walled carbon nanotubes (SWNT) were loaded with 5.2wt% hydrogen at a hydrogen pressure of 3GPa and T=620K, quenched to 80K and studied at ambient pressure and 15K by inelastic neutron scattering (INS) in the range of energy transfers 3–400meV. An analysis of the measured INS spectra showed that the quenched SWNT & H sample contained hydrogen in two different forms, as H atoms covalently bound to the carbon atoms (∼4.7wt%) and as H2 molecules (∼0.5wt%) exhibiting nearly free rotational behavior. Annealing the sample in vacuum at 332K removed about 65% of the H2 molecules and annealing at 623K removed all of them. This demonstrates that H2 molecules were kept in this sample more tightly than in earlier studied SWNT & H samples that were hydrogenated at lower pressures and temperatures and lost all molecular hydrogen on heating in vacuum to room temperature.

Born-Oppenheimer (BO) potential in any material. The proton potential surfaces in the hydrogen bonded superprotonic conductor Rb3H(SO4)2 are extracted from the momentum distribution measured using Deep Inelastic Neutron Scattering(DINS). The potential has a single minimum along the bond direction, which accounts for the absence of the antiferroelectric transition seen in the deuterated material, and a saddle point off the bond direction for tunneling into the next well with a barrier height of 350 meV. The measured potential is in qualitative agreement with phenomenological double Morse potentials that have been used to describe hydrogen bonds in other systems.

The single atom kinetic energy kappa of high purity solid hcp 4He has been measured by neutron Compton scattering, at temperatures between 0.07 and 0.4 K and a pressure of 40 bar. Within statistical error of approximately 2% no change in kappa was observed. The values of kappa at approximately 0.07 K were the same in a single crystal and a polycrystalline sample and were also unaffected (within statistical error) by the addition of 10 ppm of 3He. The lattice constant was also found to be independent of temperature to within 1 part in 2000. These results suggest that the supersolid transition in 4He has a different microscopic origin to the superfluid transition in the liquid.