Experimental Form Factors Research Articles

Moments of the Charge Distribution Observed through Electron Scattering in 3H and 3He

Abstract The moments of the charge distributions obtained by the sum-of-Gaussians (SOG) analysis of electron-scattering data are examined in $^3$H and $^3$He, together with those obtained by the Fourier–Bessel (FB) analysis. The SOG and FB methods reproduce well the experimental form factors available at present, but provide different charge distributions from each other. As a result, they do not yield the same values of the moments of the charge distribution, although their analyses are called “model-independent.” The moments are sensitive to the tail of the charge distribution. The present experimental data are not enough for SOG and FB analyses to determine with reasonable accuracy the shape of the tails, in a quantum mechanical point of view. New, accurate experimental data at small momentum transfer squared less than 0.1 fm$^{-2}$ are desired.

Molecular form factor data for tissue equivalent materials

In the diagnostic X-ray energy range, elastic (Coherent) scattering is dominant and can be obtained using an appropriate form factor. When experimental Form Factor data is not available at certain momentum transfer values, molecular form factor data that can be compatible with experimental data should be theoretically obtained. Using these molecular form factor data, molecular coherent scattering coefficients can be calculated, and linear attenuation coefficients of tissue equivalent structures can be estimated. In this study, PMMA, CIRS 70/30, CIRS 50/50, CIRS 30/70, RMI 454, and BR 12, which are equivalent complex molecular structures to human breast tissue, were examined, and the theoretical molecular form factor F(x) values compatible with the experimental form factor values for each were obtained. We believe that our results will find a significant place in the literature and will be beneficial for our future studies and also in the studies of other researchers who make models.

Chiral sum rule on the light front and the 3D image of the pion

The lightest meson, the pion, features two faces – one is the elementary Goldstone boson of QCD and the other is the structured bound state of quarks and gluons. To accommodate both in a single light-front wave function in the valence space, we obtain a sum rule by analyzing the conserved axial-vector current and the general structures of the wave functions. Using an analytic model motivated by holography, we show this sum rule is consistent with requirements of chiral symmetry breaking in AdS/QCD. Within this model, we find a remarkable feature of the pion, namely that the density is mostly uniform inside its radius; furthermore, we obtain good agreement with the experimental pion form factor at spacelike momenta.

Low-Energy Quark Mass Test for U and D via Elastic Form Factors

Abstract The study was aimed at providing a device to estimate the range of values of the u- and d-quark masses through the elastic ep-scattering form factors at the low energy regime. ROOT generated dcsep data sets, from theoretical and experimental form factors, were compared to modified dcseq and their intersections were determined from the average of a total of 3000 events for each dcs at various scattering angles selected randomly from 0° to 180°. The proton mass was required as a parameter used in the relativistic recoil factor of dcseq to shift its distribution closer to dcsep thereby attaining the critical intersections. For quarks carrying effective masses, the extrapolated energy intersection of dcsep generated from the average of all form factors with the modified dcseu is 226.00013MeV 2 and this is lesser than that of the modified dcsed at 1093.00004MeV 2 with bin size of 1MeV 2 and their respective dcs intersections are 10.07049x10-4 and 0.36976x10-4, in barns. Summary of results are also given for quark masses derived from MS scheme and Lattice QCD. By considering all possible scattering angles at fixed transfer momentum, the relativistic recoil factor was treated as a constant that shifted the distribution and gave rise to a tool in estimating quark mass range.

Molecular Structure of Sphingomyelin in Fluid Phase Bilayers Determined by the Joint Analysis of Small-Angle Neutron and X-ray Scattering Data.

We have determined the fluid bilayer structure of palmitoyl sphingomyelin (PSM) and stearoyl sphingomyelin (SSM) by simultaneously analyzing small-angle neutron and X-ray scattering data. Using a newly developed scattering density profile (SDP) model for sphingomyelin lipids, we report structural parameters including the area per lipid, total bilayer thickness, and hydrocarbon thickness, in addition to lipid volumes determined by densitometry. Unconstrained all-atom simulations of PSM bilayers at 55 °C using the C36 CHARMM force field produced a lipid area of 56 Å2, a value that is 10% lower than the one determined experimentally by SDP analysis (61.9 Å2). Furthermore, scattering form factors calculated from the unconstrained simulations were in poor agreement with experimental form factors, even though segmental order parameter (SCD) profiles calculated from the simulations were in relatively good agreement with SCD profiles obtained from NMR experiments. Conversely, constrained area simulations at 61.9 Å2 resulted in good agreement between the simulation and experimental scattering form factors, but not with SCD profiles from NMR. We discuss possible reasons for the discrepancies between these two types of data that are frequently used as validation metrics for molecular dynamics force fields.

Studying the influence of short-range correlation of two-Body for heavy nuclei at high-energy electron scattering

Systematic expressions of the cluster expansion for one and two-body terms of elastic form factors and charge densities for 1g-2d shell nuclei with N≠Z (such as: 4292Mo,46104Pd,50118Sn,60142Nd,62152Smand64154Gd) are derived. Using the harmonic oscillator size parameter b and the correlation parameter β which creates from the Jastrow correlation function. Here, the parameters b and β are determined via the fitting to the experimental elastic form factors. The inserting of short-range correlations imitates the measured elastic form factors at the high momentum transfers (q ≥ 2 fm−1). It is seen that embedding this effect is important for obtaining an adjustment in the calculated elastic form factors which leads to defining the data of electron scattering well through all range of considered momentum transfers.

Scattering from colloidal cubic silica shells: Part II, static structure factors and osmotic equation of state

HypothesisThe shape of colloidal particles affects the structure of colloidal dispersions. The effect of the cube shape on the thermodynamics of colloidal cube dispersions has not yet been studied experimentally. Static light scattering measurements on colloidal cubic silica shells at finite concentrations allows us to measure the structure factor of colloidal cube fluids and to test theoretical predictions for the equation of state of hard convex superballs. ExperimentsHollow silica nanocubes of varying concentrations in N,N,-dimethylformamide were studied with static light scattering. The structure factor was extracted from the scattering curves using experimental form factors. From this experimental structure factor, the specific density of the particles, and the osmotic compressibility were obtained. This osmotic compressibility was then compared to a theoretical equation of state of hard superballs. FindingsThe first experimental structure factors of a stable cube fluid are presented. The osmotic compressibility of the cube fluid can be described by the equation of state of a hard superball fluid, showing that silica cubes in N,N,-dimethylformamide with LiCl effectively interact as hard particles.

NUCLEAR MOMENTUM DISTRIBUTION WITH FRACTIONAL OCCUPATION PROBABILITIES OF THE SURFACE ORBITS

Simplified expressions for calculating nucléon momentum distributions are derived in the context of the harmonic oscillator shell model and in its modification in which fractional occupation probabilities of the surface orbits are used. The method is applied to study the proton momentum distribution of the spherical nucleus 40Ca. The values of the partial occupation probabilities used had been previously determined by fitting to the experimental elastic form factor data.

Systematic study of the effect of short range correlations on the form factors and densities of s-p-d shell nuclei

Analytical expressions of the one- and two-body terms in the cluster expansion of the charge form factors and densities of the s-p and s-d shell nuclei with N=Z are derived. They depend on the harmonic oscillator parameter 6 and the parameter β which originates from the Jastrow correlation function. These expressions are used for the systematic study of the effect of short range correlations on the form factors and densities and of the mass dependence of the parameters ò and β. These parameters have been determined by fit to the experimental charge form factors. The inclusion of the correlations reproduces the experimental charge form factors at the high momentum transfers (q > 2 fm^-1). It is found that while the parameter β is almost constant for the closed shell nuclei, 4He, 16O and 40Ca, its values are larger (less correlated systems) for the open shell nuclei, indicating a shell effect in the closed shell nuclei.

The Location of the Hydrophobic Proteins SP-B and SP-C in Fluid-Phase Bilayers

Pulmonary surfactant is a mixture of lipids and proteins that lowers surface tension in the lungs. The material acts as a surfactant, forming a film on the liquid layer that lines the alveoli. Two hydrophobic proteins, the homodimeric SP-B and monomeric SP-C, are essential for surfactant function. SP-B, which accelerates adsorption of the surfactant lipids to form the interfacial film, belongs to the Saposin-like family of proteins, which adopt a saposin fold in the open or closed configuration. A model membrane containing a single lipid, dioleoyl phosphatidylcholine, allowed molecular dynamics simulation of the bilayer with each protein. Simulations considered SP-B in both the open and closed configuration, and SP-C as transmembrane or deeply buried in the hydrophobic region. X-ray diffuse scattering (XDS) provided experimental structural information. The experimental and simulated form factors agreed best with SP-B in the closed configuration, and SP-C in the hydrocarbon interior. XDS also provided structural information for bilayers of extracted calf surfactant, which contains the physiological mixture of lipids and proteins. The location of the proteins, determined by analyzing the data with the Scattering Density Profile program, again showed SP-B in the headgroup region of the bilayer and SP-C in the hydrocarbon interior. Electron density profiles with component groups, as well as dynamic snapshots from simulations, yielded a visual representation of where the proteins are located.

One-body density matrix and momentum distribution in s-p and s-d shell nuclei

Analytical expressions of the one- and two- body terms in the cluster expansion of the one-body density matrix and momentum distribution of the s-p and s-d shell nuclei with Ν — Ζ are derived. They depend on the harmonic oscillator parameter b and the parameter β which originates from the Jastrow correlation function. These parameters have been determined .by least squares fit to the experimental charge form factors. The inclusion of short-range correlations increases the high momentum component of the momentum distribution, 7i(k) for all nuclei we have considered while there is an A dependence of ra(k) both at small values of k and the high momentum component. The A dependence of the high momentum com- . ponent of n(k) becomes quite small when the nuclei 24Mg, 28Si and 32S are treated as ld-2s shell nuclei having the occupation probability of the 2s-state as an extra free parameter in the fit to the form factors

Scattering from colloidal cubic silica shells: Part I, particle form factors and optical contrast variation

HypothesisColloidal cubic silica shells, prepared from cuprous oxide cubes, with a typical size of 100 nm are promising model particles for scattering studies on dilute, as well as concentrated fluids, of non-spherical colloids. ExperimentsSmall angle X-ray scattering, and static light scattering are employed to determine form factors of cubic silica shells and silica covered cuprous oxide cubes. Contrast variation experiments are performed to assess the refractive index and optical homogeneity of the cubic silica shells, which is important for the extension of the scattering study to concentrated dispersions of cubic shells in Part II (Dekker, submitted for publication). ResultsThe experimental form factors, which compare well to theoretical form factors, manifest cubic silica shells that are dispersed as single stable colloids with a shape intermediate between a sphere and a perfect cube. Contrast variation demonstrates that the silica shells are optically homogeneous, with a refractive index that is independent of the shell thickness. The results presented here open up the possibility to extract structure factors from light scattering measurements on concentrated cube dispersions in Part II.

Model dependence of the pion form factor extracted from pion electroproduction

In 2008 the Jefferson Laboratory $F_\pi$ Collaboration released results for the pion electromagnetic form factor, which they extracted from pion electro-production data. The measured values for the pion form factor are model dependent, and require the use of the Vanderhaeghen, Guidal and Laget Regge Model for their extraction. While agreement between this model and data is impressive, the theoretical implementation of gauge invariance is less satisfying. We would like to establish how well the extracted form factor corresponds to the true form factor. To do this, we use a simple toy model, which imposes gauge invariance in a more theoretically satisfying way. The model form factor is extracted from our model cross section using the method employed by the $F_\pi$ Collaboration to extract the experimental pion form factor. We conclude that the reconstructed model form factor is a reasonable representation of the true model form factor for the kinematics chosen, although we note that the extracted form factor is smaller than the true form factor. This suggests that current extracted values of pion form factor may be overestimated.

Effects of tree age and waterlogging duration on the form factors of eastern cottonwood (Populus deltoides Bartr. ex Marsh.)

Abstract Stem form is the short name of the tree trunk shape. Stem form determines the quantity and quality of trunk volume, and affects forest timber volume and stand merchantable volume. Based on Populus deltoides Bartr. ex Marsh. in the Dongting Lake region of Hunan Province in China, changes in the breast-height form factor (f 1.3) and experimental form factor (f a) under different waterlogging durations and stand ages were analyzed using the two-way analysis of variance (ANOVA). The results showed that the differences in waterlogging duration for f 1.3 were not significant, but were significant for f a. Tree age has significant effects on f 1.3 and f a. In addition, the f a of P. deltoides grown in stands with a waterlogging duration of 24 days and 33 days were slightly larger than the other three 50, 64, 86 days, which indicated that trees grown in these stands (24, 33 days) had larger tree volumes. In addition, the waterlogging duration of longer than 86 days was not suitable for the growth of P. deltoides.

Reexamining the proton-radius problem using constrained Gaussian processes

Background: The "proton radius puzzle" refers to an eight-year old problem that highlights major inconsistencies in the extraction of the charge radius of the proton from muonic Lamb-shift experiments as compared against experiments using elastic electron scattering. For the latter, the determination of the charge radius involves an extrapolation of the experimental form factor to zero momentum transfer. Purpose: To estimate the proton radius by introducing a novel non-parametric approach to model the electric form factor of the proton. Methods: Within a Bayesian paradigm, we develop a model flexible enough to fit the data without any parametric assumptions on the form factor. The Bayesian estimation is guided by imposing only two physical constraints on the form factor: (a) its value at zero momentum transfer (normalization) and (b) its overall shape, assumed to be a monotonically decreasing function of the momentum transfer. Variants of these assumptions are explored to assess the impact of these constraints. Results: So far our results are inconclusive in regard to the proton puzzle, as they depend on both, the assumed constrains and the range of experimental data used. For example, if only low momentum-transfer data is used, adopting only the normalization constraint provides a value compatible with the smaller muonic result, while imposing only the shape constraint favors the larger electronic value. Conclusions: We have presented a novel technique to estimate the proton radius from electron scattering data based on a non-parametric Gaussian process. We have shown the impact of the physical constraints imposed on the form factor and of the range of experimental data used. In this regard, we are hopeful that as this technique is refined and with the anticipated new results from the PRad experiment, we will get closer to resolve of the puzzle.

Modelling realistic microgels in an explicit solvent

Thermoresponsive microgels are polymeric colloidal networks that can change their size in response to a temperature variation. This peculiar feature is driven by the nature of the solvent-polymer interactions, which triggers the so-called volume phase transition from a swollen to a collapsed state above a characteristic temperature. Recently, an advanced modelling protocol to assemble realistic, disordered microgels has been shown to reproduce experimental swelling behavior and form factors. In the original framework, the solvent was taken into account in an implicit way, condensing solvent-polymer interactions in an effective attraction between monomers. To go one step further, in this work we perform simulations of realistic microgels in an explicit solvent. We identify a suitable model which fully captures the main features of the implicit model and further provides information on the solvent uptake by the interior of the microgel network and on its role in the collapse kinetics. These results pave the way for addressing problems where solvent effects are dominant, such as the case of microgels at liquid-liquid interfaces.

The Molecular Structure of Sphingomyelin in Fluid Phase Bilayers Determined by the Joint Analysis of Neutron and X-Ray Scattering Data

We have determined the fluid bilayer structure of palmitoyl sphingomyelin (PSM) and stearoyl sphingomyelin (SSM) by simultaneously analyzing small-angle neutron and X-ray scattering data. We report structural parameters obtained using the newly developed scattering density profile (SDP) model for sphingomyelin lipids, including the area per lipid, total bilayer thickness and hydrocarbon thickness, in addition to lipid volumes determined by densitometry. Unconstrained all-atom simulations of PSM bilayers at 55°C using the C36 CHARMM force field produced a lipid area of 56 A2, a value that was 10% lower than the one determined experimentally (61.9 A2). Furthermore, scattering form factors calculated from the unconstrained simulations were in poor agreement with experimental form factors, despite the fact that segmental order parameter (SCD) profiles calculated from the simulations were in relatively good agreement with previously published SCD profiles obtained from NMR experiments. Conversely, constrained area simulations at 61.9 A2 resulted in good agreement between the simulation and experimental scattering form factors, but not with SCD profiles. We discuss possible reasons for the discrepancies between these two important types of data that are frequently used as validation metrics for molecular dynamics force fields.

Analysis of nucleon electromagnetic form factors from light-front holographic QCD: The spacelike region

We present a comprehensive analysis of the spacelike nucleon electromagnetic form factors and their flavor decomposition within the framework of light-front holographic QCD. We show that the inclusion of the higher Fock components $\ket {qqqq\bar{q}}$ has a significant effect on the spin-flip elastic Pauli form factor and almost zero effect on the spin-conserving Dirac form factor. We present light-front holographic QCD results for the proton and neutron form factors at any momentum transfer range, including asymptotic predictions, and show that our results agree with the available experimental data with high accuracy. In order to correctly describe the Pauli form factor we need an admixture of a five quark state of about 30$\%$ in the proton and about 40$\%$ in the neutron. We also extract the nucleon charge and magnetic radii and perform a flavor decomposition of the nucleon electromagnetic form factors. The free parameters needed to describe the experimental nucleon form factors are very few: two parameters for the probabilities of higher Fock states for the spin-flip form factor and a phenomenological parameter $r$, required to account for possible SU(6) spin-flavor symmetry breaking effects in the neutron, whereas the Pauli form factors are normalized to the experimental values of the anomalous magnetic moments. The covariant spin structure for the Dirac and Pauli nucleon form factors prescribed by AdS$_5$ semiclassical gravity incorporates the correct twist scaling behavior from hard scattering and also leads to vector dominance at low energy.

Power of two: Assessing the impact of a second measurement of the weak-charge form factor ofPb208

[Background] Besides its intrinsic value as a fundamental nuclear-structure observable, the weak-charge density of 208Pb - a quantity that is closely related to its neutron distribution - is of fundamental importance in constraining the equation of state of neutron-rich matter. [Purpose] To assess the impact that a second electroweak measurement of the weak-charge form factor of 208Pb may have on the determination of its overall weak-charge density. [Methods] Using the two putative experimental values of the form factor, together with a simple implementation of Bayes' theorem, we calibrate a theoretically sound - yet surprisingly little known - symmetrized Fermi function, that is characterized by a density and form factor that are both known exactly in closed form. [Results] Using the charge form factor of 208Pb as a proxy for its weak-charge form factor, we demonstrate that using only two experimental points to calibrate the symmetrized Fermi function is sufficient to accurately reproduce the experimental charge form factor over a significant range of momentum transfers. [Conclusions] It is demonstrated that a second measurement of the weak-charge form factor of 208Pb supplemented by a robust theoretical input in the form of the symmetrized Fermi function, would place significant constraints on the neutron distribution of 208Pb and, ultimately, on the equation of state of neutron-rich matter.

Penetration of HIV-1 Tat47-57 into PC/PE Bilayers Assessed by MD Simulation and X-Ray Scattering

The interactions of the basic, cell-penetrating region (Y47GRKKRRQRRR57) of the HIV-1 Tat protein with dioleoylphosphatidylcholine (DOPC) bilayers were previously assessed by comparing experimental X-ray diffuse scattering with atomistic molecular dynamics simulations. Here, we extend this investigation by evaluating the influence of phosphatidylethanolamine (PE) lipids. Using experimental bilayer form factors derivedfrom X-ray diffuse scattering data as a guide, our simulations indicate that Tat peptides localize close to the carbonyl-glycerol group in the headgroup region of bilayers composed of either DOPC or DOPC:DOPE (1:1) lipid. Our results also suggest that Tat peptides may more frequently insert into the hydrophobic core of bilayers composed of PC:PE (1:1) lipids than into bilayers composed entirely of PC lipids. PE lipids may facilitate peptide translocation across a lipid bilayer by stabilizing intermediate states in which hydrated peptides span the bilayer.