Nuclear Momentum Distribution Research Articles

Proton tunneling in the dissociation of H2+ and its asymmetric isotopologues driven by circularly polarized THz laser pulses.

Light-induced deprotonation of molecules is an important process in photochemical reactions. Here, we theoretically investigate the tunneling deprotonation of H2+ and its asymmetric isotopologues driven by circularly polarized THz laser pulses. The quasi-static picture shows that the field-dressed potential barrier is significantly lowered for the deprotonation channel when the mass asymmetry of the diatomic molecule increases. Our numerical simulations demonstrate that when the mass symmetry breaks, the tunneling deprotonation is significantly enhanced and the proton tunneling becomes the dominant dissociation channel in the THz driving fields. In addition, the simulated nuclear momentum distributions show that the emission of the proton is directed by the effective vector potential for the deprotonation channel and, meanwhile, the angular distribution of the emitting proton is affected by the alignment and rotation of the molecule induced by the rotating field.

Nuclear quantum dynamics in Hexamethylenetetramine and its deuterated counterpart: a DFT-augmented neutron study

Despite being one of the most thoroughly characterised molecular crystals, hexamethylenetetramine (HMT) and its deuterated counterpart (DHMT), are still not fully understood, especially regarding anharmonic and nuclear quantum effects. In this work, an unprecedented combination of experimental techniques, including neutron and x-ray diffraction, inelastic neutron scattering, neutron transmission, and Compton scattering, all augmented ab initio by harmonic lattice dynamics calculations, was applied. The main question that motivated the presented work was the interplay between the phonon anharmonicity and isotope and nuclear quantum effects related to the zero-point energies of proton and deuteron. Signatures of the combined effects of isotopic substitution, temperature, anharmonicity and nuclear quantum effects were found in data from all experimental methods. In the case of neutron and x-ray diffraction, these signatures manifested as systematic discrepancies between the structural and atomic displacement parameters and thermal diffuse scattering obtained from harmonic lattice calculations and their experimental counterparts. To this end, an important effect was found that could not have been explained by the harmonic lattice modelling; the reverse Ubbelohde effect, i.e. the observation that deuteration decreases hydrogen bond length in HMT. In the case of neutron transmission, further discrepancies between theoretical predictions and experimental data were found at cryogenic temperatures. Finally, applying the diabatic theory of the local potential of the intermolecular hydrogen bond in HMT, it was possible to elucidate the degree of anharmonicity of the C–H···N bonds by relating it to the magnitude of the vibrational isotope effect for the C–H bond stretching observed in inelastic and neutron Compton scattering experiments. It was found that the combined nuclear quantum and anharmonic effects of the protons (deuterons) in hydrogen bonds in HMT (DHMT) manifest as systematic discrepancies between the ab initio predictions for the widths of nuclear momentum distributions and the experimental values.

Effects of nucleon-nucleon short-range correlations on inclusive electron scattering

The nucleon-nucleon short-range correlation (NN-SRC) is one of the key issues of nuclear physics, which typically manifest themselves in high-momentum components of the nuclear momentum distributions. In this paper, the nuclear spectral functions based on the axially deformed relativistic mean-field model are developed to involve the NN-SRC. With the spectral functions, the inclusive electron scattering $(e,{e}^{\ensuremath{'}})$ cross sections are calculated within the plane-wave impulse approximation (PWIA) framework, including the quasielastic (QE) part and $\mathrm{\ensuremath{\Delta}}$ production part. Especially in the $\mathrm{\ensuremath{\Delta}}$ production region, we reconsider the electromagnetic structures of the nucleon resonance $\mathrm{\ensuremath{\Delta}}$(1232) and the scattering mechanisms, and thereby the theoretical calculations are improved effectively and the cross sections are well consistent with the experimental data. The theoretical $(e,{e}^{\ensuremath{'}})$ cross sections are further divided into NN-SRC and mean-field contributions. It is found that, at the kinematics $0.5\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}<{Q}^{2}<1\phantom{\rule{0.16em}{0ex}}{\mathrm{GeV}}^{2}$, the QE peak and $\mathrm{\ensuremath{\Delta}}$ production peak not only reflect the mean-field structure but also are sensitive to the NN-SRC information. Finally, we provide another method to extract the strengths of NN-SRC from experimental cross sections for selected nuclei at the suitable kinematics.

Force constant disorder in the Ni44Nb56 bulk metallic glass as observed by deep inelastic neutron scattering augmented by isotopic substitution

In this work, the force-constant disorder in nickel-niobium metallic glass, Ni44Nb56, was studied using the deep inelastic neutron scattering (DINS) technique augmented by isotopic substitution. The distributions of DINS observables (the nuclear kinetic energies, the width of the nuclear momentum distributions, and the effective force constants) were measured in Ni44Nb56 and compared with their counterparts obtained from ab initio harmonic lattice (HLD) simulations for the crystalline forms of nickel, niobium, and the NiNb crystal and from the reverse Monte Carlo (RMC) simulations augmented by effective force fields performed for Ni44Nb56. The force-constant distribution of nickel, obtained from the analysis of the results of the DINS experiments, was found to be two times broader than its counterparts estimated based on the HLD and RMC simulations. In the case of niobium, the force-constant distribution inferred from the DINS experiments is estimated to be an order of magnitude broader than the ab initio HLD prediction in the NiNb crystal. Moreover, no disorder-induced softening (with respect to its crystalline counterparts) of the effective force constants of Ni and Nb in Ni44Nb56 was observed. The lack of disorder-induced softening in Ni44Nb56 is consistent with the correlation between the short-range order, defined by the average coordination number and the interatomic distances, and the magnitudes of the effective force constants. The obtained results are consistent with a picture, whereby disorder induces symmetrical broadening of phonon dispersion curves, and phonon softening is limited to low-energy modes carrying negligible amounts of nuclear kinetic energy. The obtained results have important ramifications for engineering the properties of bulk metallic glasses.

Distribution function of nuclei from e± scattering in the presence of a strong primordial magnetic field

The amplitude of the primordial magnetic field (PMF) is constrained from observational limits on primordial nuclear abundances. Within this constraint, it is possible that nuclear motion is regulated by Coulomb scattering with electrons and positrons ($e^\pm$'s), while $e^\pm$'s are affected by a PMF rather than collisions. For example, at a temperature of $10^9$ K, thermal nuclei typically experience $\sim 10^{21}$ scatterings per second that are dominated by very small angle scattering leading to minuscule changes in the nuclear kinetic energy of order $\mathcal{O}$(1) eV. In this paper the upper limit on the effects of a possible discretization of the $e^\pm$ momenta by the PMF on the nuclear momentum distribution is estimated under the extreme assumptions that the momentum of the $e^\pm$ is relaxed before and after Coulomb scattering to Landau levels, and that during Coulomb scattering the PMF is neglected. This assumption explicitly breaks the time reversal invariance of Coulomb scattering, and the Maxwell-Boltzmann distribution is not a trivial steady state solution of the Boltzmann equation under these assumptions. We numerically evaluate the collision terms in the Boltzmann equation, and show that the introduction of a special direction in the $e^\pm$ distribution by the PMF generates no directional dependence of the collisional destruction term of nuclei. Large anisotropies in the nuclear distribution function are then constrained from big bang nucleosynthesis. Ultimately, we conclude that a PMF does not significantly affect the isotropy or BBN.

Nuclear momentum distributions governed by Rabi flopping in the dissociation of hydrogen molecular ions in strong laser fields

We study the Rabi flopping between the $1s{\ensuremath{\sigma}}_{g}$ and $2p{\ensuremath{\sigma}}_{u}$ states during the dissociation of hydrogen molecular ions in strong laser fields by numerically simulating the time-dependent Schr\"odinger equation. Starting either from a certain vibrational state or from coherently superimposed vibrational states weighted with Frank-Condon factors, the dissociative nuclear momentum distributions present multiple angular nodes and maxima due to molecular alignment-dependent Rabi flopping. The Rabi frequency and nuclear angular distribution depend on the laser chirp and laser ellipticity. Rabi flopping also determines the population on the $2p{\ensuremath{\sigma}}_{u}$ state and thus the dissociation probability. The deep understanding of Rabi flopping in molecular dissociation gives clues to control ultrafast molecular dynamics.

Local structure and dynamics of tungsten oxide-based glasses: insights from concurrent neutron diffraction and Compton scattering

In this work, following our previous work on molybdate glasses, we employ a combination of neutron diffraction and neutron Compton scattering, augmented by ab initio harmonic lattice dynamics and Reverse Monte Carlo modelling to characterise the force-constant disorder in the tungsten oxide-based glasses. Specifically, we discuss the correlations between the average interatomic force constant magnitudes inferred from neutron Compton scattering and the glass formation ability, measured in terms of the value of the glass transition temperature, as well as the average bond-lengths and interatomic distances obtained from diffraction data analysis. Moreover, we provide a comparative analysis of the widths of force-constant distributions of individual atomic species in glasses and their precursor metal oxides based on the distributions of the widths of nuclear momentum distributions. Furthermore, we assess the degree of softening of atom-projected vibrational densities of states induced by the force-constant disorder in the glasses.

The effective isotropy of the hydrogen local potential in biphenyl and other hydrocarbons.

We present an experimental investigation of the hydrogen nuclear momentum distribution in biphenyl using deep inelastic neutron scattering. Our experimental results suggest that the local potential affecting hydrogen is both harmonic and isotropic within experimental uncertainties. This feature is interpreted as a consequence of the central limit theorem, whereby the three-dimensional momentum distribution is expected to become a purely Gaussian function as the number of independent vibrational modes in a system increases. We also performed ab initio phonon calculations on biphenyl and other saturated hydrocarbons, from methane to decane. From the results of the simulations, one can observe that the nuclear momentum distribution becomes more isotropic as the number of atoms and normal modes in the molecule increases. Moreover, the predicted theoretical anisotropy in biphenyl is clearly larger than in the experiment. The reason is that the total number of normal modes necessary to reproduce the experimental results is much larger than the number of normal modes encompassed by a single unit cell due to the presence of structural disorder and intermolecular interactions in the real crystal, as well as coupling of different normal modes. Finally, experimental data were collected, over a subset of detectors on the VESUVIO spectrometer at ISIS, with a novel setup to increase the count rate and signal-to-background ratio. We envision that such an optimized experimental setup can provide faster measurements and more stringent constraints for phonon calculations.

Hydrogen Dynamics in Supercritical Water Probed by Neutron Scattering and Computer Simulations.

In this work, an investigation of supercritical water is presented combining inelastic and deep inelastic neutron scattering experiments and molecular dynamics simulations based on a machine-learned potential of ab initio quality. The local hydrogen dynamics is investigated at 250 bar and in the temperature range of 553-823 K, covering the evolution from subcritical liquid to supercritical gas-like water. The evolution of libration, bending, and stretching motions in the vibrational density of states is studied, analyzing the spectral features by a mode decomposition. Moreover, the hydrogen nuclear momentum distribution is measured, and its anisotropy is probed experimentally. It is shown that hydrogen bonds survive up to the higher temperatures investigated, and we discuss our results in the framework of the coupling between intramolecular modes and intermolecular librations. Results show that the local potential affecting hydrogen becomes less anisotropic within the molecular plane in the supercritical phase, and we attribute this result to the presence of more distorted hydrogen bonds.

Interference of nuclear wave packets carrying different angular momenta in the dissociation of H2+ in strong circularly polarized laser pulses

We systematically investigate the interference of nuclear wave packets carrying different angular momenta by numerically solving the time-dependent Schr\odinger equation for the dissociation of ${{\mathrm{H}}_{2}}^{+}$ in strong circularly polarized laser pulses. ${{\mathrm{H}}_{2}}^{+}$ exposed to strong laser pulses may absorb different numbers of photons and dissociate along different pathways carrying different angular momenta. In case dissociation pathways differ by an even number of photons, the respective wave packets have the same parity and thus interfere with each other, leading to spiral nuclear momentum distributions for the dissociative fragments. Inversely, by investigating the interference structure of the angle-resolved kinetic energy release of the dissociative fragments, the molecular dissociation pathways can be extracted. The spiral nuclear momentum distribution provides another approach to explore ultrafast molecular dynamics.

Spiral nuclear momentum distribution for the dissociation of H2+ in a circularly polarized laser pulse

The dissociation of ${\mathrm{H}}_{2}{}^{+}$ in a circularly polarized laser pulse is numerically studied by simulating the time-dependent Schr\odinger equation. After absorbing one or three photons, the nuclear wave packets carrying the angular momenta $\ensuremath{\hbar}$ and $3\ensuremath{\hbar}$ dissociate along the $2p{\ensuremath{\sigma}}_{u}$ state. Due to the broad initial kinetic-energy distribution of the superimposed nuclear vibrational states, the one-photon and three-photon dissociation pathways may end with the same kinetic energy. These coexisting dissociation pathways with same parities but different orbital angular momenta interfere with each other, resulting in the spiral nuclear momentum distribution in the laser polarization plane. The interference structure in the nuclear momentum distribution offers another freedom to identify the dissociation pathways of molecules in strong laser fields.

Neutron Compton Scattering: from proton momentum distribution to muonium hyperfine coupling constant in the isopropyl radical

We establish a fast and reliable benchmarking protocol for predictions of Muon Spin Resonance observables. To this end, we apply neutron Compton scattering (NCS) to study the nuclear momentum distributions of the proton and deuteron in the condensed phase of the isopropyl and d-isopropyl alcohols. By subtracting the time-of-flight NCS spectra of both compounds we demonstrate that the proton momentum distribution in the OH group of isopropanol and the deuteron momentum distribution in the OD group in d-isopropyl can be studied selectively. The site-selective application of the NCS method enables the calculation of the magnitude of the frequency isotope effect for the proton in OH along the hydrogen bond direction. By comparing the magnitude of the frequency isotope effect with values predicted for simple model potentials we are able to perform the appraisal of the degree of anharmonicity of the OH proton environment. Assuming that the effective potential felt by the OH proton along the hydrogen-bond direction can be satisfactorily described by the Morse potential, we are able to calculate its dissociation constant D and decay constant a. Finally, assuming that the same Morse potential describes the local binding of Muonium in the mioniated isopropyl radical, we are able to predict its width of momentum and position distributions and the kinetic and zero-point energy. Based on these results, we are able to provide a conservative bound for the magnitude of the isotope effect on the muonium hyperfine interaction without resorting to a complicated and computationally expensive methodology based on the application of path integrals.

Nuclear kinetic energies from final-state effects in the harmonic limit

This work shows a simple, yet quite powerful, data pre-treatment protocol for mass-resolved neutron spectroscopy, aimed at a better estimation of the main quantum observable linked to a nuclear-momentum distribution, its second moment. From a methodological point of view, the immediate benefit of having such a protocol is twofold. Firstly, a good estimate of a second moment of a nuclear-momentum distribution, and hence nuclear kinetic energy, provided as input for subsequent data fitting, accelerates the convergence of a data fit and minimises the likelihood of it being stuck in a non-physical solution. Secondly, it provides a simple screening tool in the search for quantum systems exhibiting statistically significant departures for a classical behaviour of equipartition of kinetic energy at any given temperature. This second benefit renders the presented protocol an important data screening tool in the search of materials exhibiting exotic properties, possibly attributed to nuclear quantum effects.

Mass-selective neutron spectroscopy of glassy versus polycrystalline structures in binary mixtures of beryllium and zirconium

Exploiting the unique tandem of VESUVIO and TOSCA inverted geometry spectrometers at the ISIS pulsed neutron and muon source in the United Kingdom, specifically the capability of VESUVIO to measure concurrently neutron diffraction and Compton spectroscopy, we have performed a global study of the structural and dynamical origins of disorder in Zr —Be metallic glasses. To this end, a polycrystalline Zr30Be70 and an amorphous Zr40Be60 systems were investigated in a wide range of temperatures ranging from 10 to 300K. For the first time, neutron diffraction has provided clues as to the structural composition of the polycrystalline Zr30Be70. The Rietveld refinement of the diffraction data has revealed that the polycrystalline system is made up of three distinct structural phases; a hexagonal phase, Be2Zr, of the P6/mmm symmetry amounting to 87.11%, a second hexagonal phase, Be5Zr, of the P6/mmm point group symmetry, amounting to 12.89%, as well as trace amounts of a third orthorhombic phase of unspecified stoichiometry. The overall sample stoichiometry, inferred from the dissection of the diffraction data, was in excellent agreement with the Compton results, both confirming the Zr30Be70 formulation. The analysis of INS data agreed very well with the theoretical results from the recursion method. The INS data were cross-validated by the nuclear momentum distributions of both Zr and Be, obtained from the analysis of the NCS data. Systematic differences between the crystalline and amorphous Zr —Be systems were identified in the whole temperature range and attributed to low-frequency mode softening, when going from crystalline to the amorphous phase.

Enhancement of counting statistics and noise reduction in the forward-scattering detectors on the VESUVIO spectrometer

New evidence of the increased count rate in deep inelastic neutron scattering spectra is provided. Experiments were performed using photon-sensitive yttrium-aluminum-perovskite detectors, installed on the VESUVIO spectrometer at the ISIS pulsed neutron and muon source. At present, these detectors work with a low-level discrimination threshold measuring photons with energy greater than 600 keV in order to avoid background photons from the boron in the beam stop, and other environmental sources. We discuss the advantage in reducing the level of the threshold so as to detect some high-intensity low-energy promptgamma rays emitted after the radiative capture of 4.9 eV neutrons by gold, used as energy analyser on the VESUVIO spectrometer. This work shows an improvement of the statistical poissonian error bars and noise on the difference of spectra recorded with and without the energy analyser. The application of such new acquisition strategy discussed here will improve the detection limit of hydrogen atoms in samples, as well as allow a more precise line-shape analysis of nuclear momentum distributions, mentioning just few applications of deep inelastic neutron scattering experiments on VESUVIO.

Fractal dimension as a scaling law for nuclear quantum effects: a neutron Compton scattering study on carbon allotropes

In this work, we tackle the problem of the sensitivity of neutron Compton scattering, measured through the widths of nuclear momentum distributions, to the degree of complexity and ordering of the structural motif characterising the surrounding environment felt by a particular nucleus (carbon). In doing so, we replace the usual concept of the bond strength categorised in terms of its thermodynamical or electronic properties with a novel observable inspired by the language of mathematical topology, the Hausdorff-Besicovitch fractal dimension. We derive a relatively straightforward connection between the fractal dimension of a given system under consideration and the nuclear kinetic energy. To achieve this, we modify the concept of the energy equipartition theorem for solid-state systems composed of carbon atoms where the atom-ordering topology does not follow a simple two or three-dimensional order, but rather atoms are placed along curves in space that have an intermediate dimension related to the varying amounts of information they contain. A series of results from past neutron Compton scattering studies, as well as new results on Buckminsterfullerene (C60), correlate with the topological measures of surface roughness and bending, as categorised quantitatively by the fractal dimension of the system. Namely, for the same formal chemical binding motif (sp2 C) and with decreasing system dimensionality from nearly 3 towards 1, the quantum nature of the system becomes more pronounced. The simple scaling law developed in this work allows for relatively simple assessment of the nuclear “quantumness” of a given system with potentially important ramifications in the ab initio modelling of nuclear quantum effects in condensed matter.

Model selection in neutron Compton scattering - a Bayesian approach with physical constraints

This work analyses the performance of the maximum-likelihood estimation approach in fitting Gram-Charlier expansion curves to nuclear momentum distributions with non-negativity constraints. The presented approach guarantees that the most likely model selected to describe the recorded data is also a physically meaningful one, i.e., corresponds to a non-negative probability distribution function. For the case of the most popular momentum distribution model, containing the information about the variance and excess kurtosis of the distribution, we derive a simple and easy to implement non-negativity criterion. We test the performance of the newly developed approach by applying it to interpret proton momentum distribution obtained from neutron Compton scattering from solid phosphoric acid, a system in which nuclear quantum tunnelling was proposed in the limit of low temperature. From a methodological point of view, this work provides a screening tool in the search for systems exhibiting the so-called ‘non-trivial nuclear quantum effects’.

Neutron-resonance capture analysis on the VESUVIO spectrometer: Towards high-throughput material characterisation

We discuss the possibility to characterise nuclear quantum effects on the dynamics of heavy nuclei by means of neutron-resonance capture analysis on the VESUVIO spectrometer at ISIS. VESUVIO is equipped with yttrium-aluminium-perovskite gamma-sensitive detectors that can be used to record the Doppler-broadened line shape from a neutron-induced resonance in the neutron-energy range between 1 and 100 eV. The measurement of nuclear momentum distributions for heavy atoms using deep inelastic neutron scattering, the traditional technique for light-weight nuclei from hydrogen to fluorine, is currently severely limited by the resolution of the instrument. On the other hand, gamma-Dopplerimetry studies as the one presented here on gold allow for exquisite precision and short data-collection measurements, of the order of one hour, for the measurements, rendering the technique ideal for high-throughput investigations.

Correction to "Direct Measurements of Quantum Kinetic Energy Tensor in Stable and Metastable Water near the Triple Point: An Experimental Benchmark".

This study presents the first direct and quantitative measurement of the nuclear momentum distribution anisotropy and the quantum kinetic energy tensor in stable and metastable (supercooled) water near its triple point, using deep inelastic neutron scattering (DINS). From the experimental spectra, accurate line shapes of the hydrogen momentum distributions are derived using an anisotropic Gaussian and a model-independent framework. The experimental results, benchmarked with those obtained for the solid phase, provide the state of the art directional values of the hydrogen mean kinetic energy in metastable water. The determinations of the direction kinetic energies in the supercooled phase, provide accurate and quantitative measurements of these dynamical observables in metastable and stable phases, that is, key insight in the physical mechanisms of the hydrogen quantum state in both disordered and polycrystalline systems. The remarkable findings of this study establish novel insight into further expand th...

Direct Measurements of Quantum Kinetic Energy Tensor in Stable and Metastable Water near the Triple Point: An Experimental Benchmark.

This study presents the first direct and quantitative measurement of the nuclear momentum distribution anisotropy and the quantum kinetic energy tensor in stable and metastable (supercooled) water near its triple point, using deep inelastic neutron scattering (DINS). From the experimental spectra, accurate line shapes of the hydrogen momentum distributions are derived using an anisotropic Gaussian and a model-independent framework. The experimental results, benchmarked with those obtained for the solid phase, provide the state of the art directional values of the hydrogen mean kinetic energy in metastable water. The determinations of the direction kinetic energies in the supercooled phase, provide accurate and quantitative measurements of these dynamical observables in metastable and stable phases, that is, key insight in the physical mechanisms of the hydrogen quantum state in both disordered and polycrystalline systems. The remarkable findings of this study establish novel insight into further expand the capacity and accuracy of DINS investigations of the nuclear quantum effects in water and represent reference experimental values for theoretical investigations.