Differential Elastic Scattering Cross Sections Research Articles

Slope, curvature, and higher parameters inppandp¯pscattering, and the extrapolation of measurements ofdσ(s,t)/dttot=0

We study the effects of curvature in the expansion of the logarithm of the differential elastic scattering cross section near $t=0$ as $d\sigma(s,t)/dt=d\sigma(s,0)/dt\,\times\exp(Bt+Ct^2+Dt^3\cdots)$ in an eikonal model for $pp$ and $\bar{p}p$ scattering, and use the results to discuss the extrapolation of measured differential cross sections and the slope parameters $B$ to $t=-q^2=0$. We find that the curvature effects represented by the parameters $C$ and $D$, while small, lead to significant changes in the forward slope parameter relative to that determined in a purely exponential fit, and to smaller but still significant changes in the forward elastic scattering and total cross sections. Curvature effects should therefore be considered in future analyses or reanalyses of the elastic scattering data.

Differential elastic scattering cross sections of protons from Al in 2.4–4.8 MeV energy range

Measurement of differential elastic cross section of protons from aluminum was taken at 165° degree in the 2.4–4.8 MeV energy range. The results and measured energy resonances were compared with reported measurements. These data will improve the reliability of backscattering analysis of Al with protons in this energy region.

Combined experimental and theoretical study on the differential elastic scattering cross sections for acetone by electron impact energy of 7.0–50 eV

Combined experimental and theoretical study on the differential elastic scattering cross sections for acetone by electron impact energy of 7.0–50 eV

Impact ofLi6resonances on the near-barrier elastic scattering withSm144

Converged continuum discretized coupled-channel calculations of elastic-scattering differential cross sections for reactions induced by the $^{6}\mathrm{Li}$ projectile on the $^{144}\mathrm{Sm}$ target, at energies around the Coulomb barrier, are presented. The impact of the low-lying $\ensuremath{\alpha}$-deuteron resonant states in $^{6}\mathrm{Li}$ $(l=2,{J}^{\ensuremath{\pi}}={3}^{+},{2}^{+},{1}^{+})$ on those elastic angular distributions is quantified. This is done by two types of calculations, namely, (a) by omitting from the continuum energy spectrum all states where the resonances are constructed in the discretization process, and (b) by considering only the resonance discretized space. Dynamical polarization potentials are used for interpreting the effect of continuum couplings. Resonant couplings play a more significant role than nonresonance ones at back-scattering angles and at incident energies below the Coulomb barrier. However, their effect becomes weaker as the incident energy increases above the barrier energy.

Predicting reaction observables from back-scattering measurements in low-energy heavy-ion collisions

A simplified, reliable and useful method, based on reaction theory, for calculating a number of integrated and differential cross sections in low-energy heavy-ion collisions is presented. Simplified formulae provide predictions of reaction, capture and elastic-scattering differential cross sections, using experimental information about elastic and quasi-elastic back-scattering excitation functions.

Comprehensive fits to high energy data forσ,ρ, andB, and the asymptotic black-disk limit

We demonstrate that the entirety of the data on proton--proton and antiproton--proton forward scattering between 6 GeV and 57 TeV center-of-mass energy is sufficient to show that $\sigma_{\rm elas}/\sigma_{\rm tot} \rightarrow 1/2$, and that $8\pi B/\sigma_{\rm tot}\rightarrow 1$ at very high energies, where $B$ the forward slope parameter for the differential elastic scattering cross sections. The relations demonstrate convincingly that the asymptotic $pp$ and $\bar{p}p$ scattering amplitudes approach those of scattering from a black disk. This result obviously has implications for any new physics that modifies the forward scattering amplitudes.

Investigation of 17F+p elastic scattering at near-barrier energies

The 17F +p elastic scattering at two near-barrier energies of 3.5 and 4.3 MeV/nucleon, have been analyzed in the framework of the single folding approach. The folded potentials are constructed by folding the density-dependent (DDM3Y) effective nucleon-nucleon interaction over the nuclear density of the one-proton halo nucleus 17F. Two versions of the density are considered. In addition, two versions of the one-nucleon knock-on exchange potentials are introduced to construct the real microscopic potentials. The derived potentials supplemented by phenomenological Woods-Saxon imaginary and spin-orbit potentials produced excellent description of the differential elastic scattering cross sections at the higher energy without need to introduce any renormalization. At the lower energy, however, in order to successfully reproduce the data, it is necessary to reduce the strength of the constructed real DDM3Y potential by about 25% of its original value. Furthermore, good agreement with data is obtained using the extracted microscopic DDM3Y potentials for both real and imaginary parts. Moreover, the interesting notch test is applied to investigate the sensitivity of the elastic scattering cross section to the radial distribution of the constructed microscopic potentials. The extracted reaction (absorption) cross sections are, also, investigated.

Dispersive optical-model potential for protons in 100 ⩽ A ⩽ 132 even–even tin isotopes

Data on single-particle energies, differential elastic-scattering cross sections, and total cross sections for proton-induced reactions on stable tin isotopes were analyzed on the basis of the dispersive optical model. Good agreement with experimental data was obtained by setting the parameters of the dispersive optical potential to values averaged over the tin isotopic chain and by assuming that the dependence of surface absorption on the neutron–proton asymmetry is close to a traditional dependence. Predictive calculations for single-particle proton spectra and total reaction cross sections were performed for the doubly magic isotopes 100,132Sn. The calculated values of the energy gap between the 1h11/2–1g7/2 and 1g7/2–2d5/2 states were found to be in good agreement with the results of calculations performed with allowance for the tensor component of the effective nucleon–nucleon interaction.

Low energy positron interactions with uracil--total scattering, positronium formation, and differential elastic scattering cross sections.

Measurements of the grand total and total positronium formation cross sections for positron scattering from uracil have been performed for energies between 1 and 180eV, using a trap-based beam apparatus. Angular, quasi-elastic differential cross section measurements at 1, 3, 5, 10, and 20 eV are also presented and discussed. These measurements are compared to existing experimental results and theoretical calculations, including our own calculations using a variant of the independent atom approach.

Insights into low-energy elastic scattering of halo nuclei

Recent measurements of low-energy (quasi)elastic-scattering angular distribution of halo nuclei have shown a strong suppression of the Coulomb-nuclear interference peak. Examining the components of the elastic-scattering differential cross sections for 11Be+64Zn and 6He+208Pb at energies near the Coulomb barrier, this appears to be caused by a dramatic phase-change (destructive) of the reduced Coulomb-nuclear interference term due to continuum couplings.

New Resolved Resonance Region Evaluation for 63,65Cu for Nuclear Criticality Safety Program

A new resolved resonance region evaluation of 63,65Cu was done in the energy region from 10−5 eV to 99.5 keV. The R-Matrix SAMMY method using the Reich-Moore approximation was used to create a new set of consistent resonance parameters. The new evaluation is based on three experimental transmission data sets: two measured at ORELA and one at MITR, plus two radiative capture experimental data sets from GELINA. A total of 141 new resonances were identified for 63Cu and 117 for 65Cu. The corresponding set of external resonances for each isotope is based on the identified resonances above 99.5 keV from the ORELA transmission data. The negative external levels (bound levels) have been determined to match the thermal cross section measured at the MITR. Differential elastic scattering cross sections have been calculated from the new set of resonance parameters. Benchmarking calculations were carried out on a set of ICSBEP benchmarks.

Reprint of: Neon interatomic potentials from scattering data and crystalline properties

Interatomic potentials for Ne2 derived from recent differential elastic scattering cross section measurements and properties of solid neon are presented. Cross sections and second virial coefficients are calculated with the proposed potentials and comparisons with experiment are made. The Ne2 potential derived from scattering data only is shown to provide a good fit to the solid state data.

Monte Carlo study of electron-beam penetration and backscattering in multi-walled carbon nanotube materials: The effect of different scattering models

A systematic study of electron-beam penetration and backscattering in multi-walled carbon nanotube (MWCNT) materials for beam energies of ∼0.3 to 30 keV is presented based on event-by-event Monte Carlo simulation of electron trajectories using state-of-the-art scattering cross sections. The importance of different analytic approximations for computing the elastic and inelastic electron-scattering cross sections for MWCNTs is emphasized. We offer a simple parameterization for the total and differential elastic-scattering Mott cross section, using appropriate modifications to the Browning formula and the Thomas-Fermi screening parameter. A discrete-energy-loss approach to inelastic scattering based on dielectric theory is adopted using different descriptions of the differential cross section. The sensitivity of electron penetration and backscattering parameters to the underlying scattering models is examined. Our simulations confirm the recent experimental backscattering data on MWCNT forests and, in particular, the steep increase of the backscattering yield at sub-keV energies as well as the sidewalls escape effect at high-beam energies.

Testing scaling laws for the elastic scattering of protons

Theoretical proposals of scaling laws for the differential elastic scattering cross sections of protons are confronted with experimental data over a wide energy range. Different combinations of the transferred momentum and energy resulting from the solution of the definite partial differential equation are attempted as scaling variables. Reasonable scaling of the differential cross sections in the diffraction cone has been shown for one of these variables. The violation of the geometrical scaling is ascribed to the increase of the proton blackness with energy. The origin of high-t region violations of scaling laws is discussed.

Erratum: Re-evaluation of neutron-4He elastic scattering data near 20 MeV [Phys. Rev. C83, 064616 (2011)

Measured differential elastic scattering cross sections of 17.71-, 20.97-, and 23.72-MeV neutrons from liquid helium-4 were re-evaluated and corrected for sample size and multiple scattering effects by means of a Monte Carlo technique implemented in a more recent code (MCNPX). Results indicate that earlier corrections via a code, MAGGIE-2, overestimated the size of multiple scattering effects by an order of magnitude. The corrected differential cross sections and Legendre coefficients obtained by least-squares fits are given.

Differential elastic and total electron scattering cross sections of tetrahydrofuran

Differential elastic scattering cross sections of tetrahydrofuran for electrons were measured absolutely in the energy range from 20 eV to 1 keV at scattering angles between 5\ifmmode^\circ\else\textdegree\fi{} and 135\ifmmode^\circ\else\textdegree\fi{}. The measurements were carried out using a crossed-beam arrangement without the application of the widely used relative flow technique. The experimental differential scattering cross sections could be put on an absolute scale by means of the total electron scattering cross sections of tetrahydrofuran and of the current loss of the primary electron beam in the forward direction arising due to the scattering by the molecular beam. The total scattering cross sections were determined for electron energies between 6 eV and 1 keV using a separate linear transmission experiment. The differential cross sections of tetrahydrofuran for the elastic scattering of electrons were also calculated in the energy range between 60 eV and 1 keV by applying the modified independent-atom model. A comparison with the experimental results showed a satisfactory agreement, indicating that the selected theoretical model is adequate for these calculations.

Comparative analysis of the characteristics of the elastic scattering of protons by lithium isotopes 6, 7, 8, 9Li, performed using Glauber’s multiple diffraction scattering theory

Differential cross sections and vector analyzing powers are calculated for the elastic scattering of protons by lithium isotopes 6Li, 7Li, 8Li, and 9Li at energies of 60 and 200 MeV. The calculations are performed using Glauber’s multiple diffraction scattering theory in the two-particle (for 7Li) and three-particle (for 6,8,9Li) models with realistic intercluster interaction potentials. An analysis of the relationship between the differential elastic scattering cross section and various wave functions, calculated using different interaction potentials, is presented for the 8, 9Li isotopes.

Elastic scattering at 7 TeV and high-energy cross section for cosmic ray studies

The recent measurements of the elastic cross section by the TOTEM Collaboration together with the first estimations of the inelastic cross sections by other LHC detectors are used to test the simplest version of the geometrical model of the proton–proton scattering. We show that the description found for lower energy data, with the modest adjustment of the model parameter extrapolation, could be, in principle, used to describe the LHC measurement and to predict the cross sections in very high energy cosmic ray domain. However, the shape of the first elastic dip in the elastic differential scattering cross section suggests that the ratio of the real to the imaginary part of the elastic amplitude falls rather fast and the analysis of the elastic cross-section fraction suggests that the geometrical picture and scaling of the proton–proton collision should be modified when entering the ultrahigh-energy domain.

Relativistic nucleon optical potentials with isospin dependence in a Dirac-Brueckner-Hartree-Fock approach

The relativistic optical model potential (OMP) for nucleon-nucleus scattering is investigated in the framework of Dirac-Brueckner-Hartree-Fock (DBHF) approach using the Bonn-B One-Boson- Exchange potential for the bare nucleon-nucleon interaction. Both real and imaginary parts of isospin-dependent nucleon self-energies in nuclear medium are derived from the DBHF approach based on the projection techniques within the subtracted T -matrix representation. The Dirac potentials as well as the corresponding Schrodinger equivalent potentials are evaluated. An improved local density approximation is employed in this analysis, where a range parameter is included to account for a finite-range correction of the nucleon-nucleon interaction. As an example the total cross sections, differential elastic scattering cross sections, analyzing powers for n, p + 27Al at incident energy 100 keV < E < 250 MeV are calculated. The results derived from this microscopic approach of the OMP are compared to the experimental data, as well as the results obtained with a phenomenological OMP. A good agreement between the theoretical results and the measurements can be achieved for all incident energies using a constant value for the range parameter.

Elastic photoelectron-scattering effects in quantitative X-ray photoelectron spectroscopy

We present improved formulae for the correction parameters Qx and βeff that are used to account for elastic scattering of photoelectrons in quantitative X-ray photoelectron spectroscopy (XPS). The new formulae are based on new Monte Carlo simulations for 584 photoelectrons in 39 elemental solids that could be excited by Mg Kα and Al Kα X-rays in 315 different XPS configurations. The new simulations differed from similar earlier calculations in that differential elastic-scattering cross sections calculated from the Dirac–Hartree–Fock potential were utilized rather than those from the Thomas–Fermi–Dirac potential, a smaller analyzer acceptance angle was chosen, and the number of trajectories in each simulation was an order of magnitude larger. New values of Qx and βeff were obtained for each photoelectron line, each X-ray source, and each XPS configuration. These Qx and βeff values could be fitted to simple two-parameter expressions, each a function of the single-scattering albedo and the photoelectron emission angle. Values of Qx from the new predictive formula differed from the previous expression by less than 1%. Larger deviations in the values of βeff, up to 2.5%, were found from the new fit to the βeff parameter. The new expressions for Qx and βeff provide a convenient means for correction of elastic-scattering effects in XPS.