Momentum Transfer Interval Research Articles

Multivariate analysis of the scattering profiles of healthy and pathological human breast tissues

Scattering profiles of 106 healthy and pathological human breast samples were obtained using the angular dispersive X-ray scattering technique (AD-XRD) and synchrotron radiation covering the momentum transfer interval of 0.7 nm −1 ≤ q (=4 π sin( θ /2)/ λ )≤70.5 nm −1 . Multivariate analysis in the form of discriminant analysis was applied over the whole scattering profile curve of each sample in order to build a model for breast tissue classification. The classification results were validated and compared with histological sample classification obtained by microscopy analysis. Finally, the model allows classifying correctly 91.5% of the samples and presented values of 98.5%, 89.7% and 0.90 for sensitivity, specificity and Cohen’s κ , respectively, in correctly differentiating between healthy and pathological tissues.

Structural correlations of Ge 20Se 80− xTe x glasses based on reverse Monte Carlo simulation

Bulk chalcogenide Ge 20Se 80− x Te x (where x = 0, 10, 20 and 30 at.%) glasses were prepared using the melt-quench technique. The total structure factors of these alloys are obtained from the X-ray scattering data in the momentum transfer interval 0.61 ≤ K ≤ 16.45 Å −1. From reverse Monte Carlo (RMC) simulations of the X-ray scattering data, the short and intermediate-range order parameters are obtained. The simulations are useful to compute the partial pair distribution functions, g ij ( r), and the partial structure factors, S ij ( K). In Te-rich glass, the first sharp diffraction peak (FSDP) appears as a shoulder, instead of a peak for others, confirms that Se–Se bonds in addition to Ge–Ge bonds are responsible for the intermediate-range order inside these glasses. The partial coordination numbers and the bond angle distributions within the first coordination shell have been calculated. The ratio of the first to second peak positions ( r 1/ r 2) and the corresponding bond angle ( Θ) have confirmed that the Ge(Se 1/2) 4 tetrahedra, connected by Se–Se chains, can be considered as the main building units inside the investigated glasses.

On structural features of fullerene C60 dissolved in carbon disulfide: Complementary study by small-angle neutron scattering and molecular dynamic simulations

The parameters of fullerene C(60) dissolved in carbon disulfide CS(2) are analyzed by small-angle neutron scattering (SANS) in a wide interval of momentum transfer. To exclude the influence of nonequilibrium conditions, the solutions are prepared without applying shaking, stirring or ultrasound. No indication of the equilibrium cluster state of C(60) (with the cluster size below 60 nm) in the final solutions is revealed. Molecular dynamic simulations are complementary used to find out the partial volume of C(60) in CS(2) and the scattering contribution of the solvent organization at the interface with the fullerene molecule, which is shown to be small. Among several approaches for describing SANS data the preference is given to the model, which takes into account the presence of stable C(60) dimers (comprising 10% of the total particle number density) in the solution.

Assessment of the differential linear coherent scattering coefficient of biological samples

New differential linear coherent scattering coefficient, μ CS , data for four biological tissue types (fat pork, tendon chicken, adipose and fibroglandular human breast tissues) covering a large momentum transfer interval (0.07≤ q≤70.5 nm −1), resulted from combining WAXS and SAXS data, are presented in order to emphasize the need to update the default data-base by including the molecular interference and the large-scale arrangements effect. The results showed that the differential linear coherent scattering coefficient demonstrates influence of the large-scale arrangement, mainly due to collagen fibrils for tendon chicken and fibroglandular breast samples, and triacylglycerides for fat pork and adipose breast samples at low momentum transfer region. While, at high momentum transfer, the μ CS reflects effects of molecular interference related to water for tendon chicken and fibroglandular samples and, fatty acids for fat pork and adipose samples.

X-ray scattering profiles of some normal and malignant human breast tissues

The angular distribution of photons scattered by breast tissue samples (20 normal and 13 malignant) was measured in the interval of momentum transfer 0.02 A−1 ≤ x ≤ 0.62 A−1, using a powder diffractometer apparatus operating in reflection mode and equipped with a monochromator in the scattering beam. The x-ray tube had a Cu anode and added Ni filtration. Experimental data was corrected for all background sources, polarization, self-attenuation and geometric effect in order to provide the linear differential scattering coefficient µs (scattering profile) of each sample. Discriminant analysis was applied to these profiles in order to quantify the differences existing between normal and malignant tissues. In this analysis, each momentum transfer measured was considered as an independent variable, and the scores of each sample on a discriminant function were obtained. The classification method of decision tree induction was applied to these scores, which allowed tissue characterization. The classification results were validated and compared with histological sample classifications obtained by microscopic analyses. The results have shown that discriminant analysis was able to successfully identify differences between the scattering profiles from normal and malignant tissues. Also, classification results allowed the correct identification of 97% of the analyzed samples. These results suggest that the scattering profile may be an effective marker to be used in the diagnosis of breast cancer. Copyright © 2006 John Wiley & Sons, Ltd.

Possible method for the determination of the neutron electric form factor based on a measurement of asymmetries for the processH⃗2(e⃗,e′n)p

We generalize the recoil polarization method for the determination of the proton form factor to the case of the disintegration of vector polarized deuterons by longitudinally polarized electrons, $\vec d(\vec e, e'n)p$. We suggest to measure for this reaction, in the kinematics of quasi-elastic $en$-scattering, the ratio $R_{xz}=A_x/A_z$ of the asymmetries induced by the $x$- and $z$-components of the deuteron vector polarization. In the framework of the relativistic impulse approximation the ratio $R_{xz}$ is sensitive to $G_{En}$ in a wide interval of momentum transfer squared, whereas it depends weakly on the details of the $np$-interaction and on the choice of the deuteron wave function. Moreover, in the range $0.5\le Q^2\le$1.5 GeV$^2$, the ratio $R_{xz}$ shows a smooth dependence on $Q^2$, making the analysis simpler.

The Bjorken sum rule in the analytic approach to perturbative QCD

Results of applying analytic perturbation theory (APT) to the Bjorken sum rule are presented. We study the third-order QCD correction within the analytic approach and investigate its renormalization scheme dependence. We demonstrate that, in the framework of the method, theoretical predictions of the Bjorken sum rule are, practically, scheme independent for the entire interval of momentum transfer.

Evidence for eikonal zeros in the momentum transfer space

We present the results of fitting elastic $\mathrm{pp}$ differential cross section data at 23.5$<~\sqrt{s}<~$62.5 GeV with a novel analytic parametrization for the scattering amplitude. Making use of a fitting method, the errors from the free parameters are propagated to the imaginary part of the eikonal in the momentum transfer space. A novel systematic study of the effects coming from data at large momentum transfer is also performed. We find statistical evidence for the existence of eikonal zeros in the interval of momentum transfer 5--9 GeV${}^{2}$.

Photon Scattering by Compounds: an Assessment of the Validity of the Independent Atomic Model Approximation

The validity of the independent atomic model (IAM) for x-ray scattering, which assumes that each atom in the sample scatters independently of the others, was examined for materials and irradiation geometries where interatomic and intermolecular cooperative effects are expected to provide a non-negligible contribution. Samples of water, fat, polymers and powder were investigated by means of a simple powder diffractometer in the interval of momentum transfer 0.017⩽χ⩽0.67 {χ=E[sin(θ/2)]/12.4, E being the incident photon energy and θ the scattering angle}. Accurate evaluation of self-absorption, air scattering and other contamination was carried out by means of a Monte Carlo code. Simulation of the incident photon spectra permitted an assessment of non-monochromaticity effect. This allowed the accurate evaluation of the scattering intensities in terms of fundamental impact parameters. All the materials investigated showed marked discrepancies from the corresponding IAM theoretical results, even for intervals of momentum transfer in which this model is usually claimed to be valid. However, this work shows that the errors introduced by corrections are relatively low, making it possible to validate the use of simple diffractometry to evaluate the scattering factors in real samples without having to resort to sophisticated irradiation facilities. © 1997 John Wiley & Sons, Ltd.

Theg B*Bϱ andg D*Dϱ coupling constants in QCD

ThegB*Bϱ andgD*Dϱ coupling constants are calculated at the intermediate momentum transfer interval 0.5 GeV2≤Q2≤1.5 GeV2, in the context of QCD sum rules. Our predictions are in good agreement with those of the Vector Dominance Model

Coulomb sum rule on12C

We have measured the deep inelastic electron scattering from carbon up to and including the Δ region at 36°, 60°, 90° and 145°. The systematic decomposition of the transverse and longitudinal response functions has been obtained by means of a Rosenbluth-type analysis of the data in the momentum transfer interval 200 MeV/c<|q|<550 MeV/c. A comparison with theoretical calculations which extend over the quasi-elastic and Δ peak regions is presented. A reduction of the differences between our data and theory seems obtainable through the introduction of meson exchange currents, resonant and nonresonant meson production and the use of the shell model. Our experimental Coulomb sum rule estimates at higher |q| agree with independent-particle model predictions.

Deep-inelastic electron scattering from carbon

We have measured the deep-inelastic electron scattering from carbon up to and including the Δ-region at 36°, 60°, 90° and 145°. The systematic decomposition of the transverse and longitudinal response functions has been obtained by means of a Rosenbluth-type analysis of the data in the momentum transfer interval 200 MeV/c /s | q| /s 600 MeV/c. A comparison with theoretical calculations which extend over the quasielastic and Δ-peak regions is presented. A reduction of the differences between our data and theory seems obtainable through the introduction of meson-exchange currents, resonant and non-resonant meson production, and the use of the shell model. Our experimental Coulomb sum-rule estimates at higher | q| agree with independent particle model predictions. We compare our results in the vicinity of the Δ-peak with the total absorption cross section for real photons.

Measurement of the polarization parameter in pp elastic scattering at 150 GeV/ c

The polarization parameter in pp elastic scattering at 150 GeV/ c, and in the momentum transfer interval 0.4 ⩽ − t ⩽ 3.0 GeV 2, has been measured in an MWPC and scintillation counter experiment at the CERN SPS using a polarized proton target. The polarization is decreasing steadily from zero to ≈ − 10% in the range 0.4 < − t < 1.3 GeV 2; for higher | t| the data suggests a change of sign. Results are also given for the differential cross section, which exhibits a small dip at − t = (1.46 ± 0.01) GeV.

Measurement of the ReactionsBe9(p,π±) at 800 MeV

Angular distributions from the (p,..pi../sup +/) and (p,..pi../sup -/) reactions on /sup 9/Be leading to discrete isobaric analog states in /sup 10/Be and /sup 10/C have been measured at 800 MeV over the momentum-transfer interval 600--800 MeV/c. The ratio between the (p,..pi../sup +/) and (p,..pi../sup -/) production cross sections is found to be much larger at 800 MeV than at lower energy. The angular distributions from the (p,..pi../sup -/) reaction show a pronounced slope not observed in previous data.

Baryon spin-parity tests using polarized proton targets or beams

A new method is proposed for performing combined spin and parity tests on baryon resonances generated in quasi-two-body production experiments, without any dynamical hypothesis, using polarized proton targets or beams. These tests present the advantage of being applicable to data averaged over intervals of momentum transfer and mass. In order to estimate the sensitivity of the tests to experimental errors, a simulated experiment with random errors is analysed, and quite good stability is found.

Elastic scattering of [formula omitted] AT 39 AND 44.5 GeV/c

The differential cross sections for elastic π − p, K − p, p p and π + p, pp scattering at 39 and 44.5 GeV/ c, respectively, have been measured in the interval of momentum transfer squared 0.15 ≤ ovbt| ≤ 2 (GeV/ c) 2.

K +P elastic scattering at 32 GeV/ c

Elastic scattering of 32.1 GeV/ c K + on protons has been measured in a bubble chamber experiment. Results are presented in the momentum transfer interval 0.06–1.40 GeV 2 and compared with data at different energies. An effective Regge trajectory is calculated using K +p elastic data from 10 to 175 GeV/ c.

Antiproton charge exchange on protons at 25 and 35 GeV/ c

Cross sections for p ̄ p → n ̄ n at 25 and 35 GeV/ c have been measured. The cross sections decrease with increasing momentum as 1/ P 2. A narrow peak is observed in the momentum transfer interval 0 ⩽ − t ≲ 0.02 (GeV/ c 2 in the differential cross sections. Neither ϱ nor A 2 exchange contribute to the process in the investigated energy range.

Elastic scattering of π−p, K −p and [formula omitted] at 25 and 40 GeV/c

Elastic diffraction scattering of π −, K − and p on protons has been measured at 25 and 40 GeV/c at the Serpukhov Proton Accelerator. Differential elastic cross sections and diffraction slopes are presented in the momentum-transfer interval 0.07–0.80 (GeV/ c) 2 and compared with existing data at lower energies.