Ratio Of Differential Cross Sections Research Articles

An experimental study on cross-section ratio of coherent to incoherent scattering for 145 keV incident gamma photons

The coherent (Rayleigh) to incoherent (Compton) scattering cross-section ratio of elements, in the range 6 ≤ Z ≤ 82, are determined experimentally for 145 keV incident gamma photons. An HPGe (High purity germanium) semiconductor detector is employed, at scattering angle of 50°, 70° and 90°, to record the spectra originating from interactions of incident gamma photons with the target under investigation. The intensity ratio of Rayleigh to Compton scattered peaks observed in the recorded spectra, and corrected for photo-peak efficiency of gamma detector and absorption of photons in the target and air, along with the other required parameters provides the differential cross-section ratio. The measured values of cross-section ratio are found to agree with theoretical predictions (corresponding to 4.939, 6.704 and 8.264 Å−1 photon momentum transfer) based upon non-relativistic form factor, relativistic form factor, modified form factor and S-matrix theory.

Cross sections for elastic scattering of electrons by CF3Cl, CF2Cl2, and CFCl3

Differential, integral, and momentum transfer cross sections have been determined for the elastic scattering of electrons from the molecules CF3Cl, CF2Cl2, and CFCl3.With the help of a crossed electron beam–molecular beam apparatus using the relative flow technique, the ratios of the elastic differential cross sections (DCSs) of CF3Cl, CF2Cl2, and CFCl3 to those of He were measured in the energy region from 1.5 to 100 eV and at scattering angles in the range 15° to 130°. From those ratios, the absolute DCSs were determined by utilizing the known DCS of He. For CF3Cl and CF2Cl2, at the common energies of measurement, we find generally good agreement with the results from the independent experiments of Mann and Linder [J. Phys. B 25, 1621 (1992)10.1088/0953-4075/25/7/030; Mann and Linder J. Phys. B 25, 1633 (1992)10.1088/0953-4075/25/7/031]. In addition, as a result of progressively substituting a Cl-atom, undulations in the angular distributions have been found to vary in a largely systematic manner in going from CF4 to CF3Cl to CF2Cl2 to CFCl3 and to CCl4. These observed features suggest that the elastic scattering process is, in an independently additive manner, dominated by the atomic-Cl atoms of the molecules. The present independent atom method calculation typically supports the experimental evidence, within the screened additivity rule formulation, for each species and for energies greater than about 10–20 eV. Integral elastic and momentum transfer cross sections were also derived from the measured DCSs, and are compared to the other available theoretical and experimental results. The elastic integral cross sections are also evaluated as a part of their contribution to the total cross section.

Measurement of the differential [formula omitted]-jet cross section and the ratio of differential [formula omitted] and [formula omitted] cross sections in [formula omitted] collisions at [formula omitted

We present measurements of the differential cross section dσ/dpTγ for the associated production of a c-quark jet and an isolated photon with rapidity |yγ|<1.0 and transverse momentum 30<pTγ<300 GeV. The c-quark jets are required to have |yjet|<1.5 and pTjet>15 GeV. The ratio of differential cross sections for γ+c to γ+b production as a function of pTγ is also presented. The results are based on data corresponding to an integrated luminosity of 8.7 fb−1 recorded with the D0 detector at the Fermilab Tevatron pp¯ Collider at s=1.96 TeV. The obtained results are compared to next-to-leading order perturbative QCD calculations using various parton distribution functions, to predictions based on the kT-factorization approach, and to predictions from the sherpa and pythia Monte Carlo event generators.

J/ψ and ψ(2S) production in pp collisions at s√=7Tev

A measurement of the J/ψ and ψ(2S) production cross sections in pp collisions at √s = 7TeV with the CMS experiment at the LHC is presented. The data sample corresponds to an integrated luminosity of 37 pb^(−1). Using a fit to the invariant mass and decay length distributions, production cross sections have been measured separately for prompt and non-prompt charmonium states, as a function of the meson transverse momentum in several rapidity ranges and integrated in the kinematical regions considered in this study. In addition, cross sections restricted to the acceptance of the CMS detector are given, which are not affected by the polarization of the charmonium states. The ratio of the differential production cross sections of the two states, where systematic uncertainties largely cancel, is also determined. The branching fraction of the inclusive B → ψ(2S)X decay is extracted from the ratio of the non-prompt cross sections to be: B(B → ψ(2S)X) = (3.08±0.12(stat+syst.)±0.13(theor.)±0.42(B_(PDG)10^(−3)

Systematic analysis of the incoming quark energy loss in cold nuclear matter

The investigation into the fast parton energy loss in cold nuclear matter is crucial for a good understanding of the parton propagation in hot-dense medium. By means of four typical sets of nuclear parton distributions and three parametrizations of quark energy loss, the parameter values in quark energy loss expressions are determined from a leading order statistical analysis of the existing experimental data on nuclear Drell–Yan differential cross section ratio as a function of the quark momentum fraction. It is found that with independence on the nuclear modification of parton distributions, the available experimental data from lower incident beam energy rule out the incident-parton momentum fraction quark energy loss. Whether the quark energy loss is linear or quadratic with the path length is not discriminated. The global fit of all selected data gives the quark energy loss per unit path length α=1.21±0.09 GeV/fm by using nuclear parton distribution functions determined only by means of the world data on nuclear structure function. Our result does not support the theoretical prediction: the energy loss of an outgoing quark is three times larger than that of an incoming quark approaching the nuclear medium. It is desirable that the present work can provide useful reference for the Fermilab E906/SeaQuest experiment.

The dependence of J/ψ-nucleon inelastic cross section on the Feynman variable

By means of two typical sets of nuclear parton distribution functions, meanwhile taking account of the energy loss of the beam proton and the nuclear absorption of the charmonium states traversing the nuclear matter in the uniform framework of the Glauber model, a leading order phenomenological analysis is given in the color evaporation model of the E866 experimental data on J/ψ production differential cross section ratios RFe/Be(xF). It is shown that the energy loss effect of beam proton on RFe/Be(xF) is more important than the nuclear effects on parton distribution functions in the high Feynman variable xF region. It is found that the J/ψ-nucleon inelastic cross section depends on the Feynman variable xF and increases linearly with xF in the region xF > 0.2.

Electron interference in fast ion collisions with H2 and the frequency parameter

The Young-type interference effect has been investigated in electron emission from molecular hydrogen in collision of 5 MeV u− 1F9+ ions. The double differential cross section ratios of molecular-to-atomic hydrogen exhibits oscillatory structure, which is discussed in terms of the Young-type electron interference. We have obtained the frequencies of such oscillation for different angles. A comparative study of the frequency parameter is given with early measurements performed by other groups.

Second-order interference in collisions of 4-MeV/uF9+ions withH2

Frequency doubling in interference oscillations in fast-ion-induced electron emission spectrum from H2 is investigated. Experimentally observed oscillatory structure is well explained by a model calculation based on the rescattering of emitted electron from the second H center. The second-order contribution is found to be as large as 10%. The doubling of oscillation frequency is found out to be independent of angle of observation. Derived analytical expression for the double differential cross section ratio including the first- and secondorder interference terms, fits the observed oscillatory structure quite well. The present analysis is in broad agreement with the earlier observations by Stolterfoht et al.

Influence of quark energy loss on extracting nuclear sea quark distribution from nuclear Drell–Yan experimental data

By means of two typical kinds of quark energy loss parametrization and the nuclear parton distributions determined only with lepton-nuclear deep inelastic scattering experimental data, a leading order analysis is performed on the proton-induced Drell–Yan differential cross section ratios of tungsten versus deuterium as a function of the quark momentum fraction in the beam proton and target nuclei. It is found that the theoretical results with quark energy loss are in good agreement with the experimental data. The quark energy loss effect produces approximately 3% to 11% suppression on the Drell–Yan differential cross section ratios RW/D in the range 0.05 ≤ x2 ≤ 0.3. The application of nuclear Drell–Yan data with heavy targets is remarkably subject to difficulty in the constraint of the nuclear sea quark distribution.

Uncertainty due to quark energy loss in determining the nuclear sea quark distribution from nuclear Drell-Yan data

By means of two different parametrizations of quark energy loss and the nuclear parton distributions determined only with lepton-nuclear deep inelastic scattering experimental data, a leading order phenomenological analysis is performed on the nuclear Drell-Yan differential cross section ratios for E772 experimental data. Uncertainty due to the quark energy loss effect is quantified in determining the nuclear sea quark distribution by using nuclear Drell-Yan data. It is found that the quark energy loss effect on nuclear Drell-Yan cross section ratios becomes greater with the increase of quark momentum fraction in the target nuclei. The uncertainty from the quark energy loss becomes bigger as the nucleus A becomes heavier. The Drell-Yan data on proton incident middle and heavy nuclei versus deuterium would result in an overestimate for nuclear modification in the sea quark distribution with neglecting the quark energy loss.

Inhomogeneous Shadowing Effect in High-Energy p-A Drell–Yan Process

Having studied the initial state energy loss versus nuclear shadowing for the Drell–Yan dimuon pair production in the color string model, the inhomogeneous shadowing effect is considered in this paper. We find that the inhomogeneous shadowing effect does amend the rate of energy loss per unit path length, -dE/dz. Finally, the theoretical results for the Drell–Yan differential cross-section ratios are compared with the E772 and E866 data. It is found that the theoretical results are in good agreement with the experimental data.

Energy dependence of forward 1S0 diproton production in the [formula omitted] reaction

The pp→{pp}sπ0 differential cross section has been measured with the ANKE spectrometer at COSY-Jülich for seven proton beam energies Tp between 0.51 and 1.97 GeV. By selecting proton pairs with an excitation energy of less than 3 MeV it is ensured that the final {pp}s system is in the S01 state. In the measured region of θppcm≲18°, the data reveal a forward dip for Tp⩽1.4 GeV whereas a forward peaking is seen at 1.97 GeV. The energy dependence of the forward cross section shows a broad peak in the 0.6–0.8 GeV region, probably associated with Δ(1232) excitation, and a minimum at 1.4 GeV. Some of these features are similar to those observed for the spin–isospin partner reaction, pp→dπ+. However, the ratio of the forward differential cross sections of the two reactions shows a significant suppression of single pion production associated with a spin-singlet final nucleon pair.

The extraction of the nuclear sea-quark distribution and energy loss effect in a Drell–Yan experiment

A next-to-leading order and a leading order analysis are performed of the differential cross section ratios from the Drell–Yan process. It is found that the effect of next-to-leading order corrections on the differential cross section ratios as a function of the quark momentum fraction in the proton beam and the target nuclei for the current Fermilab and future lower proton energy beam can be considered negligible. The nuclear Drell–Yan reaction is an ideal tool to study the energy loss of fast quarks moving through cold nuclei. In a leading order analysis, the theoretical results with the quark energy loss are in good agreement with the Fermilab E866 experimental data on the Drell–Yan differential cross section ratios as a function of the momentum fraction of the target parton. It is shown that the quark energy loss effect has a significant impact on the Drell–Yan differential cross section ratios. Therefore, it is important to understand the energy loss effects for determining nuclear sea-quark distributions from future nuclear Drell–Yan experiments at the lower energy proton beams bombarding nuclei.

Nuclear effects in lepton-pair production in hadron-nucleus collisions

The results of experimental investigations of Drell-Yan dimuon production in pBe and pW collisions at an energy of 800 GeV on a fixed target are analyzed. The ratios of the inclusive differential cross sections for lepton-pair production are calculated. It is shown that allowance for the effect of multiple soft rescattering of a projectile-hadron quark inside the target nucleus improves agreement between theoretical and experimental results.

Review of absolute doubly differential cross-section experiments and cross-section ratios for electron bremsstrahlung from rare gas atom and thin-film targets

We discuss doubly differential cross-section experiments for electron bremsstrahlung from free gas atom and thin-film targets for electron energies of 100 keV or less. We compare cross-section ratios for different target atoms with two theoretical models: ordinary bremsstrahlung and total bremsstrahlung calculated in the stripping approximation. Ratios of cross sections have been used to improve the comparison between experiment and theory when only relative cross sections are available or when the error in the absolute cross section is large. We also discuss additional background processes that may be more important in gas target experiments.

Non-dipole second order parameters of the photoelectron angular distribution for elements Z = 1–100 in the photoelectron energy range 1–10 keV

Presented here are the photoelectron angular distribution non-dipole parameters associated with the terms of the second order O [( kr) 2] ( k is the photon energy and r is the radius of the ionized atomic shell) for both unpolarized and linearly polarized radiation. The parameters are given for atomic shells with binding energies lower than 2 keV of all elements 1 ⩽ Z ⩽ 100 for four values of photoelectron energy in the range 1−10 keV. In this range, the second-order terms are shown to make a significant contribution (up to ∼30%) to the angular differential cross section. The inclusion of these terms becomes all the more important in calculations of the differential cross section ratio for the fixed geometry of angles which is measured experimentally in the case of linearly polarized radiation. The Dirac–Fock–Slater potential is used in the calculations. The hole left by the emitted electron is taken into account in the frozen orbital approximation.

Initial-state nuclear effects in proton-nucleus collisions

Two important initial-state nuclear effects in hadron-nucleus collisions are considered. The ratios of inclusive differential cross-sections for Drell-Yan dimuon production are calculated. The calculated results are compared to the E866 data. It is shown that the consideration of multiple soft rescatterings of incident quarks in nuclei and initial-state quark energy loss effects allow to get a good agreement between the calculated results and the experimental data.

Cross section measurements of charged pion photoproduction in hydrogen and deuterium from 1.1 to 5.5 GeV

The differential cross section for the gamma +n --> pi- + p and the gamma + p --> pi+ n processes were measured at Jefferson Lab. The photon energies ranged from 1.1 to 5.5 GeV, corresponding to center-of-mass energies from 1.7 to 3.4 GeV. The pion center-of-mass angles varied from 50 degree to 110 degree. The pi- and pi+ photoproduction data both exhibit a global scaling behavior at high energies and high transverse momenta, consistent with the constituent counting rule prediction and the existing pi+ data. The data suggest possible substructure of the scaling behavior, which might be oscillations around the scaling value. The data show an enhancement in the scaled cross section at center-of-mass energy near 2.2 GeV. The differential cross section ratios at high energies and high transverse momenta can be described by calculations based on one-hard-gluon-exchange diagrams.

Electron impact excitation of argon and krypton: improved r-ratios

New differential cross-section ratios (r) for electron impact excitation of the metastable states of argon and krypton are presented. The new measurements are taken with improved energy resolution and a novel moveable source method which yields overall better statistical errors than earlier measurements. These measurements were taken to check the accuracy of the r-ratios observed in the earlier experiments with argon (Khakoo et al 2004 J. Phys. B: At. Mol. Opt. Phys. 37 247) which displayed significant deviations from the (statistical weight ratio) value of 5 at small scattering angles, and suggested the possibility of second-order effects in the electron impact excitation process. The measurements show that the r-ratios for argon stay close to the value of 5, in contrast to the earlier experiments, implying that second-order effects can be considered small. Additionally, new and similarly improved r-ratios for krypton were measured. These measurements reproduce the results of earlier measurements taken by our group which showed significant departures of r from the value of 5.

Influence of nondipolar effects on the photoelectron angular distribution upon photoionization of 2p and 3d atomic shells

Relativistic calculations of the angular distribution of photoelectrons upon photoionization of 2p and 3d shells in the range of photoelectron energies from 1 to 10 keV are carried out for unpolarized and linearly polarized radiation. An exact expression for the angular distribution of photoelectrons that takes into account nondipolar terms of the order of O[(kr)2] (k is the photon energy and r is the radius of the ionized shell) is obtained in the case of unpolarized radiation. It is shown that the contribution of the O[(kr)2] terms to the differential cross section can be considerable, reaching 24% at the maximum energy considered. Accounting for such terms in the calculation of the ratio of differential cross sections, which is experimentally measured at a certain geometry of angles in the case of linearly polarized radiation, can change this ratio twofold. The parameters of the angular distribution, which are necessary for the conduction of a quantitative x-ray photoelectron analysis, are given for the 2p1/2 and 2p3/2 shells of elements with 11≤Z≤29 and for the 3d3/2 and 3d5/2 shells of elements with 30≤Z≤54.