Proton Elastic Scattering Cross Sections Research Articles

Benchmark measurements of non-Rutherford proton elastic scattering cross section for boron

In the literature several elastic scattering cross-sections data sets are available for protons on 10B and 11B at energies and scattering angles suitable for elastic backscattering spectrometry (EBS) analysis. However, agreement between these different data sets is generally poor, with systematic differences up to 20%, well beyond the stated absolute uncertainties. To resolve the conflict between the different data sets in the absence of the evaluated cross-section data, a benchmark experiment was performed. Proton backscattering spectra were obtained with a thick uniform B4C target at beam energies in the range of 2.0–4.0MeV and at different scattering angles, followed by a standard direct simulation with the SIMNRA code using the available experimental cross-section data. As a result, recommendation on the most appropriate data set to be used in proton EBS analysis of boron is given.

243Am neutron-induced fission cross section in the fast neutron energy range

The existing evaluations of the ${}^{243}$Am neutron-induced fission cross section have been questioned by recent measurements performed at the GNEISS facility. In the neutron energy range from 1 to 6 MeV, the GNEISS data present deviations of more than 15$%$ with respect to the evaluations. In order to solve this problem, we have measured this cross section in reference to three different standard cross sections. The first standard reaction used corresponds to the neutron on proton elastic scattering cross section, which is known with a precision better than 0.5$%$ over a wide neutron-energy range of 1 meV to 20 MeV. The other two experiments were conducted in reference to the ${}^{235}$U(n, f) and ${}^{238}$U(n, f) reactions. The comparison between these three standard reactions ensures that systematic parameters have been correctly evaluated. Moreover, a sensitivity analysis of parameters and correlations of parameters is described and a complete variance-covariance matrix of the measurements is presented and discussed.

Measurement and parametrization of proton elastic scattering cross sections for nitrogen

The cross sections for the elastic scattering of protons from natural nitrogen at non-Rutherford scattering energies were measured at three laboratory scattering angles: 118°, 150°, and 165°. The experimental data were parametrized in the framework of nuclear physics models. A benchmark experiment was performed in order to prove that the excitation functions obtained in the present work can be used to adequately simulate the yield from a thick target containing nitrogen.

Evaluation of non-Rutherford proton elastic scattering cross section for nitrogen

The available experimental information on the proton elastic scattering from 14N in the energy range up to 5MeV was compiled. The critical analysis of the revealed discrepancies was performed taking into account the applied experimental technique and possible error sources. Based on this, the apparently reliable experimental points were selected. Model calculations with comparison and fitting to the experimental data were used for parameterization of the cross section. The R-matrix theory was employed in the calculations, the phase shifts calculated for Saxon–Woods potential well being substituted for commonly used hard-sphere ones in order to take into account direct potential scattering. The result of the evaluation is that the required excitation functions for proton elastic scattering from nitrogen may be calculated for any scattering angle with reliability exceeding that for any individual measurement. The evaluated cross sections are provided by the SigmaCalc web site at www-nds.iaea.org/sigmacalc/.

Is there model-independent evidence of the two-photon-exchange effect in the electron–proton elastic scattering cross section?

We re-analyze the data of the elastic electron proton scattering to look for model-independent evidence of the two-photon-exchange (TPE) effect. In contrast to previous analyses, TPE effect is parametrized in forms which are free of kinematical-singularity, in addition to being consistent with the constraint derived from crossing symmetry and the charge conjugation. Moreover, we fix the value of R=GE/GM as determined from the data of the polarization transfer experiment. We find that, at high Q2⩾2 GeV2 values, the contribution of the TPE effect to the slope of σR vs. ε is large and comparable with that arising from GE. It also behaves quasi-linearly in the region of current data, namely, in the range of 0.2<ε<0.95. Hence the fact that the current elastic ep cross section data shows little nonlinearity with respect to ε cannot be used to exclude the presence of the TPE effect. More precise data at extreme angles will be crucial for a model-independent extraction of the TPE effect.

Investigations of thick metal oxide films on steel surface using proton non-Rutherford backscattering technique

Protective oxide films on steel surface were investigated using proton elastic backscattering (EBS) technique. Proton elastic scattering cross sections for oxygen and iron needed for spectra simulation were measured in the energy range from 3.2 to 4.1MeV. Oxide films structure and films penetrability by heavy metal under different conditions were studied.

Proton elastic scattering cross sections of titanium from 1.0 to 3.0 MeV at the laboratory angle of 151°

For the interest in using high energy proton elastic backscattering to detect very light elements such as deuterium in titanium, the proton elastic cross sections of titanium were measured at the laboratory angles of 151° (1.0–3.0 MeV) and 170° (2.5–3.1 MeV). These cross section data show clear resonant behavior when the proton energy is higher than 2.0 MeV. A proton backscattering measurement of TiD x film was performed at 151° to serve as an application of the new cross sections. The simulation results of the backscattering spectra were satisfactory and accurate concentration results were obtained.

Analysis of proton elastic recoil cross section by using R-matrix theory

R-matrix theory is used to calculate proton elastic recoil cross sections. The Los Alamos R-matrix parameters which are based upon the proton elastic scattering cross section, are used in the calculation, and the center-of-mass energy is extended down to 0.12 MeV. The normalization is adjusted by minimizing the χ 2 value between the experimental and calculated cross sections. By comparison it is hence confirmed that our recent experimental data are consistent with the calculated results, at the measured energy range and recoil angles. The proton elastic recoil cross sections obtained by R-matrix analysis are suggested for practical ERD application since they are quite consistent with the published proton scattering cross sections for proton laboratory energy range of 0.2–17.8 MeV.

Proton elastic scattering cross section for carbon: confrontation of theory and experiment

The discrepancy between the evaluated 12C(p,p)12C cross sections and the results of the new measurement recently reported is discussed. It is shown that the basic assumption made while normalizing the new experimental data is inconsistent with the theoretical predictions. A classical approach to the estimation of the limits of Rutherford scattering is shown to be misleading.

Evaluation of non-Rutherford proton elastic scattering cross section for silicon

The experimental data available for silicon (p,p) elastic scattering cross section have been reviewed. The analysis of the data was made using the theoretical model approach. The obtained results provide the evaluated differential cross sections for silicon (p,p) elastic scattering in the energy region up to 3.0 MeV.

Proton elastic scattering cross section on carbon from 350 keV to 3 MeV

Using our set-up for the simultaneous many-angle detection of backscattered particles [1], we have measured the proton elastic scattering cross section on carbon, in the angular range from 100° to 170° (in steps of 5°) and for beam energies from 350 keV to 3 MeV. Thin self-supporting natural carbon foils have been used, ∼ 13 μg/cm 2 for the measurements from 350 to 700 keV, ∼ 50 μg/cm 2 above 700 keV. A scattering spectrum was also simultaneously recorded at 15° (purely Rutherford cross section at all energies) for normalisation purposes. Thanks to the simultaneous acquisition of this spectrum, the uncertainties in the effective target thickness and in the integrated beam charge do not affect the deduced backscattering cross section values, whose overall accuracy is estimated to be ±4% (maximum error) at all the beam energies and angles.

Evaluation of non-Rutherford proton elastic scattering cross section for carbon

The experimental data available for carbon (p,p) elastic scattering cross section have been briefly reviewed. Some discrepancies have been revealed. The analysis of the data was made using the theoretical model approach. The obtained results provide the evaluated differential cross sections for carbon (p,p) elastic scattering in the energy region up to 3.5 MeV.

Evaluation of non-Rutherford proton elastic scattering cross section for oxygen

The experimental data available for oxygen (p,p) elastic cross section have been briefly reviewed. Applicability of a theoretical approach for the proton elastic scattering cross sections evaluation has been demonstrated. Calculations were performed in frameworks of the optical model and S-matrix theory. Free model parameters were adjusted by fit to the available experimental data. The obtained results provide the evaluated differential cross sections for oxygen (p,p) elastic scattering throughout the energy region up to 4 MeV at any backward angle.

Dirac optical-model analysis of polarized protons elastic scattering from12C,16,18O,20Ne and24,26Mg at 800 MeV

Proton elastic-scattering cross-sections and analysing powers at 800 MeV have been used to derive, within the Dirac formalism, optical-model parameters for six elements from12C to26Mg. The best set of Dirac optical parameters has been obtained by searching on all nine parameters which showed a large negative real scalar potential, a large positive real vector potential and a large negative imaginary vector potential. These calculations have been found to be consistent with an imaginary scalar potential set to zero (V s i =0). Considerable improvements were obtained by using the Dirac formalism compared to the traditional Schrodinger one with a similar number of parameters.

Proton elastic scattering cross sections of carbon, nitrogen and silicon for backscattering analysis in the energy range 0.7—2.5 MeV

Differential elastic scattering cross sections of 0.7—2.5 MeV protons for carbon, nitrogen and silicon have been determined at a scattering angle θ = 170°. Results from previous measurements near θ = 170° show large variations, of the order of 10–30% in the nonresonant regions. The purpose of the present investigations is to tabulate cross section data for backscattering analysis at a single scattering angle for many elements. Proton backscattering in the non-Rutherford energy region is more sensitive in the detection of C, N and many other light elements than other ion beam methods when a high background from the matrix is absent. Proton backscattering by using the present scattering cross sections and computer data analysis are outlined. The possible interference from other nuclear reactions is considered.

Oxygen detection by non-Rutherford proton backscattering below 2.5 MeV

Oxygen detection by proton backscattering has been investigated. The oxygen detection sensitivity of 2.5 MeV proton backscattering is shown to exceed that of 4He backscattering by even a factor of about 15 depending on the matrix. The needed proton elastic scattering cross sections of oxygen for θ lab = 170° have been measured in the energy range E lab = 770–2480 keV relative to Ti and Sn elastic scattering cross sections using thin TiO 2 and SnO 2 samples. The angular dependence of the cross section was measured at energies E lab = 1790, 1990, 2191, and 2382 keV for backscattering angles. The experimental cross sections were found to be 1.1–5.7 times the pure Coulomb cross section. Theoretical calculations for the scattering cross sections were performed and their inapplicability to experimental purposes is demonstrated. Fits to experimental data are given.

Proton elastic scattering fromCa40,42,44,48at 800 MeV

New and/or corrected 800 MeV $p+^{40,42,44,48}\mathrm{Ca}$ elastic angular distributions are presented. The data, together with analyzing power measurements, are analyzed to investigate the isotopic neutron and matter density differences between these four calcium isotopes. The analysis employs a local, spin-dependent form of the second order Kerman, McManus, and Thaler optical potential in which approximately model-independent forms for the neutron densities are assumed. Nucleon-nucleon amplitude uncertainties which occur at 800 MeV are taken into account in determining the empirical isotopic density differences. The deduced neutron and matter density differences are compared to the results of other intermediate energy proton and alpha particle scattering analyses and to Hartree-Fock predictions. The various empirical results are generally in good agreement with each other and with the Hartree-Fock predictions, except for $^{48}\mathrm{Ca}$ where the results obtained here and elsewhere suggest that the $^{48}\mathrm{Ca}$ neutron excess is not distributed at quite as large a radius as predicted by Hartree-Fock theory.NUCLEAR REACTIONS Proton elastic scattering cross sections; targets, $^{40,42,44,48}\mathrm{Ca}$; ${E}_{\mathrm{lab}}=800$ MeV; second order Kerman, McManus, and Thaler optical potential; neutron and matter isotopic density differences.

Elastic scattering of polarized protons fromC13for9.1&lt;Ep&lt;18.4MeV

The proton elastic scattering cross sections for $^{13}\mathrm{C}$ have been measure at eight angles for proton energies from 9.1 to 18.4 MeV. Angular distributions of cross sections and analyzing powers were measured at 20 angles in 7.5\ifmmode^\circ\else\textdegree\fi{} steps over the range of 30\ifmmode^\circ\else\textdegree\fi{} to 155\ifmmode^\circ\else\textdegree\fi{} at ten energies between 10 and 17.5 MeV. A spin-\textonehalf{} on spin-\textonehalf{} phase-shift analysis was performed starting with spin-\textonehalf{} on spin-0 phase shifts obtained from an optical model analysis. The transformation from the \textonehalf{} on 0 case to the \textonehalf{} on \textonehalf{} case, when the second \textonehalf{} spin is totally ineffective, is presented and utilized. The results suggest that broad resonances are present near ${E}_{x}=21.5$ MeV in $^{14}\mathrm{N}$.NUCLEAR REACTIONS $^{13}\mathrm{C}(\stackrel{\ensuremath{\rightarrow}}{p}, p)$; measured $\ensuremath{\sigma}(E, \ensuremath{\theta})$, $E=9.1\ensuremath{-}18.4$ MeV; measured $A(E, \ensuremath{\theta})$, $E=10\ensuremath{-}17.5$ MeV. Phase-shift analyzed. Examined for effects of broad resonances. Enriched targets.

An energy-independent nonlocal potential model for bound and scattering states

The general expression of the nucleon-nucleus optical potential has been obtained using Watson's multiple scattering theory and Wolfenstein's parametrization of the nucleon-nucleon scattering amplitude. The resulting theoretical potential is nonlocal and consists of an energy-independent central volume plus surface real and imaginary potential and of a Thomas-like spin-orbit term. The analysis has been restricted to N = Z spherical nuclei, so that neither isospin-isospin nor spin-spin interactions have been included. The widely used Perey-Buck, Greenlees, and Watson expressions of the optical potential are easily obtained as particular cases. For practical purposes, the nonlocal potential has been parametrized in the Frahn-Lemmer form, using Woods-Saxon radial form factors, and the equivalent local potential (ELP) has been calculated by a Perey-Buck-like transformation. The ELP has a radial behavior very similar to the original nonlocal one, but the potential depths and radii are energy dependent. The six free parameters in the ELP have been adjusted to fit the available experimental data in the −70 to + 150 MeV range of interest in nuclear reactions, namely, energies of single hole and single particle states, charge distributions, proton elastic scattering cross sections, and polarizations. The fitted potential depths show an energy dependence in remarkable agreement with the model predictions with a central nonlocality range β ≅ 1 F and a spin-orbit nonlocality range β 3 ≅ 0.8 F. The relative importance of surface and volume dependence in the real central potential in also discussed.

Elastic scattering of polarized protons fromFe56in the giant resonance region ofCo57

The proton elastic scattering cross sections and analyzing powers for $^{56}\mathrm{Fe}$ have been measured for proton energies from 8.0 to 17.0 MeV. Excitation curves were measured in 100 keV steps at eight angles from ${E}_{p}=9.3 \mathrm{to} 16.5$ MeV. Angular distributions of cross sections and analyzing powers were measured at 18 angles in \ensuremath{\sim} 7.5\ifmmode^\circ\else\textdegree\fi{} steps over the range of \ensuremath{\sim} 20\ifmmode^\circ\else\textdegree\fi{} to \ensuremath{\sim} 150\ifmmode^\circ\else\textdegree\fi{} in 1.0 MeV steps from 8.0 to 17.0 MeV. A phase shift analysis indicates that the ${d}_{\frac{5}{2}}$ partial wave has the most significant energy dependence in this energy region. It is shown that this energy dependence can be essentially accounted for by the presence of a single resonance with parameters consistent with those which would be expected for the giant dipole resonance of $^{57}\mathrm{Co}$.NUCLEAR REACTIONS $^{56}\mathrm{Fe}(\stackrel{\ensuremath{\rightarrow}}{p},p)$; measured $\ensuremath{\sigma}(E,\ensuremath{\theta})$, $E=8\ensuremath{-}17$ MeV; measured $A(E,\ensuremath{\theta})$, $E=8\ensuremath{-}17$ MeV. Phase-shift analyzed. Deduced resonance parameters. Enriched targets.