Momentum Transfer Range Research Articles

Real-space local self-motion of protonated and deuterated water.

We report on the self-part of the Van Hove correlation function, the correlation function describing the dynamics of a single molecule, of water and deuterated water. The correlation function is determined by transforming inelastic scattering spectra of neutrons or x rays over a wide range of momentum transfer Q and energy transfer E to space R and time t. The short-range diffusivity is estimated from the Van Hove correlation function in the framework of the Gaussian approximation. The diffusivity has been found to be different from the long-range macroscopic diffusivity, providing information about local atomic dynamics.

A compact approach to higher-resolution resonant inelastic x-ray scattering detection using photoelectrons

The detection of inelastically scattered soft x-rays with high energy resolution usually requires large grating spectrometers. Recently, photoelectron spectrometry for analysis of x-rays (PAX) has been rediscovered for modern spectroscopy experiments at synchrotron light sources. By converting scattered photons to electrons and using an electron energy analyser, the energy resolution for resonant inelastic x-ray scattering (RIXS) becomes decoupled from the x-ray spot size and instrument length. In this work, we develop PAX towards high energy resolution using a modern photoemission spectroscopy setup studying Ba2Cu3O4Cl2 at the Cu L 3-edge. We measure a momentum transfer range of 24% of the first Brillouin zone simultaneously. Our results hint at the observation of a magnon excitation below 100 meV energy transfer and show intensity variations related to the dispersion of dd-excitations. With dedicated setups, PAX can complement the best and largest RIXS instruments, while at the same time opening new opportunities to acquire RIXS at a range of momentum transfers simultaneously and combine it with angle-resolved photoemission spectroscopy in a single instrument.

Probing valence quark width of the proton in deeply virtual Compton scattering at high energies* *Supported by the National Natural Science Foundation of China (12165004), the Basic and Applied Basic Research Project of Guangzhou Science and Technology Bureau (202201011324), the Education Department of Guizhou Province, China (QJJ[2022]016) and the National Key Research and Development Program of China (2018YFE0104700, CCNU18ZDPY04)

We use the refined hot spot model to study the valence quark shape of the proton with the deeply virtual Compton scattering at high energies in the color glass condensate framework. To investigate the individual valence quark shape, a novel treatment of the valence quark width is employed. We calculate the cross-sections for coherent and incoherent deeply virtual Compton scattering using, for the first time, different widths ( and ) for the profile density distributions of the up and down quarks instead of using the same width as in the literature. We find that the cross-sections calculated with at each collision energy are consistent with each other, which is in agreement with theoretical expectations, whereas those computed with show some discrepancies. This outcome implies that the up quark might emit more gluons than the down quark, leading to at high energy. The impact of energy on the outcome is estimated. Our results show that as the collision energy increases, the aforementioned discrepancies are not only significantly broadened, but also shift to a relatively smaller momentum transfer range at the future Electron-Ion Collider (EIC) and Large Hadron Electron Collider (LHeC) energies, which indicates that the EIC and LHeC can provide an unprecedented chance to access the shape of the valence quark of the proton.

Tripling of the scattering vector range of X-ray reflectivity on liquid surfaces using a double-crystal deflector.

The maximum range of perpendicular momentum transfer (q z) has been tripled for X-ray scattering from liquid surfaces when using a double-crystal deflector setup to tilt the incident X-ray beam. This is achieved by employing a higher-energy X-ray beam to access Miller indices of reflecting crystal atomic planes that are three times higher than usual. The deviation from the exact Bragg angle condition induced by misalignment between the X-ray beam axis and the main rotation axis of the double-crystal deflector is calculated, and a fast and straightforward procedure to align them is deduced. An experimental method of measuring scattering intensity along the q z direction on liquid surfaces up to q z = 7 Å-1 is presented, with liquid copper serving as a reference system for benchmarking purposes.

XrdPlanner: exploring area detector geometries for powder diffraction and total scattering experiments.

xrdPlanner is a software package designed to aid in the planning and preparation of powder X-ray diffraction and total scattering beam times at synchrotron facilities. Many modern beamlines provide a flexible experimental setup and may have several different detectors available. In combination with a range of available X-ray energies, it often makes it difficult for the user to explore the available parameter space relevant for a given experiment prior to the scheduled beam time. xrdPlanner was developed to provide a fast and straightforward tool that allows users to visualize the accessible part of reciprocal space of their experiment at a given combination of photon energy and detector geometry. To plan and communicate the necessary geometry not only saves time but also helps the beamline staff to prepare and accommodate for an experiment. The program is tailored toward powder X-ray diffraction and total scattering experiments but may also be useful for other experiments that rely on an area detector and for which detector placement and achievable momentum-transfer range are important experimental parameters.

Composite Hydrogels Based on Bacterial Cellulose and Poly-1-vinyl-1,2,4-triazole/Phosphoric Acid: Supramolecular Structure as Studied by Small Angle Scattering.

New composite hydrogels (CH) based on bacterial cellulose (BC) and poly-1-vinyl-1,2,4-triazole (PVT) doped with orthophosphoric acid (oPA), presenting interpenetrating polymeric networks (IPN), have been synthesized. The mesoscopic study of the supramolecular structure (SMS) of both native cellulose, produced by the strain Komagataeibacter rhaeticus, and the CH based on BC and containing PVT/oPA complex were carried out in a wide range of momentum transfer using ultra- and classical small-angle neutron scattering techniques. The two SMS hierarchical levels were revealed from 1.6 nm to 2.5 μm for the objects under investigation. In addition, it was shown that the native BC had a correlation peak on the small-angle scattering curves at 0.00124 Å-1, with the correlation length ξ being equal to ca. 510 nm. This motive was also retained in the IPN. The data obtained allowed the estimation of the fractal dimensions and ranges of self-similarity and gave new information about the BC mesostructure and its CH. Furthermore, we revealed them to be in coincidence with Brown's BC model, which was earlier supported by Fink's results.

Neutron facilities of the compact neutron source DARIA: parameters and features

The compact neutron source DARIA based on a linear proton accelerator is designed to create neutron beams for a diffractometer, a reflectometer, and a small-angle scattering setup. The experimental setups are optimized in terms of the range of momentum transfer, instrumental resolution, geometric dimensions, as well as in terms of the repetition rate and duration of neutron pulses.

Dynamic structure factors of polymer melts as observed by neutron spin echo: Direct comparison and reevaluation.

In this work, we compare the single chain dynamic structure factors for five different polymers: polyolefins (PE and PEP), poly-dienes (PB and PI), and a polyether (PEO). For this purpose, we have extended the De Gennes approximation for the dynamic structure factor. We describe the single chain dynamic structure factor in multiplying the coherent scattering functions for local reptation and Rouse motion within the Rouse blob. Important results are (i) the simple De Gennes structure factor S(Q, t)DG approximates within a few Å the outcome for the tube diameter of the more elaborate structure factor (exception PI); (ii) the extended De Gennes structure factor together with the Rouse blob describes the neutron spin echo spectra from the different polymers over the complete momentum transfer range and the full time regime from early Rouse motion to local reptation; and (iii) the representation of the scattering functions could significantly be improved by introducing non-Gaussianity corrections to the Rouse-blob dynamics. (iv) The microscopic tube step length in all cases is significantly larger than the rheological one; further tweaking the relation between tube length and entanglement blob size may indicate a possible trend toward an anisotropic lean tube with a step-length larger than the lateral extension. (v) All considered polymer data coincide after proper (Q, t) scaling to a universal behavior according to the length scale of the tube, while the relevant time scale is the entanglement time τe. (vi) In terms of the packing model, the required number of chains spanning the entanglement volume consistently is about 40% larger than that obtained from rheology.

Derivation of transition density from the observed 4He(e, e′)4He(02+) form factor raising the α-particle monopole puzzle

Abstract Recently, the monopole transition form factor of the electron-scattering excitation of the $0^+_2$ state (Ex = 20.21 MeV) of the 4He nucleus was observed over a broad momentum transfer range ($0.5 \le q^2 \le 5.0 \, {\rm fm}^{-2}$) with dramatically improved precision compared with older sets of data; modern nuclear forces, including those derived from the chiral effective field theory, failed to reproduce the form factor, which is called the α-particle monopole puzzle. To resolve this puzzle by improving the study of the spatial structure of the $0^+_2$ state, we derive in this letter a possible $0^+_1\!\rightarrow \! 0^+_2$ transition density ρtr(r) for r ≳ 1 fm from the observed form factor. The shape of the transition density is significantly different from that obtained theoretically in the literature.

Experimental determination of differential scattering coefficients for nickel by means of linearly polarized x-ray radiation

Performing an x-ray scattering analysis can underpin the quantitative description of a sample of interest, for example, to complement an x-ray fluorescence analysis. However, the reliability of such an analytical approach depends on good knowledge of scattering coefficients (or scattering cross-sections), which describe the probability of interaction and are characteristic of each chemical element. In this work, a metrological study of experimentally determining differential Rayleigh and Compton scattering coefficients for nickel is presented. Angular scans of the scattering intensities at different positions are enabled by a flexible experimental set-up and, therefore, allow for the robust determination of differential scattering coefficients at a wide range of forward and backward scattering angles. As a result, scattering coefficients in the range from cm2 g−1 sr−1 to cm2 g−1 sr−1 were determined in the momentum transfer range of 12.1 nm−1 to 22.4 nm−1. In addition, utilizing monochromatized and highly linearly polarized synchrotron radiation () ensures direct comparability to theoretical databases.

Advanced polarization analysis capability on the very small-angle neutron scattering instrument at the NIST Center for Neutron Research

The Very Small Angle Neutron Scattering (VSANS) diffractometer at the National Institute of Standards and Technology has been commissioned and is in the user program. A large available space of nearly 2 m along the beam in the sample area not only enhances the existing SANS polarization analysis capability, but also makes it possible for implementation of other polarization analysis capabilities which would not be easily available on existing SANS instruments, including grazing-incidence small-angle neutron scattering with polarization analysis and spherical neutron polarimetry. We present two polarized setups, one for high magnetic sample fields and the other for low magnetic sample fields, together with a versatile and flexible operational platform for polarized beam experiments. The design of a magnetostatic cavity device that provides better field homogeneity and thus longer 3He polarization relaxation time is discussed. It consists of an end-compensated magnetic shielded solenoid with non-identical holes to accommodate the divergent scattered beam in a constrained distance. Significant improvement in polarized neutronic performance, 3He polarization relaxation time, and an extended momentum transfer range for polarization analysis are presented. Improved neutron polarizing devices, double V-shaped supermirror polarizer, adiabatic radio-frequency spin flipper, and a 3He spin analyzer have yielded an initial instrumental flipping ratio of 100, allowing for higher sensitivity to detection of weak magnetic features in the sample.

Efficient calculation of k -integrated electron energy loss spectra: Application to monolayers of MoS2, hBN, and graphene

The theoretical scattering cross section of electron energy loss spectroscopy (EELS) is essentially given by $\ensuremath{-}\text{Im}\phantom{\rule{0.16em}{0ex}}{\ensuremath{\varepsilon}}^{\ensuremath{-}1}(\mathbf{k},\ensuremath{\omega})$ with the energy loss $\ensuremath{\hbar}\ensuremath{\omega}$ and the momentum transfer $\ensuremath{\hbar}\mathbf{k}$. The macroscopic dielectric function $\ensuremath{\varepsilon}(\mathbf{k},\ensuremath{\omega})$ can be calculated from first principles using time-dependent density-functional theory. However, experimental EELS measurements have a finite $\mathbf{k}$ resolution or, when operated in spatial resolution mode, yield a $\mathbf{k}$-integrated loss spectrum, which deviates significantly from EEL spectra calculated for specific $\mathbf{k}$ momenta. On the other hand, integrating the theoretical spectra over $\mathbf{k}$ is complicated by the fact that the integrand varies over several (typically six) orders of magnitude around $k=0$. In this article, we present a stable technique for integrating EEL spectra over an adjustable range of momentum transfers. The important region around $k=0$, where the integrand is nearly divergent, is treated partially analytically, allowing an analytic integration of the near divergence. The scheme is applied to three prototypical two-dimensional systems: monolayers of ${\mathrm{MoS}}_{2}$ (semiconductor), hexagonal BN (insulator), and graphene (semimetal). Here, we are confronted with the added difficulty that the long-range Coulomb interaction leads to a very slow supercell (vacuum size) convergence. We address this difficulty by employing an extrapolation scheme, enabling an efficient reduction of the supercell size and thus a considerable speedup in computation time. The calculated $\mathbf{k}$-integrated spectra are in very favorable agreement with experimental EEL spectra.

Form factors and branching fraction calculations for $$B_s \rightarrow D_s^{(*)} \ell ^+ \nu _\ell$$ in view of LHCb observation

In light of the LHCb observations about the $$B_s \rightarrow D_s^{(*)}\ell \nu _\ell$$ semileptonic decays, we study these channels within the standard model framework of covariant confined quark model. The necessary transition form factors are computed in the entire dynamical range of momentum transfer squared with built-in infrared confinement. Our computed ratios of the decay widths from tau mode to muon mode for $$D_s$$ and $$D_s^*$$ mesons are found to be $$R(D_s) = 0.271 \pm 0.069$$ and $$R(D_s^*) = 0.240 \pm 0.038$$ . We further determine the ratio of the decay width from $$D_s$$ and $$D_s^*$$ channel for muon mode $$\Gamma (B_s \rightarrow D_s \mu ^+ \nu _\mu )/\Gamma (B_s \rightarrow D_s^* \mu ^+ \nu _\mu ) = 0.451 \pm 0.093$$ . Our results are in excellent agreement with the data from the latest LHCb experiments as well as lattice quantum chromodynamics simulations. We also compare the shape of differential decay distribution for $$B_s \rightarrow D_s^* \mu ^+ \nu _\mu$$ with the LHCb data, and our results are in very good agreement throughout all the individual bins. Some other physical observables such as forward-backward asymmetry and longitudinal polarizations of leptons in the final state are also computed.

B→K and D→K form factors from fully relativistic lattice QCD

We present the result of lattice QCD calculation of the scalar, vector and tensor form factors for the $B\to K\ell^+\ell^-$ decay, across the full physical range of momentum transfer. We use the highly improved staggered quark (HISQ) formalism for all valence quarks on eight ensembles of gluon field configurations generated by the MILC collaboration. These include four flavours of HISQ quarks in the sea, with three ensembles having the light $u/d$ quarks at physical masses. In the first fully relativistic calculation of these form factors, we use the heavy-HISQ method. This allows us to determine the form factors as a function of heavy quark mass from the $c$ to the $b$, and so we also obtain new results for the $D\to K$ tensor form factor. The advantage of the relativistic formalism is that we can match the lattice weak currents to their continuum counterparts much more accurately than in previous calculations; our scalar and vector currents are renormalised fully nonperturbatively and we use a well-matched intermediate momentum-subtraction scheme for our tensor current. Our scalar and vector $B\to K$ form factors have uncertainties of less than 4% across the entire physical $q^2$ range and the uncertainty in our tensor form factor is less than 7%. Our heavy-HISQ method allows us to map out the dependence on heavy-quark mass of the form factors and we can also see the impact of changing spectator quark mass by comparing to earlier HPQCD results for the same quark weak transition but for heavier mesons.

The TAS-IN8 upgrade: Towards the limit of a three-axis spectrometer performance

IN8 is a high-flux three-axis thermal neutron spectrometer designed to measure inelastic neutron scattering on single crystals in a wide energy and momentum transfer range. It is the highest thermal flux spectrometer worldwide with the monochromatic flux at the sample up to 109 neutrons/cm2/s where users can perform demanding experiments not possible anywhere else. In recent years, the IN8 spectrometer has undergone several major upgrades that have further extended the capabilities of the instrument to the limits achievable with the standard setup. The first part of the upgrade was centred on the replacement of the monochromator assembly, now consisting of four double focusing reflecting crystal faces with enhanced luminosity. The ensuing upgrade was to replace the entire secondary spectrometer. As the result, the new spectrometer, called Thermes, profits from a compact design and it is well shielded against ambient experimental background. All the incorporated modifications have given the instrument an unprecedented and unique luminosity combined with an optimal signal-to-noise level and a remarkable configuration flexibility for a broad range of experimental requirements.

Magnetic structure of few-nucleon systems at high momentum transfers in a chiral effective field theory approach

The five low-energy constants (LECs) in the electromagnetic current derived in chiral effective field theory ($\chi$EFT) up to one loop are determined by a simultaneous fit to the $A\,$=$\,2$--3 nuclei magnetic moments and to the deuteron magnetic form factor and threshold electrodisintegration at backward angles over a wide range of momentum transfers. The resulting parametrization then yields predictions for the $^3$He/$^3$H magnetic form factors in excellent accord with the experimental values for momentum transfers ranging up to $\approx 0.8$ GeV/c, beyond the expected regime of validity of the $\chi$EFT approach. The calculations are based on last-generation two-nucleon interactions including high orders in the chiral expansion and derived by Entem, Macheleidt, and Nosyk [Phys.\ Rev.\ C {\bf 96}, 024004 (2017)] and by Piarulli {\it et al.} [Phys.\ Rev.\ C {\bf 94}, 054007 (2016)], using different $\chi$EFT formulations. In the $A\,$=$\,3$ calculations, (chiral) three-nucleon interactions are also accounted for. The model dependence resulting from these different formulations of the interactions is found to be mild for momentum transfer below $\approx0.8$ GeV/c. An analysis of the convergence of the chiral expansion is also provided.

Chiral surface spin textures in Cu2OSeO3 unveiled by soft X-ray scattering in specular reflection geometry

ABSTRACT Resonant elastic soft X-ray magnetic scattering (XRMS) is a powerful tool to explore long-periodic spin textures in single crystals. However, due to the limited momentum transfer range imposed by long wavelengths of photons in the soft x-ray region, Bragg diffraction is restricted to crystals with the large lattice parameters. Alternatively, small-angle X-ray scattering has been involved in the soft energy X-ray range which, however, brings in difficulties with the sample preparation that involves focused ion beam milling to thin down the crystal to below a few hundred nm thickness. We show how to circumvent these restrictions using XRMS in specular reflection from a sub-nanometer smooth crystal surface. The method allows observing diffraction peaks from the helical and conical spin modulations at the surface of a Cu 2 OSeO 3 single crystal and probing their corresponding chirality as contributions to the dichroic scattered intensity. The results suggest a promising way to carry out XRMS studies on a plethora of noncentrosymmetric systems hitherto unexplored with soft X-rays due to the absence of the commensurate Bragg peaks in the available momentum transfer range.

Relativistic composite-particle theory of the gravitational form factors of the pion: Quantitative results

We use a version of the instant-form relativistic quantum mechanics of composite systems to obtain the gravitational form factors of the pion in a common approach to its electroweak and gravitational properties. In the preceding work [Phys. Rev. D 103, 014029 (2021)], we formulated the mathematical background, presented the principal scheme of calculation and testified the obtained qualitative results to satisfy the general constraints given by the principles of the theory of hadron structure. In the present work, we give the detailed calculation of the gravitational form factors in the large range of momentum transfer, their static limits, and the slopes at zero value, the mean-square mass and mechanical radii of the pion. Now we take into account the gravitational structure of the constituent quarks. We show that the results are almost insensitive to the type of model two-quark wave function in a close analogy to the case of the pion electromagnetic form factor. We present a correct calculation of the form factor $D$ and corresponding matrix element of the energy-momentum tensor, going beyond the scope of the modified impulse approximation. Most of the parameters that we use for the calculation had been fixed even earlier in our works on the pion electromagnetic form factors. The only free parameter is the $D$-term of the constituent quark, which we fix by fitting the result for the slope at zero of the normalized to pion $D$-term form factor $D$ of the pion, to a chosen experimental value.

Generalized oscillator strength of the core-excited states of molecular nitrogen studied by nonresonant inelastic x-ray scattering

Fast electron impact was used to study the generalized oscillator strengths of the inner-shell excitations in atoms and molecules previously. In this work, a nonresonant inelastic x-ray scattering technique is extended to determine the generalized oscillator strengths of $(1{\ensuremath{\sigma}}_{g}\ensuremath{\rightarrow}1{\ensuremath{\pi}}_{g})+(1{\ensuremath{\sigma}}_{u}\ensuremath{\rightarrow}1{\ensuremath{\pi}}_{g})$ inner-shell excitations of molecular nitrogen in the squared momentum transfer range of 0.86 to 14.40 a.u. at a photon energy of about 10 keV and an energy resolution of about 1.3 eV. The present generalized oscillator strength strictly follows the first Born approximation and thus provides a rigorous test to the previously calculated results and the experimental ones measured by the electron energy loss spectroscopy. The presently extrapolated optical oscillator strength at zero momentum transfer is in accord with most experimental results and the theoretical data with the correlation effect considered carefully. This work indicates that the nonresonant inelastic x-ray scattering technique is a powerful tool to study the core excitation mechanism in atoms and molecules.

Opportunities for inclusive diffraction at EIC

The possibilities for inclusive diffraction in the Electron Ion Collider, EIC, in the US, are analyzed. We find that thanks to the excellent forward proton tagging, the EIC will be able to access a wider kinematical range of longitudinal momentum fraction and momentum transfer of the leading proton than at HERA. This opens up the possibility to measure subleading diffractive exchanges. The extended t-range would allow the precise extraction of 4-dimensional reduced cross section in diffraction. In addition, the varying beam energy setups at the EIC would allow for precise measurements of the longitudinal diffractive structure function.