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

The experimental data available for magnesium (p,p) elastic scattering cross-section at angles and energies suitable for Ion Beam Analysis have been evaluated using the theoretical model approach together with additional measurements and benchmark experiments. The results obtained provide the evaluated differential cross-sections for magnesium (p,p) elastic scattering in the energy region up to 2.7 MeV.     

Cross-section for D(p,p)D elastic scattering from 1.8 to 3.2 MeV at the laboratory angles of 155° and 165°

The D(p,p)D cross-sections for elastic scattering of proton on deuterium over incident proton energy range from 1.8 to 3.2 MeV at both laboratory angles of 155° and 165° were measured. A thin solid state target Ni/TiD_x/Ta/Al used for cross-section measurement was fabricated by firstly depositing layers of Ta, Ti and Ni film on the Al foil substrate of about 7 μm in turn using magnetron sputtering and then deuterating under the deuterium atmosphere. The areal density of metal element in each layer of film was measured with RBS analysis by using a 4.0 MeV ⁴He ion beam, while the areal density of the deuterium absorbed in the Ti film was measured with ERD analysis by using a 6.0 MeV ¹⁶O ion beam. The results show that the cross-sections of p-D scattering under this experimental circumstance were much enhanced over the Rutherford cross-section value. It was found that the enhancement increases linearly as the energy of the incident beam increases. The total uncertainty in the measurements was less than 7.5%.     

An efficient deterministic method for generating non-negative scattering cross-sections

In the conventional discrete ordinates approach, the scattering source is approximated as a truncated Legendre series. In case of highly anisotropic scattering problems (e.g., incident beam problems), the truncated Legendre scattering cross-sections give unphysical negative cross-sections in some values of μ (cosine of scattering angle). These unphysical artifacts cause negative scattering sources and negative angular fluxes. In addition to that, negative angular fluxes may cause wrong scalar flux as well. A new method to generate non-negative scattering cross-sections, which is very efficient and deterministic, is proposed in this paper. The main idea of this method is to make non-negative scattering cross-sections that produce equivalent scattering sources. This method does not have a practical limitation to generate non-negative scattering cross-sections because the calculations of the scattering sources are performed with the conventional truncated cross-section data provided from the standard processing codes. In the both neutron and the photon/electron coupled cases, an inadequate truncated Legendre order causes problems, e.g., inaccurate angular distribution of scattering for low order, oscillations of differential scattering cross-sections where cross-sections are small for high order expansions, and negative differential scattering cross-sections in some values of μ.

In the neutron case, if the anisotropy is very high compared to the truncated Legendre order, inaccurate angular distributions of scattering occur especially in within-group scattering. Even if the truncated Legendre order is quite high to represent angular distribution of scattering in the photon/electron coupled case, it still causes oscillations where the cross-sections are small.

The method in this paper achieves both an accurate angular distribution of scattering and non-negative scattering cross-sections for neutron and photon/electron coupled cases. The generated non-negative scattering cross-sections with the new method are compared to the conventional scattering cross-sections and tested in the transport calculations. The numerical results tested in the transport calculation give accurate results without unphysical negative angular fluxes.     

Measurements and evaluation of the cross-section for helium elastic scattering from nitrogen

The cross-sections for the elastic scattering of alphas from natural nitrogen were measured at three laboratory scattering angles: 118°, 150° and 165° at non-Rutherford scattering energies from 2.5 to 4.0 MeV. Experimental data obtained in this work, together with all previously published data, were used for the cross-section evaluation. Model calculations with comparison and fitting to the experimental data were used for the evaluation of the cross-section. As a result of the work, the recommended cross-sections for scattering of alphas from nitrogen have been produced in the energy region of 1.6-4.6 MeV.     

An empirical formula for L line X-ray production cross-section of elements from Ag to U for protons below 3.5 MeV

When computing element concentration from proton induced X-ray emission analysis, an important parameter is the X-ray production cross-section. There have been numerous experimental and theoretical works in this field. Nonetheless, although there is a simple analytical formula to compute K X-ray cross-sections, there is no such ones for the L lines. We present here analytical formulas for the cross-section of the three main X-ray lines L, L_β and L_γ based on experimental data. So far, nearly 3000 values of cross-sections for elements from Ag to U and proton energy ranging from 0.5 to 3.5 MeV have been collected from various references. This experimental data set has been fitted for each X-ray line with an exponential function depending on the proton energy and on the element atomic number. These fitted values have then been compared to the experimental data and with theoretical values obtained by the ECPSSR theory and Coster–Kronig fluorescence yields.     

Comparison and sensitivity analysis of the core characteristics of a sodium-cooled fast breeder reactor with 750 MWe output evaluated by JENDL-4.0 and ADJ2000R

Core characteristics of a sodium-cooled fast breeder reactor (FBR) with 750 MWe output using highly decontaminated uranium and plutonium and highly minor-actinide-containing compositions were evaluated using the fast reactor cross-section set generated by the new Japanese nuclear data library JENDL-4.0. The core characteristics were compared with those obtained using the unified cross-section set ADJ2000R in order to investigate the differences between both the results. The effects on the core characteristics caused by the differences in the nuclear data of important reactions and nuclides in the cross-section sets were analyzed by a burnup sensitivity analysis. It was confirmed that adopting JENDL-4.0 to the FBR core design improves the breeding ratio, the burnup reactivity, and the reactivity control balance, because of the differences in the capture cross-sections of U-238 and Pu-239 of both the libraries. The difference in the sodium void reactivity evaluated with both the libraries was less than 1% because the increase caused by the differences in the elastic scattering cross-sections of sodium, the inelastic scattering cross-section, and the μ-average value of U-238 was practically cancelled out by the decrease caused by the differences in the capture cross-sections of Pu-239, the inelastic scattering cross-section of iron, and the capture cross-sections of Am-241.     

Applying elastic backscattering spectrometry when the nuclear excitation function has a fine structure

For some nuclei the (non-Rutherford) elastic scattering cross-section has a fine structure with a typical width of the resonances of 1–10 keV. It is shown that bulk sample backscattering spectra can be calculated correctly in these cases only if these are carefully taken into account. The proton elastic backscattering (EBS) spectrum from bulk aluminium was measured just above the interval 1.35–1.75 MeV where a strong resonance structure in the ²⁷Al(p,p₀)²⁷Al cross-section has a relatively high density. Different sets of the Al cross-section data were employed in the simulation: the high resolution proton resonance measurement results retrieved by R-matrix calculations and experimental data obtained later especially for use in IBA. These data sets were consistent, but the latter sets did not resolve the fine structure of the cross-section. The simulations reproduce the spectra well only for the high resolution data: that is, EBS spectra can be simulated provided that the scattering cross-section include all the detail of the fine structure.     

Neutron elastic scattering angular distribution in the resolved and unresolved resonance regions

We derive a simple relationship between observed total cross sections and elastic scattering angular distributions for neutron-induced reactions in the fast energy range by combining resonance theory and the optical model (OM). This relationship enables us to estimate the anisotropy in the scattering angular distribution when experimental total cross-section data are available. We apply this method to the angular distributions of ⁵⁸Ni and ⁵⁶Fe and compare with the evaluated values which are based on the experimental data. We also explore the method with ⁹⁰Zr for which the multi-level Breit-Wigner resonance parameters are given.     

Comparison of the analytical sensitivities for non-1/v elements in different neutron beams

Irregular nuclides such as ¹¹³Cd, and some rare-earth isotopes show different analytical sensitivities in PGAA performed at different facilities, because the cross-sections of these nuclides have strong low-energy resonances which partly overlap the energy range of typical neutron beams used for activation. A series of systematic measurements has been performed in the spectrally different cold and thermal neutron beams of the Budapest Research Reactor, Hungary and at the research reactor of NIST, Gaithersburg, USA to quantitatively study the non-1/v behaviour of irregular nuclides. Samples were prepared that contained one of the irregular nuclides and also a regular one (¹⁰B, ³⁵Cl and ⁵⁶Fe) and their activation ratios were compared as measured in five different beams. Theoretical values of the activation ratios were calculated from estimates of the actual neutron spectra and cross-section data, and show a generally good correspondence to the experimental results, although some details are still not reproduced.     

A detailed study of the d + B system for nuclear reaction analysis - Part A: The B(d,p)B reaction in the energy region Ed,lab = 900-2000 keV

The differential cross-sections of the ¹⁰B(d,p_{0,1,2,3,4-5,6}) reactions for the determination of the depth distribution of boron in near-surface layers of materials have been determined in the projectile energy region E_d,lab = 900-2000 keV. The experiment was carried out in energy steps of 25 keV and for eight detector angles between 135° and 170° (in steps of 5°). The obtained experimental data are suitable for nuclear reaction analysis (NRA) studies. A qualitative discussion of the observed cross-section variations through the strong influence of overlapping resonances in the d + ¹⁰B system is also presented.     

Complementary use of ion beam elastic backscattering and recoil detection analysis for the precise determination of the composition of thin films made of light elements

Rutherford backscattering spectrometry (RBS) is a well known powerful technique to obtain depth profiles of the constituent elements in a thin film deposited on a substrate made of lighter elements. In its standard use the probing beam is typically 2 MeV He. Its capabilities to obtain precise composition profiles are severely diminished when the overlaying film is made of elements lighter than the substrate. In this situation the analysis of the energy of the recoiled element from the sample in the elastic scattering event, the ERDA technique may be advantageous. For the detection of light elements it is also possible to use beams at specific energies producing elastic resonances with these light elements to be analyzed, with a much higher scattering cross sections than the Rutherford values. This technique may be called non-RBS. In this work we report on the complementary use of ERDA with a 30 MeV Cl beam and non-RBS with 1756 keV H ions to characterize thin films made of boron, carbon and nitrogen (BCN) deposited on Si substrates.     

Rutherford backscattering spectroscopy and elastic recoil detection analysis with lithium ions – The better alternative to helium?

Rutherford backscattering spectroscopy (RBS) and elastic recoil detection analysis (ERDA) with lithium ions are compared to using helium ions. The availability and accuracy of backscattering cross-section and stopping power data for incident Li ions are reviewed, and energy broadening contributions due to detector resolution and energy loss straggling are discussed. Theoretical calculations of the depth resolution are compared with experimental data for RBS from Nb/Co multilayers and foil-ERDA from amorphous hydrogenated carbon multilayers. In RBS about the same or better depth resolution with Li than with He is achieved, while in ERDA for the detection of hydrogen isotopes the depth resolution is increased by a factor of about 1.5 compared to incident He.     

Parameters of the resonance levels of fissile nuclei (review)

Conclusion The development of techniques for measuring cross-sections has permitted a considerable extension of the range of energies over which these measurements can be carried out with a resolution that is sufficiently high for analysis; simultaneously, the range of nuclei studied has been extended.However, certain difficulties have appeared in processing the experimental data which complicate the interpretation of the results obtained. It is possible to compute more or less reliably the established form of statistical distributions of the level parameters only for Pu²³⁹. For fissile nuclei such as U²³³, U²³⁵ and Pu²⁴¹, the nature of the distributions indicates the existence of significant distortions, associated with the methods of data processing used. Analysis of cross-section models of fissile nuclei shows that the origin of these distortions is associated with both the neglect of interference effects and difficulties of principles, raising doubt on the feasibility of carrying out unambiguous cross-section analysis. In order to verify this conclusion, it is necessary to carry out careful interference analysis of cross-sections over wider energy ranges.At present, the possibilities of processing cross-sections are limited by insufficiently high measurement accuracy of cross-sections between resonances and the absence of information about spin mechanisms of the levels. In order to increase the reliability of the analysis it will be necessary to undertake measurements of the energy dependence of and the radiative capture cross-sections of the nuclei studied.Translated from Atomnaya Énergiya, Vol. 23, No. 1, pp. 6–19, July, 1967.     

Evaluation of neutron nuclear data for Technetium-99

Neutron nuclear data of ⁹⁹Tc was evaluated, considering cross-sections and spectra provided from recent experiments. The evaluation was made in the incident neutron energy range from 1 keV to 20 MeV, using the optical model and nuclear reaction models. The optical model calculation based on the coupled-channels method was performed for the interaction of neutrons with ⁹⁹Tc, and potential parameters appropriately chosen reasonably explain the measured data of total cross-section. The cross-section of inelastic scattering, capture, (n, 2n), (n, p), (n, α) and (n, n′α) reactions, and γ-ray emission spectra were calculated on the basis of statistical model with preequilibrium and direct components, and they were compared with available experimental data. It is found that the presently evaluated cross-sections and γ-ray emission spectra well reproduce those experimental values and that there is a large discrepancy among the present result and evaluated data for neutron emission spectra. The obtained capture cross-section increases at the energies below 1 MeV, relative to that in JENDL-4.0. This makes the transmutation efficiency of ⁹⁹Tc into stable ¹⁰⁰Ru by accelerator driven system enhanced. The production cross-section of ⁹⁹Mo important for the medical use of nuclear diagnostics reduces by 5–30% at the energies above 12 MeV, compared with JENDL-4.0.     

Modeling of ion beam induced damage in Si during channeling Rutherford backscattering spectrometry analysis

We have modeled damage creation by an analyzing beam during channeling Rutherford backscattering spectrometry (RBS) analysis. Based on classic scattering theory and the assumption that only a dechanneled ion beam can cause displacements, a chi-square approach is used to fit the modeled spectra with experimental profiles, to extract the dechanneling cross section and the displacement creation efficiency. The study has shown that, for a 2.0 MeV He beam channeled along a Si(1 0 0) axis, the efficiency of defect creation by dechanneled beams is about 8% of the value predicted from the Kichin-Pease model. This suggests a significant dynamic annealing of point defects. The modeling procedure in this work can be used to predict the displacement creation during channeling RBS analysis.     

A method for calculating proton-nucleus elastic cross-sections

Recently [Nucl. Instr. and Meth. B 145 (1998) 277; Extraction of in-medium nucleon-nucleon amplitude from experiment, NASA-TP, 1998], we developed a method of extracting nucleon-nucleon (N-N) cross-sections in the medium directly from experiment. The in-medium N-N cross-sections form the basic ingredients of several heavy-ion scattering approaches including the coupled-channel approach developed at the NASA Langley Research Center. We investigated [Proton-nucleus total cross-sections in coupled-channel approach, NASA/TP, 2000; Nucl. Instr. and Meth. B 173-174 (2001) 391] the ratio of real to imaginary part of the two body scattering amplitude in the medium. These ratios are used in combination with the in-medium N-N cross-sections to calculate proton-nucleus elastic cross-sections. The agreement is excellent with the available experimental data. These cross-sections are needed for the radiation risk assessment of space missions.     

Proton elastic scattering and proton induced γ-ray emission cross-sections on Na from 2 to 5 MeV

Differential cross-sections for proton elastic scattering on sodium and for γ-ray emission from the reactions ²³Na(p,p′γ)²³Na (E_γ = 440 keV and E_γ = 1636 keV) and ²³Na(p,α′γ)²⁰Ne (E_γ = 1634 keV) were measured for proton energies from 2.2 to 5.2 MeV using a 63 μg/cm² NaBr target evaporated on a self-supporting thin C film.The γ-rays were detected by a 38% relative efficiency Ge detector placed at an angle of 135° with respect to the beam direction, while the backscattered protons were collected by a Si surface barrier detector placed at a scattering angle of 150°. Absolute differential cross-sections were obtained with an overall uncertainty estimated to be better than ±6.0% for elastic scattering and ±12% for γ-ray emission, at all the beam energies.To provide a convincing test of the overall validity of the measured elastic scattering cross-section, thick target benchmark experiments at several proton energies are presented.     

Measurement of (p,p) elastic differential cross-sections for carbon, nitrogen, oxygen, aluminium and silicon in the 500–2500 keV range at 140° and 178° laboratory scattering angles

We measured the (p,p) elastic scattering cross-sections of natural samples of carbon, nitrogen, oxygen, aluminium and silicon at energies ranging between 500 and 2500 keV and at laboratory scattering angles of 178° and 140°. Results are compared with previous literature data and simulations and are presented in graphical form. The measured cross-sections have been used to simulate spectra taken from know samples and have been found appropriate for quantitative calculations.     

Cross-section for proton-tritium scattering from 1.4 to 3.4 MeV at the laboratory angle of 165°

The elastic scattering cross-section for proton scattering from tritium was measured at a laboratory angle of 165° and over an incident proton energy range from 1.4 to 3.4 MeV. A thin solid target containing 1.62 × 10¹⁷ T atoms/cm² was prepared by absorption of tritium into a film of titanium on aluminium foil backing. The cross-section increases almost linearly with decreasing energy in the higher energy region of 2-3.4 MeV. The currently measured cross-section data are compared with data available in the literature values and they show a similarly linear trend in a similar higher energy range. The maximum difference in the cross-section at almost the same scattering angle between current data and the previous results is no worse than 2.3%.