Depth resolution and recoil cross section for analyzing hydrogen in solids using elastic recoil detection with 4He beam

Two aspects of the elastic recoil detection technique for analyzing H and D are described; i) experimental factors which effectively limit the depth resolution in Al film, and ii) determination of the recoil cross section for H(⁴He, ⁴He)H and D(⁴He, ⁴He)D reactions in the range of 1.5–3.0 MeV energy of ⁴He. Both experimental and theoretical estimates of the depth resolution are presented and are in good agreement each other. The theoretical estimate therefore provides a reliable guide to find optimum resolution conditions. The recoil cross section for H is more than double the theoretical Rutherford scattering value and that for D becomes greater than 30 times Rutherford near the resonance energy of 2.1 MeV ⁴He.     

The calculation of the differential cross sections for recoil protons in 4He-p Scattering

The equation relating phase shift to energy given by the effective range theory for charged particle reactions and the effective range parameters which can well fit the experimental data of P-⁴He elastic scattering have been used to obtain the phase shifts and differential cross sections of protons in p-⁴He elastic scattering. Thereafter the differential cross section of recoil protons in ⁴He-p elastic scattering are calculated through the principle of detailed balance and compared with the experimental data and Rutherford cross sections. Better consistency between experimental and theoretical values than in previous work is achieved.     

Stopping of 0.3-1.2 MeV/u protons and alpha particles in Si

The stopping cross sections ε(E) of silicon for protons and alpha particles have been measured over the velocity range 0.3-1.2 MeV/u from a Si//SiO₂//Si (SIMOX) target using the Rutherford backscattering spectrometry (RBS) with special emphasis put on experimental aspects. A detection geometry coupling simultaneously two solid-state Si detectors placed at 165° and 150° relative to each side of the incident beam direction was used to measure the energies of the scattered ions and determine their energy losses within the stopping medium. In this way, the basic energy parameter, E_x, at the Si/SiO₂ interface for a given incident energy E₀ is the same for ions backscattered in the two directions off both the Si and O target elements, and systematic uncertainties in the ε(E) data mainly originating from the target thickness are significantly minimized. A powerful computer code has been elaborated for extracting the relevant ε(E) experimental data and the associated overall uncertainty that amounts to less than 3%. The measured ε(E) data sets were found to be in fair agreement with Paul’s compilation and with values calculated by the SRIM 06 computer code. In the case of ⁴He⁺ ions, experimental data for the γ effective charge parameter have been deduced by scaling the measured stopping cross sections to those of protons crossing the same target with the same velocity, and compared to the predictions of the SRIM 06 computer code. It is found that the γ-parameter values generated by the latter code slightly deviate from experiment over the velocity region around the stopping cross section maximum where strong charge exchanges usually occur.     

Measurement of Average Cross Section for 233U(n, 2n)232U Reaction

Isotopically pure ²³³U samples, with only 3 × l0^?3 ppm²³²U content, were prepared by thermal neutron irradiation of thoria and subsequent chemical processing. The ²³³U sample thus obtained was reirradiated with a fission neutron spectrum in the core of the Kyoto University Reactor (KUR), and measurements were made of the fission spectrum average cross section for the ²³³U(n, 2n) ²³²U reaction. A value of 4.08±0.30 mb was obtained for this cross section, in agreement with the renormalized value of Halperin et al. within the limits of experimental error.

In order to assess the energy dependent cross section from the value of this integral measurement, the ²³³U (n, 2n) cross section was calculated assuming a Maxwellian-type fission spectrum and adopting the energy dependent evaluated cross sections of ENDF/B-III and other authors. The values of the cross section thus determined were found to be about 32 to 91% larger than the measured cross section given above. The result of Pearlstein's calculation of the ²³³U(n, 2n) cross section by the statistical model, again assuming the Maxwellian distribution, is smaller than the measured cross section by about 19%.     

Measurement of 4He-p recoil cross sections

The recoil cross sections of protons induced by ⁴He⁺ particles were experimentally determined in an energy range of 1.3–2.1 MeV at recoil angles of 20° and 30 ° . The angular dependence of the recoil cross section at 2.0 MeV was also measured. By using the principle of detailed balance, a calculation of ⁴He-p recoil cross sections were calculated from p-⁴He phase shift data. Good agreement between the experimental data and theoretical values was found. The results show that recoil cross sections at low energies are non-Rutherford and are larger than the Rutherford value by approximately a factor of 2 at 2.0 MeV.     

A method to measure the validity of trajectory simulation by removing the boundary-dependent coherent scattering contribution

A method is shown for measuring the validity of trajectory simulation, as compared to exact quantum calculation. The object is to calculate the differential cluster cross section obtained by multiple elastic scattering of a particle in a cluster of N randomly distributed point scatterers. After discussing the application of the analytic Foldy theory to the calculation of the coherent part of the cluster cross section, i.e. the diffraction pattern that is associated with the finite size of the cluster, it is shown that, for N up to ∼10³, this coherent part can be removed by a simple, exact procedure, allowing the trajectory simulation to be compared with the remaining incoherent part. A scalar measure of the relative error in the trajectory differential cluster cross section is introduced. In the examples shown, this relative error is negligible at a low density of scatterers, but increases substantially with increasing density. The relevance for low-energy electron scattering is discussed.     

Measurement of 76Se and 78Se (γ, n) Cross Sections

The (γ, n) cross sections of Se isotopes (⁷⁶Se,⁷⁸Se) were measured to supply fundamental data for estimating the inverse reaction cross section, i.e., the ⁷⁹Se(n, γ)⁸⁰Se cross section. The enriched samples and a reference ¹⁹⁷Au sample were irradiated with laser-Compton scattering (LCS) γ-rays. The excitation function of each (γ, n) cross section was determined for the energy range from each near neutron separation energy to the threshold energy of (γ, 2n) reaction. The energy point corresponding to each cross section was deduced using the accurately determined energy distribution of LCS γ-rays. Systematic (γ, n) cross sections for Se isotopes including ⁸⁰Se were compared with those calculated by using a statistical model calculation code TALYS.     

Measurements of Neutron Capture Cross Section of 237Np for Fast Neutrons

The neutron capture cross section of ²³⁷Np has been measured for fast neutrons supplied at the center of the core in the Yayoi reactor. The activation method was used for the measurement, in which the amount of the product ²³⁸Np was determined by γ-ray spectroscopy using a Ge detector. The neutron flux at the center of the core calculated by the Monte Carlo simulation code MCNP was renormalized by using the activity of a gold activation foil irradiated simultaneously. The new convention is proposed in this paper to make possible a definite comparison of the integral measurement by the activation method using fast reactor neutrons with differential measurements using accelerator-based neutrons. “Representative neutron energy” is defined in the convention at which the cross section deduced by the activation measurement has a high sensitivity. The capture cross section of ²³⁷Np corresponding to the representative neutron energy was deduced as 0:80 ± 0:04b at 214 ± 9 keV from the measured reaction rate and the energy dependence of the cross section in the nuclear data library ENDF/B-VII.0. The deduced cross section of ²³⁷Np at the representative neutron energy agrees with the evaluated data of ENDF/B-VII.0, but is 15% higher than that of JENDL-3.3 and 13% higher than that of JENDL/AC-2008.     

Evaluation of 17O(n,a)14C Cross Section

The ¹⁷O(n, a)¹⁴C cross section has been evaluated for incident neutron energies from 10^?5eV to 20MeV for accurate calculation on the ¹⁴C production in nuclear reactors. Evaluation was based on the single-level Breit-Wigner formula for the thermal to resonance energy regions. In the higher energy region, a multi-step evaporation model code PEGASUS was used, and the results were normalized using the ¹⁶O(n, a) cross section ratio of JENDL-3 evaluation to PEGASUS calculation. Results are given in tabular and graphical forms, and also as one-group cross sections using typical BWR, PWR and FBR spectra of ORIGEN-2.     

Thickness and MeV Si ions bombardment effects on the thermoelectric properties of Ce3Sb10 thin films

The three single layer Ce₃Sb₁₀ thin films were grown on silicon dioxide and quartz (suprasil) substrates with thicknesses of 297, 269 and 70 nm using ion beam assisted deposition (IBAD) technique. The high-energy cross plane Si ion bombardments with constant energy of 5 MeV have been performed with varying fluence from 1 × 10¹², 1 × 10¹³, 1 × 10¹⁴, 1 × 10¹⁵ ions/cm². The Si ions bombardment modified the thermoelectric properties of films as expected. The fluence and temperature dependence of cross plane thermoelectric parameters that are Seebeck coefficient, electrical and thermal conductivities were determined to evaluate the dimensionless figure of merit, ZT. Rutherford backscattering spectrometry (RBS) enabled us to determine the elemental composition of the deposited materials and layer thickness of each film.     

Stopping cross sections of He+ ions in bismuth

The stopping cross sections, ?(E), of He⁺ ions in bismuth have been measured by Rutherford backscattering spectrometry (RBS) at incident energies ranging from E = 1.6–3.4 MeV. The energy loss of He⁺ ions and thicknesses of the bismuth films deposited on aluminium substrates were determined from the RBS spectra at each energy for scattering angles of 130° and 165°. The film thicknesses of some of the samples were also measured by weighing and the results compared with those from RBS. Parameters for energy dependence of stopping cross section in the Varelas-Biersack interpolation formula have been obtained for bismuth from a fit to all the available experimental data. Accuracy of our method based on RBS is demonstrated by measurements on copper, for which ?(E) is already well studied. It is also shown that reliable ?(E) values may be obtained even on samples with non-uniform film thickness.     

Determination of 14N(n,2n)13N Reaction Cross Section for 14.7 MeV Neutrons

The cross section for the ¹⁴N(n, 2n)¹³N reaction in respect of 14.7 MeV neutrons has been determined. In this experiment, the ²⁷Al(n,p)²⁷Mg reaction was selected as reference standard, for its generation of the nuclide ²⁷Mg which has a half-life very close to that of ¹³N. The full-energy peaks of the γ-ray spectrum obtained by multi-channel pulse height spectrometer was analyzed with γ-ray energy resolution determined by means of normal probability plots.

The resulting value for the cross section is 8.2±1.1 mb, which is in remarkably good agreement with the value reported in literature.     

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 TiO₂ and SnO₂ 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.     

Polarization effects in non-relativistic ep scattering

The cross section which addresses the spin-flip transitions of a proton (antiproton) interacting with a polarized non-relativistic electron or positron is calculated analytically. In the case of attraction, this cross section is greatly enhanced for sufficiently small relative velocities as compared to the result obtained in the Born approximation. However, it is still very small, so that the beam polarization time turns out to be enormously large for the parameters of e^± beams available now. This practically rules out a use of such beams to polarize stored antiprotons or protons.     

Neutron Capture Cross Section Measurement of Praseodymium in the Energy Region from 0.003 eV to 140 keV

The neutron capture cross section of praseodymium (¹⁴¹Pr) has been measured relative to the ¹⁰B(n,αγ) standard cross section in the energy region from 0.003 eV to 140 keV by the neutron time-of-flight (TOF) method with a 46-MeV electron linear accelerator (linac) of the Research Reactor Institute, Kyoto University (KURRI). An assembly of Bi₄Ge₃O₁₂ (BGO) scintillators was used for the capture cross section measurement. In addition, the thermal neutron cross section (2,200 m/s value) of the ¹⁴¹Pr(n, γ)¹⁴²Pr reaction has been also measured by an activation method at the heavy water thermal neutron facility of the Kyoto University Reactor (KUR). The thermal neutron flux was monitored with the ¹⁹⁷Au(n, γ)¹⁹⁸Au standard cross section. The above TOF measurement has been normalized to the current activation data (11.6±1.3 b) at 0.0253 eV.

The evaluated data in JENDL-3.3, ENDF/B-VI, and JEF-2.2 have been in general agreement with the current result, except that the JENDL-3.3 and the JEF-2.2 values are clearly lower than the measurement in the cross section minimum region from about 10 to 500 eV.     

The (He, tf) as a surrogate reaction to determine (n, f) cross sections in the 10-20 MeV energy range

The surrogate reaction ²³⁸U(³He, tf) is used to determine the ²³⁷Np(n, f) cross section indirectly over an equivalent neutron energy range from 10 to 20 MeV. A self-supporting ∼761 μg/cm² metallic ²³⁸U foil was bombarded with a 42 MeV ³He²⁺ beam from the 88-Inch Cyclotron at Lawrence Berkeley National Laboratory (LBNL). Outgoing charged particles and fission fragments were identified using the Silicon Telescope Array for Reaction Studies (STARS) consisted of two 140 μm and one 1000 μm Micron S2 type silicon detectors. The ²³⁷Np(n, f) cross sections, determined indirectly, were compared with the ²³⁷Np(n, f) cross section data from direct measurements, the Evaluated Nuclear Data File (ENDF/B-VII.0), and the Japanese Evaluated Nuclear Data Library (JENDL 3.3) and found to closely follow those datasets. Use of the (³He, tf) reaction as a surrogate to extract (n, f) cross sections in the 10-20 MeV equivalent neutron energy range is found to be suitable.     

PROTON ELASTIC SCATTERING ANALYSIS OF C,N AND O COMPOSITION IN MATERIALS

Proton elastic scattering at energies around 2.0 MeV was used to determine the concentration of oxygen in a Y-Ba-Cu-O compound, nitrogen in a TiN film on steel substrate, and carbon and oxygen in a thin Mylar film. Proton scattering from light elements in this energy range exhibits non-Rutherford scattering cross section, which is enhanced by a factor of 4 to 7 relative to the Rutherford scattering cross section. Thus the sensitivity for the light element detection is considerably larger than that obtained by He~+ ion scattering. Quantitative analysis by proton scattering is discussed and compared with other methods.     

Proton energy determination using activated yttrium foils and ionization chambers for activity assay

Excitation functions of the ⁸⁹Y(p, xn) nuclear reactions were measured up to 18 MeV by the conventional activation method using the stacked-foil technique, and the irradiation of single foils. Activity assays of the irradiated foils were performed via ionization chamber and gamma spectroscopy methods. Activity ratios of the activation products were measured in two different facilities and evaluated for use as a practical and simple method for proton energy determinations. Cross section values measured in this work were compared with published data and with theoretical values as determined by the nuclear reaction model code EMPIRE II. In general, there was a good agreement between the experimental and theoretical values of the cross section data. Activity ratios of the isomeric and ground state of ⁸⁹Zr measured via ionization chamber were found to be useful for proton energy determinations in the energy range from 7 to 15 MeV. Proton energies above 13 MeV were accurately determined using the ^89gZr/⁸⁸Zr and ^89gZr/⁸⁸Y activity ratios measured via gamma spectroscopy.     

Differential cross-section measurements for the C(d, p0)C reaction and applications to surface analysis of materials

This work involves surface analysis by nuclear techniques, which are non-destructive, and computer simulation. The “energy analysis” method for nuclear reaction analysis is used. Energy spectra are computer simulated and compared to experimental data, giving target composition and concentration profile information. Measured values are presented for the differential cross-section of the ¹²C(d, p₀)¹³C reaction in the deuteron energy range 0.81-2.07 MeV for laboratory detection angles of 165° and 135°, using self-supported two-layered targets consisting of high purity thin films of typically 13 μg/cm² natural carbon and 65 μg/cm² gold. The error in the absolute differential cross-section values is generally ∼6%. The method, using these values, is successfully applied to determination of uniform concentration profiles of ¹²C, along considerable depths, for a thick flat target of high purity pyrolitic graphite. It is characterised a thin surface film of carbon on a thick flat quartz target. Uniform concentration profiles of ¹⁶O are also obtained from (d, p) and (d, α) reactions.     

Resonant Rutherford backscattering spectrometry for carbon diffusion in silicon

300 keV C⁺ ion implantation onto Si(1 0 0) wafers was carried out at temperatures of 400, 500, 550, 600, 650 and 700 °C. Depth profile of C was determined by resonant Rutherford backscattering spectrometry (RRBS) measurements using ¹²C(α,α)¹²C resonant reaction with the α-particle energy of 4.27 MeV. The concentration of the implanted carbon at the surface as a function of inverse of implantation temperature shows an Arrhenius behaviour. The activation energy for diffusion of carbon in Si was measured and found to be 0.434 eV, which is smaller than the activation energy (0.88 eV) for the C diffusion in Si in equilibrium condition. The possible mechanism of C diffusion in Si during irradiation conditions existing in our experiments where large concentration of vacancies and interstitials are produced is discussed and we find that the C diffusion during irradiation conditions could be due to the drag the carbon towards the surface by the vacancy flux.