Differential Cross Sections For Proton Research Articles

A Methodology to Estimate Single-Event Effects Induced by Low-Energy Protons

This work explains that the Coulomb elastic process on the nucleus is a major source of single-event effects (SEE) for protons within the energy range of 1–10 MeV. The infinite range of Coulomb interactions implies an exceptionally high recoil probability. This research seeks to extend the investigations under which the elastic process becomes significant in the energy deposition process by providing a simplified methodology to evaluate the elastic contribution impact on the reliability of electronics. The goal is to derive a method to provide a simple way to calculate and predict the SEE cross-section. At very low energy, we observe a significant increase in the proton differential cross-section. The use of a direct Monte Carlo approach would mainly trigger low energy recoiling ions, and a very long calculation time would be necessary to observe the tail of the spectrum. In this sense, this work provides a simple methodology to calculate the SEE cross-section. The single-event upset (SEU) cross-section results demonstrate a good agreement with the experimental data in terms of shape and order of magnitude for different technological nodes.

Lévy α-Stable Model for the Non-Exponential Low-|t| Proton–Proton Differential Cross-Section

It is known that the Real Extended Bialas–Bzdak (ReBB) model describes the proton–proton (pp) and proton–antiproton (pp¯) differential cross-section data in a statistically non-excludible way, i.e., with a confidence level greater than or equal to 0.1% in the center of mass energy range 546 GeV ≤s≤8 TeV and in the squared four-momentum transfer range 0.37 GeV2 ≤ −t ≤ 1.2 GeV2. Considering, instead of Gaussian, a more general Lévy α-stable shape for the parton distributions of the constituent quark and diquark inside the proton and for the relative separation between them, a generalized description of data is obtained, where the ReBB model corresponds to the α=2 special case. Extending the model to α<2, we conjecture that the validity of the model can be extended to a wider kinematic range, in particular, to lower values of the four-momentum transfer −t. We present the formal Lévy α-stable generalization of the Bialas–Bzdak model and show that a simplified version of this model can be successfully fitted, with α<2, to the non-exponential, low −t differential cross-section data of elastic proton–proton scattering at s=8 TeV.

Measurement of elastic backscattering differential cross sections for protons on natO in the energy range E= 4-6 MeV, suitable for EBS

In this study we present the experimental cross sections of the natO(p,p0) elastic scattering, determined via the relative measurement technique, in the proton energy range Elab=4-6 MeV, at six backscattering detector angles between 120o and 170o, with a 10o step. The measurements were performed using the Van de Graaff Tandem 5.5 MV Accelerator of N.C.S.R. “Demokritos” in Athens, Greece and a high precision goniometer.

Observation of Odderon effects at LHC energies: a real extended Bialas\u2013Bzdak model study

The unitarily extended Bialas–Bzdak model of elastic proton–proton scattering is applied, without modifications, to describe the differential cross-section of elastic proton–antiproton collisions in the TeV energy range, and to extrapolate these differential cross-sections to LHC energies. In this model-dependent study we find that the differential cross-sections of elastic proton–proton collision data at 2.76 and 7 TeV energies differ significantly from the differential cross-section of elastic proton–antiproton collisions extrapolated to these energies. The elastic proton–proton differential cross-sections, extrapolated to 1.96 TeV energy with the help of this extended Bialas–Bzdak model do not differ significantly from that of elastic proton–antiproton collisions, within the theoretical errors of the extrapolation. Taken together these results provide a model-dependent, but statistically significant evidence for a crossing-odd component of the elastic scattering amplitude at the at least 7.08 sigma level. From the reconstructed Odderon and Pomeron amplitudes, we determine the sqrt{s} dependence of the corresponding total and differential cross-sections.

Emission of High-Energy Protons and Photons in Heavy-Ion Collisions Treated on the Basis of a Hydrodynamic Approach with a Nonequilibrium Equation of State

A hydrodynamic approach involving a nonequilibrium equation of state is used in describing heavy-ion collisions at medium and intermediate energies. The double differential cross sections for proton and photon emission in collisions of various nuclei are calculated in developing this approach with allowance for nuclear-viscosity effects and amendments introduced by the microcanonical distribution. The results agree everywhere, including the cumulative region of the spectrum, with available experimental data on the emission of high-energy particles. The approach in question permits reproducing high-momentum distributions of protons from the reaction $${}^{12}\textrm{C}+\,^{9}\textrm{Be}\to p+X$$ at the $${}^{12}$$ C ion energies of 300, 600, 950, and 2000 MeV per nucleon and the energy spectra of hard photons from the reaction $${}^{12}\textrm{C}+\,^{9}\textrm{Be}\to\gamma+X$$ at the $${}^{12}$$ C ion energies of 2.0 and 3.2 GeV per nucleon.

Benchmarking evaluated proton differential cross sections for carbon

In the presented work, evaluated differential cross section data for the 12C(p,p0)12C reaction calculated by SigmaCalc 2.0 (Gurbich, 2016) were validated using benchmarking procedures. Protons in the energy range from 1.2 to 3.5 MeV were backscattered from a thick glassy carbon target at three different scattering angles: 118°, 150° and 165°. For scattering angles of 150° and 165°, agreement between experimental and simulated spectra was generally good for the investigated energy span. However, at 118°, the simulation underestimates experimental data in the whole measured energy range, indicating that the evaluated differential cross section data are too low. The results are presented in graphical and tabular form, together with the accuracy limits of the benchmarking procedure.

Benchmarking the evaluated proton differential cross sections suitable for the EBS analysis of natSi and 16O

The evaluated proton differential cross sections suitable for the Elastic Backscattering Spectroscopy (EBS) analysis of natSi and 16O, as obtained from SigmaCalc 2.0, have been benchmarked over a wide energy and angular range at two different accelerator laboratories, namely at N.C.S.R. ‘Demokritos’, Athens, Greece and at Ruđer Bošković Institute (RBI), Zagreb, Croatia, using a variety of high-purity thick targets of known stoichiometry. The results are presented in graphical and tabular forms, while the observed discrepancies, as well as, the limits in accuracy of the benchmarking procedure, along with target related effects, are thoroughly discussed and analysed. In the case of oxygen the agreement between simulated and experimental spectra was generally good, while for silicon serious discrepancies were observed above Ep,lab=2.5MeV, suggesting that a further tuning of the appropriate nuclear model parameters in the evaluated differential cross-section datasets is required.

Measurement of proton induced γ-ray emission cross sections on Na from 1.0 to 4.1 MeV

Differential cross sections for proton induced γ-ray emission from the reactions 23Na(p,p′γ)23Na (Eγ=441 and 1636keV) and 23Na(p,α′γ)20Ne (Eγ=1634keV) were measured for proton energies from 1.0 to 4.1MeV in five different ion beam laboratories. Backscattered protons were collected simultaneously for normalization purposes, avoiding the measurement of the absolute values of the collected beam charge. The overall uncertainty was estimated to be around 7–8% for the cross section of the 441keV γ-ray line from the 23Na(p,pγ1-0)23Na reaction, and of 8–12% for the cross section of the 1634–1636keV γ-ray lines from the 23Na(p,αγ1-0)20Ne and 23Na(p,pγ2-1)23Na reactions. To check the possible anisotropy of the emitted 441keV γ-ray, angular distribution measurements were performed at 1292, 1468, 1931, 2083 and 2851keV proton energy, where sharp and well separated resonances occur in the excitation function; moreover, in the energy range from 2.5 to 4.1MeV proton energy, differential cross sections at 0°, 45° and 90° were measured as well.

Double differential cross sections for proton induced electron emission from molecular analogues of DNA constituents for energies in the Bragg peak region.

For track structure simulations in the Bragg peak region, measured electron emission cross sections of DNA constituents are required as input for developing parameterized model functions representing the scattering probabilities. In the present work, double differential cross sections were measured for the electron emission from vapor-phase pyrimidine, tetrahydrofuran, and trimethyl phosphate that are structural analogues to the base, the sugar, and the phosphate residue of the DNA, respectively. The range of proton energies was from 75 keV to 135 keV, the angles ranged from 15° to 135°, and the electron energies were measured from 10 eV to 200 eV. Single differential and total electron emission cross sections are derived by integration over angle and electron energy and compared to the semi-empirical Hansen-Kocbach-Stolterfoht (HKS) model and a quantum mechanical calculation employing the first Born approximation with corrected boundary conditions (CB1). The CB1 provides the best prediction of double and single differential cross section, while total cross sections can be fitted with semi-empirical models. The cross sections of the three samples are proportional to their total number of valence electrons.

Evidence for non-exponential elastic proton–proton differential cross-section at low |t| and [formula omitted] by TOTEM

The TOTEM experiment has made a precise measurement of the elastic proton–proton differential cross-section at the centre-of-mass energy s=8 TeV based on a high-statistics data sample obtained with the β⁎=90 m optics. Both the statistical and systematic uncertainties remain below 1%, except for the t-independent contribution from the overall normalisation. This unprecedented precision allows to exclude a purely exponential differential cross-section in the range of four-momentum transfer squared 0.027<|t|<0.2 GeV2 with a significance greater than 7 σ. Two extended parametrisations, with quadratic and cubic polynomials in the exponent, are shown to be well compatible with the data. Using them for the differential cross-section extrapolation to t=0, and further applying the optical theorem, yields total cross-section estimates of (101.5±2.1) mb and (101.9±2.1) mb, respectively, in agreement with previous TOTEM measurements.

Double ionization of He by ion impact: Second-order contributions to the fully differential cross section

In this work, we present a second-order Born series treatment for the double ionization of He by ion impact. In particular, we show that the well-known independent events and independent electron models naturally result from an on-shell treatment for the second-order Born approximation. A transition amplitude which coherently includes first- and second-order terms in the projectile interaction is introduced to study the role of the two-step-1, shake-off, and two-step-2 mechanisms at different impact energies. Fully differential cross sections for proton and antiproton impact are presented and analyzed for different projectile momentum transfers.

APPLICABILITY OF A REPRESENTATION FOR THE MARTIN'S REAL-PART FORMULA IN MODEL-INDEPENDENT ANALYSES

Using a novel representation for the Martin's real-part formula without the full scaling property, an almost model-independent description of the proton–proton differential cross-section data at high energies (19.4 GeV–62.5 GeV) is obtained. In the impact parameter and eikonal frameworks, the extracted inelastic overlap function presents a peripheral effect (tail) above 2 fm and the extracted opacity function is characterized by a zero (change of sign) in the momentum transfer space, confirming results from previous model-independent analyses. Analytical parametrization for these empirical results are introduced and discussed. The importance of investigations on the inverse problems in high-energy elastic hadron scattering is stressed and the relevance of the proposed representation is commented. A short critical review on the use of Martin's formula is also presented.

Model-independent data reductions of elastic proton–proton scattering

New developments in empirical analyses of the proton–proton differential cross section data at high energies are reported. Making use of an unconstrained model-independent parametrization for the scattering amplitude and two different fit procedures, all the experimental data in the center-of-mass energy interval 19.4–62.5 GeV are quite well described (optical point and data above the region of Coulomb-nuclear interference). The contributions from the real and imaginary parts of the amplitude beyond the forward direction are discussed and compared with the results from previous analyses and phenomenological models. Extracted overlap functions (impact parameter space) are outlined and a critical discussion on model-independent analyses and results are also presented.

Four-body model for transfer excitation

We present here a four-body model for transfer-excitation collisions, which we call the four-body transfer-excitation (4BTE) model. Each two-body interaction is explicitly included in the 4BTE model, allowing us to study the effects of individual two-body interactions. We apply our model to fully differential cross sections for proton+helium collisions, and study the effect of the incident projectile-atom interaction, the scattered projectile-ion interaction, the projectile-nuclear interaction, and electron correlation within the target atom.

Quasi-elastic and elastic charge-exchange differential cross sections (critical review)

More than 50 years ago the charge-exchange of one nucleon in the quasi-elastic nucleon deuteron scattering was proposed to determine the spin independent, or the spin dependent parts of the elastic backward neutron proton differential cross section. For this purpose two measurements are to be performed using unpolarized particles only. Such a suggestion was very attractive for experimentalists, since at that time polarized beams were rare and polarized targets were nonexistent. One experiment consists in the inclusive measurement of the charge-exchange quasi-elastic nucleon deuteron differential cross section. The energy of the fast outgoing nucleon is to be approximately the same as that of the incident nucleon. The intrinsic momenta of the remaining two identical nucleons should be small. The impulse approximation has been assumed, i.e. in the final state of the two nucleons their interaction can be neglected. The quasi-elastic result is to be compared with the elastic np differential cross section in the backward direction at the same energy. The theory related the ratio RQE(π) of the quasi-elastic to the elastic np charge-exchange differential cross sections to the spin dependent part of the np backward elastic scattering amplitude. Several experiments in the nucleon kinetic energy interval below 1 GeV were carried out, where the RQE(π) values were determined. Recently the energy interval was extended up to 2 GeV by successful experiments at the JINR VBLHE Nuclotron. The quasi-elastic results can be compared with the values of the analogous quantity Rnp(π) for the np elastic scattering, calculated from the phase shift analyses below 1.3 GeV. The present paper is a critical review checking expressions for Rnp(π) in different amplitude representations, listing numerical values of elastic np quantities and results of existing quasi-elastic experiments. Conclusions and statements of some authors and the validity of the relevant theory is discussed.

Pauli correlation effect for the elastic scattering of protons by different nuclei at 800 MeV

The angular distributions of the elastic scattering of protons at an energy of 800 MeV by 16O and 20Ne nuclei are described in terms of the optical model scattering theory. Single folding model is applied to calculate the optical potential taking the effective nucleon-nucleon interaction to be in two forms. One form includes the zero-range pseudo-potential term and the other includes a two-body Pauli correlation function. Analytical expressions for the real part of the optical potential are obtained for both forms. The imaginary part of the optical potential is taken to be of the Woods-Saxon's shape. It is found that introducing the Pauli correlation function improves the agreement with the experimental data for the elastic scattering differential cross-sections of protons with the target nuclei 16O and 20Ne.

Flow at Brookhaven AGS Energy (11.6 GeV/nucleon): A barometer for high density effects?

Preliminary data on transverse energy ``flow'' and event asymmetries reported by the E877(814) Collaborations are compared to ARC (a relativistic cascade) model calculations for Au+Au at full AGS Brookhaven (Alternating Gradient Synchroton) beam energy. ARC triple differential cross sections for protons and pions are presented. Proton flow is produced in ARC, with the maximum $〈{P}_{x}〉\ensuremath{\sim}120$ MeV/$c$. For central events $〈{P}_{x}〉$ for the pions is near zero, consistent with experiment. The comparison with data provides a constraint on the size of flow at the highest energy available, to be put beside that at Bevalac energy. This sets the stage for examining flow at intermediate energies, now being measured by E895, for signs of baryon rich plasma.

Break-up and Coherent Photoproduction ofηMesons on the Deuteron

We present new break-up and coherent data for $\ensuremath{\eta}$ meson photoproduction on the deuteron, using a deuterium target and tagged bremsstrahlung photons up to 1 GeV. The differential cross sections for the coherent process were measured from threshold to 800 MeV. They are much smaller than those previously reported. The break-up channel provides a direct measurement of the neutron to proton differential cross section ratios. At the ${S}_{11}(1535)$ resonance peak, ${\ensuremath{\sigma}}_{n}/{\ensuremath{\sigma}}_{p}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.68\ifmmode\pm\else\textpm\fi{}0.06$ leading to an isoscalar to isovector amplitude ratio of ${A}_{s}{/A}_{\ensuremath{\upsilon}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.096\ifmmode\pm\else\textpm\fi{}0.02$.

Pion and kaon emission from the fireball formed in Ne + NaF collisions at 1–2 GeV/nucleon

Double differential cross sections for proton, π + and K + meson production have been measured in Ne + NaF collisions at 1 and 2 GeV/nucleon. Parameterizations of the meson spectra with Maxwell-Boltzmann distributions yield common inverse slope parameters for kaons and high-energy pions at each beam energy. No evidence for different freeze out temperatures can be deduced from the spectral slopes of the emitted particles.

Kaon production in heavy ion collisions and the nuclear equation of state

Double differential cross sections for protons, π+ and K+ are measured in Au + Au collisions at 1.0 GeV/u and Θlab=44°±4° with a new magnetic spectrometer at SIS. The pion spectra show an enhancement at low momenta with respect to a thermal distribution and little dependence on the collision centrality. The high-energetic pions measured in semi-central collisions at approximately midrapidity exhibit an anisotropic azimuthal angular distribution, peaking at 90° and 270° with respect to the reaction plane. The same feature is observed for protons. The kaon to proton ratio increases with the number of participating nucleons, i.e. with the centrality of the collision, whereas the pion to proton ratio stays constant. The first data on subthreshold K+ production in a heavy mass collision system are discussed with respect to nuclear matter properties by a comparison to microscopic transport calculations.