Values Of Momentum Transfer Research Articles

Results of an analytic calculation for the coherent atomic scattering factor for the ground state of the helium isoelectronic sequence

The analytical method developed by the authors for the determination of the expectation value of single-particle operators W = Σi W(ri) correct to second order is employed to obtain an analytic expression for the coherent atomic scattering factor F(k) for the ground state of the helium isoelectronic sequence valid for all values of momentum transfer. The trial wave function ϕot employed is an energy minimized Hartree product of hydrogenic states. For helium the results for the form factor are within 1.2% of the highly accurate values calculated using a 120 parameter configuration interaction wave function and have an accuracy equivalent to that of an analytical Hartree-Fock treatment. This error is further reduced as the atomic number is increased. The calculations are extended to the infinite momentum transfer range and the accuracy of the results are studied in this limit by employing the Kato electron-nucleus cusp condition for the exact ground state wave function of two-electron atomic systems. We observe that in the infinite momentum transfer limit our results for helium are in error by 0.57% and that this error is further diminished for each successive element of the isoelectronic sequence. In addition, we note that the cusp condition is exactly satisfied and is independent of the variational parameter employed in the trial wave function.

X-ray scattering signatures of β-thalassemia

X-ray scattering from lyophilized proteins or protein-rich samples is characterized by the presence of two characteristic broad peaks at scattering angles equivalent to momentum transfer values of 0.27 and 0.6 nm −1, respectively. These peaks arise from the interference of coherently scattered photons. Once the conformation of a protein is changed, these two peaks reflect such change with considerable sensitivity. The present work examines the possibility of characterizing the most common cause of hemolytic anaemia in Egypt and many Mediterranean countries; β-thalassemia, from its X-ray scattering profile. This disease emerges from a genetic defect causing reduced rate in the synthesis of one of the globin chains that make up hemoglobin. As a result, structurally abnormal hemoglobin molecules are formed. In order to detect such molecular disorder, hemoglobin samples of β-thalassemia patients are collected, lyophilized and measured using a conventional X-ray diffractometer. Results show significant differences in the X-ray scattering profiles of most of the diseased samples compared to control. The shape of the first scattering peak at 0.27 nm −1, in addition to the relative intensity of the first to the second scattering peaks, provides the most reliable signs of abnormality in diseased samples. The results are interpreted and confirmed with the aid of Fourier Transform Infrared (FTIR) spectroscopy of normal and thalassemia samples.

Multiple-element spectrometer for non-resonant inelastic X-ray spectroscopy of electronic excitations

A multiple-analyser-crystal spectrometer for non-resonant inelastic X-ray scattering spectroscopy installed at beamline ID16 of the European Synchrotron Radiation Facility is presented. Nine analyser crystals with bending radii R = 1 m measure spectra for five different momentum transfer values simultaneously. Using a two-dimensional detector, the spectra given by all analysers can be treated individually. The spectrometer is based on a Rowland circle design with fixed Bragg angles of about 88 degrees . The energy resolution can be chosen between 30-2000 meV with typical incident-photon energies of 6-13 keV. The spectrometer is optimized for studies of valence and core electron excitations resolving both energy and momentum transfer.

Anomalous Thermal Expansion of Cuprites: A Combined High Resolution Pair Distribution Function and Geometric Analysis

The temperature-dependent local structures of cuprites (M2O for M = CuI, AgI) have been probed using variable-temperature (80−500 K) high-resolution pair distribution function (PDF) analysis of X-ray scattering data measured to very high values of momentum transfer (Qmax = 35 Å−1). These noble metal oxides exhibit negative thermal expansion (NTE) behavior; however, several unusual structural features and behaviors distinguish the cuprites from other NTE frameworks—the structure is inverted relative to conventional NTE frameworks and Cu2O (but not Ag2O) shows an unusual transition from negative to positive thermal expansion behavior at higher temperature—thus motivating the present in-depth analysis of the particular thermal expansion mechanisms operating here. By coupling the local structural information from the PDFs with known geometric identities of the tetrahedra that form the framework, distortions contributing to NTE have been identified and the contrasting high temperature behaviors of the two isostructural analogues have been accounted for. Specifically, we demonstrate that thermal population of low-energy vibrational modes involving the dynamic distortion of the OM4 tetrahedra, away from the regular tetrahedral geometry (through M−O−M′ bending), can induce a contraction of the average tetrahedral edge length (M···M′) and thus contribute to the NTE effect. This mechanism operates in combination with the transverse vibrational mechanism found in conventional NTE frameworks, where increasing transverse displacement of the bridging atom (O−M−O′) draws corner-bridged polyhedra closer together.

Dispersion and Damping of Gold Surface Plasmon

High-resolution electron energy loss spectroscopy was used to investigate the surface plasmon dispersion in (111)-oriented Au films grown on Cu(111). The measured dispersion of the plasmon mode was positive, as found for Ag. The centroid of the induced charge associated to the plasmon field lies well inside the jellium edge. The damping relation of the Au surface plasmon presented a critical wave vector of 0.11 A−1. For higher values of the parallel momentum transfer, the line width of Au surface plasmon considerably increased as a consequence of the opening of a new decay channel via single-particle transitions.

Relativistic Hamiltonian dynamics and few-nucleon systems

We present a preliminary calculation of the electromagnetic form factors of 3He and 3H, performed within the light-front Hamiltonian dynamics. Relativistic effects show their relevance even at the static limit, increasing at higher values of momentum transfer, as expected.

Sea-quark effects in the pion charge form factor

It is shown that the data on the pion charge form factor admit the possibility for a substantial sea-quark component in the pion wave function. If the charge form factor is calculated with instant form kinematics in a constituent quark model that is extended to include explicit $(q\overline{q}){}^{2}$ components in the pion wave function, that component will give the dominant contribution to the calculated ${\ensuremath{\pi}}^{+}$ charge form factor at large values of momentum transfer. The present experimental values ${Q}^{2}$ can be described fairly well with $(q\overline{q}){}^{2}$ component admixtures of up to 50%. The sensitivity of the calculated ${\ensuremath{\pi}}^{+}$ charge form factor to whether one of the quarks or one of the antiquarks is taken to be in the $P$ state is small.

Structure study of multi-component borosilicate glasses from high-Q neutron diffraction measurement and RMC modeling

A neutron diffraction structure study has been performed on multi-component borosilicate glasses with compositions (65−x)SiO2·xB2O3·25Na2O·5BaO·5ZrO2, x=5–15mol%. The structure factor has been measured up to a rather high momentum transfer value of 30Å−1, which made high r-space resolution available for real space analyses. Reverse Monte Carlo simulation was applied to calculate the partial atomic pair correlation functions, nearest neighbor atomic distances and coordination number distributions. The Si–O network consists of tetrahedral SiO4 units with characteristic first neighbor distances at rSi–O=1.60Å and rSi–Si=3.0Å. The boron environment contains two well-resolved B–O distances at 1.40 and 1.60Å and both 3- and 4-fold coordinated B atoms are present. A chemically mixed network structure is proposed including [4]B–O–[4]Si and [3]B–O–[4]Si chain segments. The O–O and Na–O distributions suggest partial segregation of silicon and boron rich regions. The highly effective ability of Zr to stabilize glassy and hydrolytic properties of sodium-borosilicate materials is interpreted by the network-forming role of Zr ions.

External momentum, volume effects, and the nucleon magnetic moment

We analyze the determination of volume effects for correlation functions that depend on an external momentum. As a specific example, we consider finite volume nucleon current correlators, and focus on the nucleon magnetic moment. Because the multipole decomposition relies on $SO(3)$ rotational invariance, the structure of such finite volume corrections is unrelated to infinite volume multipole form factors. One can deduce volume corrections to the magnetic moment only when a zero-mode photon coupling vanishes, as occurs at next-to-leading order in heavy baryon chiral perturbation theory. To deduce such finite volume corrections, however, one must assume continuous momentum transfer. In practice, volume corrections with momentum transfer dependence are required to address the extraction of the magnetic moment, or other observables that arise in momentum-dependent correlation functions. Additionally, we shed some light on a puzzle concerning differences in lattice form factor data at equal values of momentum transfer squared.

An Investigation of Water Dynamics in Binary Mixtures of Water and Dimethyl Sulfoxide

The motion of water molecules in mixtures of water and d6-dimethyl sulfoxide (DMSO) has been explored through molecular dynamics (MD) simulations using the SPC/E water model (J. Chem. Phys. 1987, 91, 6269) and the P2 DMSO model (J. Chem. Phys. 1993, 98, 8160). We evaluate the self-intermediate scattering functions, FS(Q,t), which are related by a Fourier transform to the incoherent structure factors, S(Q,omega), measured in quasielastic neutron scattering (QNS) experiments. We compare our results to recent QNS experiments on these mixtures reported by Bordallo et al. (J. Chem. Phys. 2004, 121, 12457). In addition to comparing the MD data to the experimental signals, which correspond to a convolution of S(Q,omega) with a resolution function, we examine the rotational and translational components of FS(Q,t) and investigate to what extent simulation results for the single-molecule dynamics follow the dynamical models that are used in the analysis of the experimental data. We find that the agreement between the experimental signal and the MD data is quite good and that the portion of FS(Q,t) due to translational dynamics is well represented by the jump-diffusion model. The model parameters and their composition dependence are in reasonable agreement with experiment, exhibiting similar trends in water mobility with composition. Specifically, we find that water motion is less hindered in water-rich and water-poor mixtures than it is near equimolar composition. We find that the extent of coupling between rotational and translational motion contributing to FS(Q,t) increases as the equimolar composition of the mixture is approached. Thus, the decoupling approximation, which is used to extract information on rotational relaxation from QNS spectra at higher momentum transfer (Q) values, becomes less accurate than that in water-rich or DMSO-rich mixtures. We also find that rotational relaxation deviates quite strongly from the isotropic rotational diffusion model. We explore this issue further by investigating the behavior of orientational time correlations for different unit vectors and corresponding to Legendre polynomials of orders 1-4. We find that the rotational time correlations of water molecules behave in a way that is more consistent with the extended jump rotation model recently proposed by Laage and Hynes (Science 2006, 311, 832).

High-resolution investigation of the 121Sb(p,t)119Sb reaction and quasiparticle–phonon model description

The 121Sb(p,t)119Sb reaction has been measured in a high-resolution experiment at an incident energy of 21 MeV. Accurate measurement of the (p,t) reaction angular distributions for the transitions to the levels of 119Sb allows us to determine energies of 59 levels, 23 of which have been identified for the first time, and to assign the angular momentum transfer values and a well-defined range for the J values. DWBA analysis has been performed in a finite-range approximation, assuming a dineutron cluster pickup mechanism, by using conventional Woods–Saxon potentials for the entrance proton and exit triton channel. The present (p,t) data have been supplemented by microscopic calculations in the framework of the quasiparticle–phonon model, giving a reasonably good description of the experimental fragmentation of the integrated cross sections and the absence of (p,t) strength above 2.9 MeV.

B-meson to light-meson transition form factors

We report a comprehensive set of results for B-meson heavy-to-light transition form factors calculated using a truncation of, and expression for, the transition amplitudes in which all elements are motivated by the study of Dyson-Schwinger equations in QCD. In this relativistic approach, which realizes confinement and dynamical chiral symmetry breaking, all physical values of momentum transfer in the transition form factors are simultaneously accessible. Our results can be useful in the analysis and correlation of the large body of data being accumulated at extant facilities, and thereby in probing the standard model and beyond.

Relativistic calculation of deuteron threshold electrodisintegration at backward angles

The threshold electrodisintegration of the deuteron at backward angles is studied in instant form Hamiltonian dynamics, including a relativistic one-pion-exchange potential (OPEP) with off-shell terms as predicted by pseudovector coupling of pions to nucleons. The bound and scattering states are obtained in the center-of-mass frame, and then boosted from it to the Breit frame, where the evaluation of the relevant matrix elements of the electromagnetic current operator is carried out. The latter includes, in addition to one-body, also two-body terms due to pion exchange, as obtained, consistently with the OPEP, in pseudovector pion-nucleon coupling theory. In order to estimate the magnitude of the relativistic effects we perform, for comparison, the calculation with a nonrelativistic phase-equivalent Hamiltonian and consistent one-body and two-body pion-exchange currents. Our results for the electrodisintegration cross section show that, in the calculations using one-body currents, relativistic corrections become significant (i.e., larger than 10%) only at high momentum transfer $Q$ (${Q}^{2}\ensuremath{\simeq}40$ fm${}^{\ensuremath{-}2}$ and beyond). However, the inclusion of two-body currents makes the relativistic predictions considerably smaller than the corresponding nonrelativistic results in the ${Q}^{2}$ region (18--40) fm${}^{\ensuremath{-}2}$. The calculations based on the relativistic model also confirm the inadequacy, already established in a nonrelativistic context, of the present electromagnetic current model to reproduce accurately the experimental data at intermediate values of momentum transfers.

The temperature dependent collective dynamics of liquid Rubidium

Liquids alkali metals show near the melting point at small momentum transfer values an upward bending of the dispersion relation. This so-called positive dispersion can be described within generalised hydrodynamics as a visco-elastic reaction of the liquid. There is a speculation that long-living clusters could be the physical reason behind this phenomenon. To shed light on this question a coherent inelastic neutron scattering experiment on liquid Rubidium was performed at four temperatures starting at the melting point. Distinct deviations from molecular dynamics simulation results occur at the lowest accessible momentum transfer values. With rising temperature the excitation frequencies soften at a momentum transfer value which is correlated with the dimensions of the supposed clusters.

Limitations of the distorted-wave impulse approximation in describing the energy dependence of theB10(n,p)Be10(g.s.) reaction

We report differential cross section measurements for the stretched transition from the $^{10}\mathrm{B}$ ground state (${J}^{\ensuremath{\pi}}={3}^{+}$) to the $^{10}\mathrm{Be}$ ground state (${J}^{\ensuremath{\pi}}={0}^{+}$) in the $^{10}\mathrm{B}$($n,p$)$^{10}\mathrm{Be}$ (g.s.) reaction. These data were obtained over the energy range from 70 to 240 MeV, covering momentum transfer values from 0.6 to 2.5 fm${}^{\ensuremath{-}1}$. In this momentum transfer range, the isovector tensor effective interaction dominates the transition. Cross sections are compared to zero- and finite-range distorted wave impulse approximation calculations using modern free and density-dependent effective interactions and a transition density consistent with ($e,{e}^{'}$) data. Good agreement is observed at energies above 120 MeV, but below this energy the cross sections are larger than the calculated values by more than 40%. The implications for DWIA calculations are discussed.

Superscaling in electroweak excitation of nuclei

Superscaling properties of $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, and $^{40}\mathrm{Ca}$ nuclear responses, induced by electron and neutrino scattering, are studied for momentum transfer values between 300 and 700 MeV/$c$. We have defined two indexes to have quantitative estimates of the scaling quality. We have analyzed experimental responses to get the empirical values of the two indexes. We have then investigated the effects of finite dimensions, collective excitations, meson exchange currents, short-range correlations, and final state interactions. These effects strongly modify the relativistic Fermi gas scaling functions, but they conserve the scaling properties. We used the scaling functions to predict electron and neutrino cross sections and we tested their validity by comparing them with the cross sections obtained with a full calculation. For electron scattering we also made a comparison with data. We have calculated the total charge-exchange neutrino cross sections for neutrino energies up to 300 MeV.

In-situ GISAXS on Nanocomposite Films of CdS Nanoparticles and Polymers

AbstractWe investigated the growth of CdS nanoparticles in polymer films by means of ex-situ and in-situ x-ray scattering experiments using synchrotron radiation. The CdS nanoparticles were synthesized by thermal decomposition of a Cd thiolate precursor dispersed in a cyclic olefin copolymer. The films were deposited by spin coating. Grazing incidence diffraction (GID) reveals the Bragg reflections of the CdS nanoparticles. In-situ diffraction and grazing incidence small angle scattering (GISAXS) experiments were recorded during the thermal treatment of the precursor/polymer films from room temperature up to 250°C. The diffraction curves show that the initial precursor structure is soon lost at 100°C. Correspondingly, the GISAXS data show a peak at a momentum transfer value q ∼ 0.2Å−1 that shifts towards smaller values with the temperature. Under UV excitation the films show photoluminescence in the range 400 – 700 nm.

X-ray optics for liquid surface/interface spectrometers

A new X-ray optics which enables precise structural investigations of liquid surfaces/interfaces is introduced. The new device is based on the use of high-energy microbeams and gives access to large momentum transfer values perpendicular to the liquid surface/interface. The performance of a prototype of this new optics, which has been constructed and implemented at the high-energy diffraction beamline ID15A at the European Synchrotron Radiation Source, is demonstrated.

Symmetrized correlation function for liquidpara-hydrogen using complex-time pair-product propagators

We present a simple and efficient method for calculating symmetrized time correlation functions of neat quantum fluids. Using the pair-product approximation to each complex-time quantum mechanical propagator, symmetrized correlation functions are written in terms of a double integral for each degree of freedom with a purely positive integrand. At moderate temperatures and densities, where the pair-product approximation to the Boltzmann operator is sufficiently accurate, the method leads to quantitative results for the early time part of the correlation function. The method is tested extensively on liquid para-hydrogen at 25 K and used to obtain accurate quantum mechanical results for the initial 0.2 ps segment of the symmetrized velocity autocorrelation function of this system, as well as the incoherent dynamic structure factor at certain momentum transfer values.

Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case

We present a double precision routine in Fortran for the precise and fast numerical evaluation of the two Master Integrals (MIs) of the equal mass two-loop sunrise graph for arbitrary momentum transfer in d = 2 and d = 4 dimensions. The routine implements the accelerated power series expansions obtained by solving the corresponding differential equations for the MIs at their singular points. With a maximum of 22 terms for the worst case expansion a relative precision of better than a part in 10 15 is achieved for arbitrary real values of the momentum transfer. Program summary Title of program: sunem Version: 1.0 Release: 1 Catalogue identifier: ADYC_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYC_v1_0 Program obtainable from: http://www-ttp.physik.uni-karlsruhe.de/Progdata/ Computers: all Operating system: all Program language used: FORTRAN77 No. of lines in distributed program, including test data, etc.:1080 No. of bytes in distributed program, including test data, etc.: 11 835 Memory required to execute: Size: 1532K No. of bits in a word: up to 32 No. of processors used: 1 Distribution format: tar.gz Other programs called: none External files needed: none Nature of the physical problem: Numerical evaluation of the two Master Integrals of the equal mass two-loop sunrise Feynman graph for arbitrary momentum transfer in d = 2 and d = 4 dimensions. Method of solution: Accelerated power series expansions obtained by solving the differential equations for the MIs at their singular points. With a maximum of 22 terms for the worse case expansion a relative precision of better than a part in 10 15 is achieved for arbitrary real values of the momentum transfer. Restrictions on complexity of the problem: Limited to real momentum transfer and equal internal masses. Typical running time: Approximately 1 μs to evaluate the four Master integrals for a fixed momentum transfer value on a Pentium IV/3 GHz Linux PC.