Neutron-scattering Length Research Articles

Data on the Neutron–Neutron Scattering Length from the nd-Breakup Reaction at En = 8 MeV and En = 11 MeV

A kinematically complete experiment devoted to studying the nd-breakup reaction at energies of 8 and 11 MeV via detecting all three secondary particles was performed. The {}^{1}S_{0} neutron–neutron (nn) scattering-length values of a_{nn}={-}19.8pm 0.4 and {-}19.0pm 0.5 fm at, respectively, E_{n}=8 and 11 MeV were obtained from a comparison of the experimental dependence of the yield of the nd-breakup reaction on the relative energy of the nn pair with the results of a simulation. An analysis of the values obtained for the nn scattering length, together with data from other experiments, confirms the hypothesis that three-nucleon forces affect the parameters of nn interaction that are extracted from reactions involving few-nucleon systems and gives a new asymptotic nn scattering length, a_{nn}={-}16.1pm 0.1 fm.

Data on Neutron–Neutron Scattering Length from the Reaction $$\boldsymbol{n+^{2}\textrm{H}\to n+n+p}$$ at $$\boldsymbol{E_{n}=60}$$ MeV

$^{1}S_{0}$ \textit{nn}-scattering length has been measured in the \textit{nd}-breakup reaction at 60 MeV. The experiment was performed in the final state interaction geometry with registration of all three secondary particles. The scattering length $a_{nn} = -16.3 \pm 0.5$~fm was obtained from a comparison of the experimental dependence of the \textit{nd}-breakup yield on the relative energy of \textit{nn}-pair with the simulation results. An analysis of this value of scattering length together with the data obtained in other experiments on \textit{nd}- and \textit{dd}-breakup confirms the hypothesis about the influence of $3N$-forces on the values of \textit{nn}-interaction parameters extracted in these reactions.

Crystal structure of Mo-substituted lanthanum tungstate La5.4W1−y Mo y O12−δ (0 ≤ y ≤ 0.2) studied by X-ray and neutron diffraction

A determination of the detailed crystal structure of an Mo-substituted lanthanum tungstate series, La6−x W1−y Mo y O12−δ (0 ≤ y ≤ 0.2, δ is the oxygen deficiency), is presented. Material of composition La5.4W0.8Mo0.2O12−δ (y = 0.2) produced by the citrate-complexation route based on the Pechini method was investigated by high-resolution X-ray diffraction and neutron diffraction in the temperature range 10 ≤ T ≤ 298 K. The results are compared with a non-substituted material La5.4WO12−δ. A structural model established earlier for lanthanum tungstates and Re-substituted lanthanum tungstates is confirmed, according to which the Wyckoff site shared by La and W is split with half site occupancies (Fm\bar 3m space group, 48h site) and also accommodates Mo atoms. Substitution of W by up to 20 mol% Mo does not change the face-centred cubic lattice: Mo atoms substitute W statistically on both 4a and 48h Wyckoff sites of the crystal structure, which is described by the Fm\bar 3m space group. These results were obtained from the combination of the average neutron-scattering length and average X-ray scattering power procedures with electron-probe micro-analysis. The temperature dependence of bond lengths in dry and wet (D2O) conditions shows that vacant oxygen sites are located on the 32f Wyckoff sites also in Mo-substituted lanthanum tungstates, and that the bond lengths between La on 4b and O on 32f increase with increasing pO2 and pD2O, reflecting the filling of oxygen vacancies and the increase in coordination of La on 4b.

LiquidLib: A comprehensive toolbox for analyzing classical and ab initio molecular dynamics simulations of liquids and liquid-like matter with applications to neutron scattering experiments

Neutron scattering is a powerful experimental technique for characterizing the structure and dynamics of materials on the atomic or molecular scale. However, the interpretation of experimental data from neutron scattering is oftentimes not trivial, partly because scattering methods probe ensemble-averaged information in the reciprocal space. Therefore, computer simulations, such as classical and ab initio molecular dynamics, are frequently used to unravel the time-dependent atomistic configurations that can reproduce the scattering patterns and thus assist in the understanding of the microscopic origin of certain properties of materials. LiquidLib is a post-processing package for analyzing the trajectory of atomistic simulations of liquids and liquid-like matter with application to neutron scattering experiments. From an atomistic simulation, LiquidLib provides the computation of various statistical quantities including the pair distribution function, the weighted and unweighted structure factors, the mean squared displacement, the non-Gaussian parameter, the four-point correlation function, the velocity auto correlation function, the self and collective van Hove correlation functions, the self and collective intermediate scattering functions, and the bond orientational order parameter. LiquidLib analyzes atomistic trajectories generated from packages such as LAMMPS, GROMACS, and VASP. It also offers an extendable platform to conveniently integrate new quantities into the library and integrate simulation trajectories of other file formats for analysis. Weighting the quantities by element-specific neutron-scattering lengths provides results directly comparable to neutron scattering measurements. Lastly, LiquidLib is independent of dimensionality, which allows analysis of trajectories in two, three, and higher dimensions. The code is beginning to find worldwide use. Program summaryProgram Title: LiquidLibProgram Files doi:http://dx.doi.org/10.17632/tyggwp7656.1Licensing provisions: GNU Lesser General Public License v3.0Programming language: C++Supplementary material: User manual of the package.External routines/libraries: BOOST (optional), GSL (optional), xdrfilelib (optional, available at ftp.gromacs.org/pub/contrib/xdrfile-1.1.1.tar.gz)Nature of problem: LiquidLib is a post-processing package for analyzing the trajectory of atomistic simulations of liquids and liquid-like matter with application to neutron scattering experiments.Solution method: We provide a collection of executables to compute statistical quantities relevant to the structure and dynamics of liquids and liquid-like matter from the simulation trajectories. Furthermore, the option to weigh the quantities by element-specific neutron-scattering lengths provides results comparable to neutron scattering measurements. The quantities computable by LiquidLib include the pair distribution function, the weighted and unweighted structure factors, the mean squared displacement, the non-Gaussian parameter, the four-point correlation function, the velocity auto correlation function, the self and collective van Hove correlation functions, the self and collective intermediate scattering functions, and the bond orientational order parameter. LiquidLib can directly read trajectories of file types .xyz, .xtc, .trr, .atom, .dump, .gro, and XDATCAR.Additional comments: Each computable quantity in LiquidLib is defined as a derived class, and has its own respective executable. Thus, LiquidLib is extendable to compute other quantities not already offered in the current version. Similarly, LiquidLib is extendable to handle simulation trajectory files with formats not already offered in the current version.Restrictions: LiquidLib reads in the complete simulation trajectory into the memory at the start of runtime. Thus, if the trajectory size is larger than the available memory of the computer, LiquidLib will fail to execute properly. In this case, the user must reduce the size of the trajectory to be read in before LiquidLib can analyze the trajectory successfully.Unusual features: We provide the option to weigh the computed quantities by the element-specific respective coherent or incoherent scattering lengths. Therefore, LiquidLib allows direct comparisons of the computed quantities to neutron scattering experiments. In addition, the dimension of the simulation trajectories can be any positive integer.

Search for long-range force between a neutron and an atom with a trap of ultracold neutrons

A method of using a gravitational ultracold neutron (UCN) spectrometer for the search for long-range forces between neutrons and atoms is proposed. The constraints on the strength of long-range forces within the range of 10${}^{\ensuremath{-}10}$--10${}^{\ensuremath{-}4}$ cm can be obtained from experiments on measurements of the total cross section of the interaction of UCN with atoms of noble gases (He, Ne, Ar, Kr) and data on the coherent neutron-scattering length of the nucleus. The first result of such an analysis is presented. Further prospects for the UCN method are discussed.

The structure of the rare-earth phosphate glass(Sm2O3)0.205(P2O5)0.795 studied by anomalous dispersion neutron diffraction

The role of the Sm3+ ions inthe structure of vitreous Sm2O3·4P2O5 has been investigated using the neutron diffraction anomalous dispersion technique, whichemploys the wavelength dependence of the real and imaginary parts of the neutronscattering length close to an absorption resonance. The data described here represent thefirst successful complete neutron anomalous dispersion study on an amorphous material.This experimental methodology permits one to determine exclusively the closest separation. Knowledge of the (R = rare-earth) pairwise correlation is key to understanding the optical and magnetic propertiesof rare-earth phosphate glasses. The anomalous difference correlation function,ΔT′′(r), shows a dominant feature pertaining to a separation, centred at 4.8 Å. The substantial width and markedasymmetry of this peak indicates that the minimum approach ofSm3+ ions could be as close as 4 Å. Information on other pairwise correlations is also revealed via analysis ofT(r) andΔT(r) correlationfunctions: Sm3+ ions display an average co-ordination number,nSm(O), of 7, with a mean Sm–O bond length of 2.375(5) Å whilst thePO4 tetrahedra have a mean P–O bond length of 1.538(2) Å. Second- and third-neighbourcorrelations are also identified. These results corroborate previous findings. Suchconsistency lends support to the application of the anomalous dispersion technique todetermine separations.

Measurement of the Coherent Neutron Scattering Length of (3) He.

By means of neutron interferometry the s-wave neutron scattering length of the (3)He nucleus was re-measured at the Institut Laue-Langevin (ILL). Using a skew symmetrical perfect crystal Si-interferometer and a linear twin chamber cell, false phase shifts due to sample misalignment were reduced to a negligible level. Simulation calculations suggest an asymmetrically alternating measuring sequence in order to compensate for systematic errors caused by thermal phase drifts. There is evidence in the experiment's data that this procedure is indeed effective. The neutron refractive index in terms of Sears' exact expression for the scattering amplitude has been analyzed in order to evaluate the measured phase shifts. The result of our measurement, b' c = (6.000 ± 0.009) fm, shows a deviation towards a greater value compared to the presently accepted value of b' c = (5.74 ± 0.07) fm, confirming the observation of the partner experiment at NIST. On the other hand, the results of both precision measurements at NIST and ILL exhibit a serious 12σ (12 standard uncertainties) deviation, the reason for which is not clear yet.

Neutron diffraction from thermally fixed gratings in photorefractive lithium niobate crystals

Iron-doped lithium niobate crystals are illuminated with a sinusoidal light pattern (period length 374 nm) at a temperature of about 180 \ifmmode^\circ\else\textdegree\fi{}C. Electrons are redistributed and ions drift in the electronic space-charge pattern (``thermal fixing''). At room temperature the ions are almost immobile. A density grating (space-charge field plus inverse-piezoelectric effect) and the ionic grating yield a refractive-index modulation for neutrons (``photorefractive effect''). Neutrons (wavelength 1.39 nm) are diffracted from this grating with an efficiency up to $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}.$ Usually hydrogen ions form the ionic grating. The ions responsible for charge compensation in dehydrated crystals have a much smaller coherent neutron-scattering length and might be identified as lithium.

Precision neutron-interferometric measurement of the coherent neutron-scattering length in silicon

The neutron-interferometry (NI) technique provides a precise and direct way to measure the bound, coherent scattering lengths $b$ of low-energy neutrons in solids, liquids, or gases. The potential accuracy of NI to measure $b$ has not been fully realized in past experiments, due to systematic sources of error. We have used a method which eliminates two of the main sources of error to measure the scattering length of silicon with a relative standard uncertainty of 0.005%. The resulting value, $b=4.1507(2)\mathrm{fm},$ is in agreement with the current accepted value, but has an uncertainty five times smaller.

SANS provides unique information on the structure and function of biological macromolecules in solution

Since neutrons are sensitive to the positions of the light elements such as H, C, N and O, which are of central importance to all biological systems, SANS can provide unique information on the structure and function of biological macromolecules. Particularly powerful is the contrast variation technique, in which the isotopic substitution of D for H is routinely used to change the scattering from a macromolecule without affecting its biochemistry. Often, this substitution is as simple as using D 2O instead of H 2O in the solvent in order to increase the contrast between molecule and solvent and to decrease the background due to incoherent scattering from H. In complexes comprised of two components with different neutron-scattering length densities, the scattering from one component can be separated from that of the other by measuring the complex in solvents with different H 2O/D 2O ratios. This provides unique structural information about each component individually, as it is interacting with the other in the complex. The role of SANS in providing unique structural information is illustrated using several examples of recent experiments.

Direct measurement of the magnetic field penetration depth in YBa 2Cu 3O 7 superconducting films by polarized neutron reflectometry

A study of the magnetic field penetration depth in a high-temperature (HT c) superconducting film was performed with polarized neutron reflectometry in two scattering geometries. The fit to the reflectivity curves yielded the neutron-scattering length density profile and thus a precise image of the composition of the film. The film had a good quality seen by a not noticeable off-specular scattering. The fit to the spin asymmetry gave a magnetic-penetration depth of 1350 ± 150 A ̊ along the c-axis at a temperature T = 2 K. The model included an intrinsic exponential decay of the penetration depth. For the first time the spin asymmetry was determined with high resolution over an extended Q-range for a HT c-film.

Toward the solution of the inverse problem in neutron reflectometry

We show that the chemical depth profile of a film of unknown structure can be retrieved unambiguously from neutron reflection data by adding to the system a known magnetic layer. Three independent reflectivities are obtained by taking measurements with the sample magnetized in a magnetic field perpendicular to the surface and subsequently parallel to it, and using in the latter geometry neutrons polarized either in the direction of the field or opposite to it. The procedure consists of two steps. First, from the three reflectivities both the real and imaginary parts of the reflection coefficient of the unknown film are extracted within the framework of the rigorous dynamical theory. Second, the neutron scatteringlength density (and consequently the chemical depth profile) is obtained by a suitable numerical technique for the conventional Schrödinger inverse scattering problem. Computer experiments were conducted for selected cases: starting from the profiles the reflectivities were calculated in a limited range of q and then the original profiles were successfully recovered. The influence on the accuracy of the recovered depth profile of the counting statistics and the cutoffs at low and high q are discussed.

Mixing of Alkanes with Surfactant Monolayers in Microemulsions

The internal structure of water-in-oil microemulsion droplets has been studied by small-angle neutron scattering (SANS). Dichained surfactants with different tail structures were investigated: synthetic phosphatidylcholines, dialkyldimethylammonium bromides, and Aerosol-OT. The oil was cyclohexane, but for AOT n-heptane was used. The data from core−shell−drop neutron contrast series were globally analyzed to investigate the possibilities that water and/or oil penetrates the curved surfactant film. Three different models for the interfacial structure were tested: sharp-step as well as linear or exponential changes in neutron-scattering length density. Penetration of water was not detected. For phosphatidylcholine and n-octadecyl-n-dodecyldimethylammonium bromide layers, the SANS data were most consistent with a volume fraction of cyclohexane ΦC6D12 between about 0.05 and 0.20. However, for DDAB and AOT there was no clear evidence for any significant oil mixing. These results indicate that the extent of alkane penetration into such negatively curved monolayers depends somewhat on the surfactant alkyl chain structure.

Low-resolution structure of the complex of human blood platelet factor 4 with heparin determined by small-angle neutron scattering

Small-angle neutron scattering was used to confirm that human platelet factor 4 was a compact tetrameric globular protein of radius of gyration 1.74 nm and indistinguishable from a sphere. The same technique, when applied to the 1:1 mol/mol complex of platelet factor and heparin of M r 14 000, revealed that the radius of gyration of the particle varied, depending on the relative proportion of 2H 2O to H 2O in the solvent. Analysis of this variation by the method of Ibel and Stuhrmann (Ibel, K. and Sturhmann, H.B. (1975) J. Mol. Biol. 93, 255–266) revealed that in the complex the material of greatest neutron-scattering length (the highly sulphated polysaccharide heparin) was furthest from the centre of the particle. This confirms the postulate of Luscombe and Holbrook (Luscombe, M.; Holbrook, J.J. (1983) in Glycoconjugates (Chester, A.M., Heingård, D., Lundblad, A. and Svensson, S., eds), pp. 818–819, Secretaria, Lund) that the exact 1:1 mole ratio of heparin ( M r > 10 000) to platelet factor in this stable complex arises from the heparin winding around the outside of a globular protein core. Proteoglycan; (Human blood)

Structure of phthalocyaninatocobalt(II) at 4.3 K: a neutron-diffraction study

The crystal and molecular structure of the β-polymorphic form of phthalocyaninatocobaIt(II), [Co(pc)], has been determined by single-crystal neutron-diffraction methods at 4.3 K. Crystals are monoclinic, space group P21/c, with a= 14.495(5), b= 4.742(4), c= 19.107(5)Å, β= 120.76(2)°, and Z= 2. Automatic diffractometry has provided Bragg intensities for 1 261 independent reflections. Data are of limited resolution along the b axis direction (hkl with k⩽ 2). The structure has been refined by full-matrix least-squares methods to R 0.031. Bond lengths at 4.3 K show systematic deviations from those determined at 295 K by X-ray diffraction data of moderate resolution. This is explained primarily in terms of errors in the X-ray determined atomic positions due to the effects of asphericity of the valence electrons, with thermal motion at 295 K having only a small effect. Within the central cavity of the macrocyclic phthalocyaninate ligand, the cobalt atom co-ordinates to a precisely planar array of nitrogen atoms, with Co–N bond lengths 1.908(2) and 1.915(2)Å at 4.3 K which differ significantly from the values obtained at 295 K by X-ray diffraction. The neutron-scattering length of cobalt has been found by least-squares refinement to be 0.252(7)× 10–l2 cm.

Neubestimmung der Neutronenstreuamplitude von Zink

By means of neutron diffraction by a mixture of zinc and nickel powder the neutronscattering length of zinc has been redetermined, resulting in a value of (0,573±0,01)·10−12 cm.

Neutron Scattering Lengths

The schematic treatment of nuclear reactions is applied to the case ${E}_{n}\ensuremath{\rightarrow}0$ as a means of interpreting measurements of the scattering length $a$. It is found that the quantity $\ensuremath{\Delta}=(a\ensuremath{-}R)$ rather than $a$ is significant for determining the resonance properties of the compound nucleus, where $R$ is the phenomenological nuclear radius. In some cases this treatment can resolve ambiguity in the evaluation of $a$ without the necessity of polarization measurements and assign the $J$ value of a low-lying resonance or two, but it can only be used successfully for separated isotopes. For practically pure isotopes it can be used to determine rough values of level spacing $D$ from the measured position of the levels nearest ${E}_{n}=0$, or conversely. Values of $D$ obtained in this way are plotted against $A$ to yield an estimate of a parameter in the statistical formula for level density; this estimate suggests a somewhat more rapid increase in level spacing with decreasing excitation than given by the simplest statistical formula.