Monte Carlo simulation of neutron transport in intense neutron fields

Common Monte Carlo (MC) codes for neutron transport are usually applied to neutron fields of low density under the assumption that the isotopic composition of the structure materials will not be changed in neutron reactions. This assumption is no longer valid in intense neutron fields, where an appreciable number of nuclei of the structural material may get transformed into other isotopes. Due to this time-dependent isotope- transformation; however, neutrons injected later into the system will see a different cross-section profile than the neutrons injected earlier.     

International Atomic Energy Agency intercomparison of ion beam analysis software

Ion beam analysis (IBA) includes a group of techniques for the determination of elemental concentration depth profiles of thin film materials. Often the final results rely on simulations, fits and calculations, made by dedicated codes written for specific techniques. Here we evaluate numerical codes dedicated to the analysis of Rutherford backscattering spectrometry, non-Rutherford elastic backscattering spectrometry, elastic recoil detection analysis and non-resonant nuclear reaction analysis data. Several software packages have been presented and made available to the community. New codes regularly appear, and old codes continue to be used and occasionally updated and expanded. However, those codes have to date not been validated, or even compared to each other. Consequently, IBA practitioners use codes whose validity, correctness and accuracy have never been validated beyond the authors’ efforts. In this work, we present the results of an IBA software intercomparison exercise, where seven different packages participated. These were DEPTH, GISA, DataFurnace (NDF), RBX, RUMP, SIMNRA (all analytical codes) and MCERD (a Monte Carlo code). In a first step, a series of simulations were defined, testing different capabilities of the codes, for fixed conditions. In a second step, a set of real experimental data were analysed. The main conclusion is that the codes perform well within the limits of their design, and that the largest differences in the results obtained are due to differences in the fundamental databases used (stopping power and scattering cross section). In particular, spectra can be calculated including Rutherford cross sections with screening, energy resolution convolutions including energy straggling, and pileup effects, with agreement between the codes available at the 0.1% level. This same agreement is also available for the non-RBS techniques. This agreement is not limited to calculation of spectra from particular structures with predetermined parameters, but also extends to extracting information from real data. In particular, we have shown data from an Sb implanted sample where the Sb fluence was certified with an uncertainty of 0.6%. For this sample, and using SRIM03 stopping powers for 1.5 MeV ⁴He in Si, the codes were able to extract the Sb fluence with an average 0.18% deviation from the certified value and a 0.11% agreement between the codes. Thus IBA is a suitable technique for accurate analysis where traceability is critical. These results confirm that available IBA software packages are, within their design limitations, consistent and reliable. The protocol established may be readily applied to validate future IBA software as well.     

Rayleigh, Compton and K-shell radiative resonant Raman scattering in 83Bi for 88.034 keV γ-rays

The Rayleigh, Compton and K-shell radiative resonant Raman scattering cross-sections for the 88.034 keV γ-rays have been measured in the ₈₃Bi (K-shell binding energy = 90.526 keV) element. The measurements have been performed at 130° scattering angle using reflection-mode geometrical arrangement involving the ¹⁰⁹Cd radioisotope as photon source and an LEGe detector. Computer simulations were exercised to determine distributions of the incident and emission angles, which were further used in evaluation of the absorption corrections for the incident and emitted photons in the target. The measured cross-sections for the Rayleigh scattering are compared with the modified form-factors (MFs) corrected for the anomalous-scattering factors (ASFs) and the S-matrix calculations; and those for the Compton scattering are compared with the Klein-Nishina cross-sections corrected for the non-relativistic Hartree-Fock incoherent scattering function S(x, Z). The ratios of the measured KL₂, KL₃, KM and KN_2,3 radiative resonant Raman scattering cross-sections are found to be in general agreement with those of the corresponding measured fluorescence transition probabilities.     

基于RMC程序的用康普顿轮廓进行束缚态电子多普勒展宽修正研究

堆用蒙特卡罗程序RMC具备中子、光子、电子耦合输运能力，能完成精确的屏蔽计算，其中光子输运过程采用光子数据库进行了康普顿散射模拟。本文对康普顿散射物理原理及多普勒展宽方法进行分析，使用康普顿轮廓数据对束缚态电子进行多普勒展宽修正，实现了RMC程序对自由电子和束缚态电子的选择性处理。通过核素算例测试，观察到了多普勒能谱展宽的效应，证明了该方法的正确性。通过对典型压水堆组件的计算和对比，验证了用康普顿轮廓进行束缚态电子多普勒展宽修正的必要性和正确性。     

Estimation of Shear Stress in Counter-Current Annular Flow

The accuracy to which the friction factor is correlated is important in counter-current flow (CCF) analysis using a two-fluid model. Current two-fluid model codes use correlations of friction factors developed for co-current flow, or correlations developed on the assumption of zero wall shear stress. An assessment of two-fluid model codes with these existing correlations shows that the downward flow rate of water is overestimated. An analytical model is developed to calculate the shear stress profile in a liquid film of the CCF in order to obtain information on the shear stress between the interface and the wall. Both this analysis and Bharathan's CCF data show that the wall shear stress acting on the falling water film is approximately of same order as the interfacial shear stress, and the correlation for co-current flow cannot be applied to CCF. Tentative correlations of interfacial and wall friction factors are developed based on the results of the present study.     

Optimization of GEANT4 settings for Proton Pencil Beam Scanning simulations using GATE

This study reports the investigation of different GEANT4 settings for proton therapy applications in the context of Treatment Planning System comparisons. The GEANT4.9.2 release was used through the GATE platform. We focused on the Pencil Beam Scanning delivery technique, which allows for intensity modulated proton therapy applications. The most relevant options and parameters (range cut, step size, database binning) for the simulation that influence the dose deposition were investigated, in order to determine a robust, accurate and efficient simulation environment. In this perspective, simulations of depth-dose profiles and transverse profiles at different depths and energies between 100 and 230 MeV have been assessed against reference measurements in water and PMMA. These measurements were performed in Essen, Germany, with the IBA dedicated Pencil Beam Scanning system, using Bragg-peak chambers and radiochromic films. GEANT4 simulations were also compared to the PHITS.2.14 and MCNPX.2.5.0 Monte Carlo codes. Depth-dose simulations reached 0.3 mm range accuracy compared to NIST CSDA ranges, with a dose agreement of about 1% over a set of five different energies. The transverse profiles simulated using the different Monte Carlo codes showed discrepancies, with up to 15% difference in beam widening between GEANT4 and MCNPX in water. A 8% difference between the GEANT4 multiple scattering and single scattering algorithms was observed. The simulations showed the inability of reproducing the measured transverse dose spreading with depth in PMMA, corroborating the fact that GEANT4 underestimates the lateral dose spreading. GATE was found to be a very convenient simulation environment to perform this study. A reference physics-list and an optimized parameters-list have been proposed. Satisfactory agreement against depth-dose profiles measurements was obtained. The simulation of transverse profiles using different Monte Carlo codes showed significant deviations. This point is crucial for Pencil Beam Scanning delivery simulations and suggests that the GEANT4 multiple scattering algorithm should be revised.     

Spatial distribution of reflected gamma rays by Monte Carlo simulation

In nuclear facilities, the reflection of gamma rays of the walls and metals constitutes an unknown origin of radiation. These reflected gamma rays must be estimated and determined. This study concerns reflected gamma rays on metal slabs. We evaluated the spatial distribution of the reflected gamma rays spectra by using the Monte Carlo method. An appropriate estimator for the double differential albedo is used to determine the energy spectra and the angular distribution of reflected gamma rays by slabs of iron and aluminium. We took into the account the principal interactions of gamma rays with matter: photoelectric, coherent scattering (Rayleigh), incoherent scattering (Compton) and pair creation. The Klein-Nishina differential cross section was used to select direction and energy of scattered photons after each Compton scattering. The obtained spectra show peaks at 0.511^∗ MeV for higher source energy. The Results are in good agreement with those obtained by the TRIPOLI code [J.C. Nimal et al., TRIPOLI02: Programme de Monte Carlo Polycin?etique à Trois dimensions, CEA Rapport, Commissariat à l’Energie Atomique. [1]].     

Reaction-yield dependence of the (γ, γ′) reaction of 238U on the target thickness

The dependence of the nuclear resonance fluorescence (NRF) yield on the target thickness was studied. To this end, an NRF experiment was performed on ²³⁸U using a laser Compton back-scattering (LCS) γ-ray beam at the High Intensity γ-ray Source facility at Duke University. Various thicknesses of depleted uranium targets were irradiated by an LCS γ-ray beam with an incident beam energy of ～2.475 MeV. The scattering NRF γ-rays were measured using an High-purity Germanium (HPGe) detector array positioned at scattering angles of 90° relative to the incident γ-beam. An analytical model for the NRF reaction yield (NRF RY model) is introduced to interpret the experimental data. Additionally, a Monte Carlo simulation using GEANT4 was performed to simulate the NRF interaction for a wide range of target thicknesses of the ²³⁸U. The measured NRF yield shows the saturation behavior. The results of both of the simulation and the analytical model can reproduce the saturation curve of the scattering NRF yield of ²³⁸U against the target thickness. In addition, we propose a method to deduce the precise integral cross section of the NRF reaction by fitting the NRF yield dependency on the target thickness without any absolute measurements.     

Monte-Carlo simulation of a stochastic differential equation

For solving higher dimensional diffusion equations with an inhomogeneous diffusion coefficient,Monte Carlo (MC) techniques are considered to be more effective than other algorithms,such as finite element method or finite difference method.The inhomogeneity of diffusion coefficient strongly limits the use of different numerical techniques.For better convergence,methods with higher orders have been kept forward to allow MC codes with large step size.The main focus of this work is to look for operators that can produce converging results for large step sizes.As a first step,our comparative analysis has been applied to a general stochastic problem.Subsequently,our formulization is applied to the problem of pitch angle scattering resulting from Coulomb collisions of charge particles in the toroidal devices.     

The effect of filters and collimators on Compton scatter and Pb K-series peaks in XRF bone lead analysis

The utility of Al, Cu and In filters and collimators of different diameters in the X-ray fluorescence measurement of lead in the bone was investigated. The changes in Compton scattering and Pb K-series peaks were analyzed with different filters and collimators. Compton scattering and fractional dead time were significantly reduced with the use of filters. The FWHM values of Pb Kα₁, Kβ_1,3 peaks decrease in a nearly linear relation with the ratio of length of collimator to the diameter as the small diameter collimator with long length reduces divergence of spectra, thus improves resolution. The measurement precisions of Kα₁ and Kβ_1,3 peaks were improved by applying an indium filter. The ratio of signal-to-noise slightly increases when an indium filter was used.     

A closed-form solution for the two-dimensional transport equation by the LTSN nodal method in the energy range of Compton effect

In the present work we report on a closed-form solution for the two-dimensional Compton transport equation by the LTS_N nodal method in the energy range of Compton effect. The solution is determined using the LTS_N nodal approach for homogeneous and heterogeneous rectangular domains, assuming the Klein–Nishina scattering kernel and a multi-group model. The solution is obtained by two one-dimensional S_N equation systems resulting from integrating out one of the orthogonal variables of the S_N equations in the rectangular domain. The leakage angular fluxes are approximated by exponential forms, which allows to determine a closed-form solution for the photons transport equation. The angular flux and the parameters of the medium are used for the calculation of the absorbed energy in rectangular domains with different dimensions and compositions. In this study, only the absorbed energy by Compton effect is considered. We present numerical simulations and comparisons with results obtained by using the simulation platform GEANT4 (version 9.1) with its low energy libraries.     

X-ray scattering in X-ray fluorescence spectra with X-ray tube excitation - Modelling, experiment, and Monte-Carlo simulation

X-ray scattering may contribute significantly to the spectral background of X-ray fluorescence (XRF) spectra. Based on metrological measurements carried out with a scanning electron microscope (SEM) having attached a well characterised X-ray source (polychromatic X-ray tube) and a calibrated energy dispersive X-ray spectrometer (EDS) the accuracy of a physical model for X-ray scattering is systematically evaluated for representative samples. The knowledge of the X-ray spectrometer efficiency, but also of the spectrometer response functions makes it possible to define a physical spectral background of XRF spectra. Background subtraction relying on purely mathematical procedures is state-of-the-art. The results produced by the analytical model are at least as reliable as those obtained by Monte-Carlo simulations, even without considering the very challenging contribution of multiple scattering. Special attention has been paid to Compton broadening. Relevant applications of the implementation of the analytical model presented in this paper are the prediction of the limits of detection for particular cases or the determination of the transmission of X-ray polycapillary lenses.     

惰性气体β-γ符合测量系统探测器能量及分辨率刻度

β-γ符合法是全面禁止核试验条约(CTBT)放射性核素核查中惰性气体氙测量的一种重要方法,探测器能量及分辨率刻度是其首要解决的关键技术。本工作详细介绍了β-γ符合测量系统NaI(Tl)闪烁体和塑料闪烁体探测器能量及分辨率刻度的方法和结果,采用γ放射性核素点源刻度NaI(Tl)γ射线能量及分辨率,利用137Cs661.66keVγ射线康普顿散射电子刻度塑料闪烁体β射线能量及分辨率,并与131Xem内转换电子刻度的β射线能量分辨率结果进行了比较。结果表明:用137Cs康普顿散射电子刻度塑料闪烁体β射线能量是一种简便可行的方法,但用其刻度的β射线分辨率比实际的大。     

A successful experimental observation of double-photon Compton scattering of γ rays using a single γ detector

The phenomenon of double-photon Compton scattering has been successfully observed using a single γ detector, a technique avoiding the use of the complicated slow-fast coincidence set-up used till now for observing this higher-order process. Here doubly differential collision cross-sections integrated over the directions of one of the two final photons, the direction of other one being kept fixed, are measured experimentally for 0.662 MeV incident γ photons. The energy spectra of the detected photons are observed as a long tail to the single-photon Compton line on the lower side of the full energy peak in the recorded scattered energy spectrum. The present results are in agreement with theory of this process.     

X-rays spectroscopy with a portable Compton selection chamber: detector design and results

In this paper a practical solution to perform spectral analysis of diagnostic X-ray beams is described, based on a miniaturized Compton selection chamber (CSC) using a Si-PIN detector. Results are compared with those obtained with a first prototype of CSC based on nitrogen cooled high purity germanium (HPGe) detector. With this method, the direct X-ray spectrum is Compton scattered inside the CSC, collected by a solid-state detector and reconstructed using a simplified scattering matrix experimentally determined.The results obtained will be compared with a reference standard, represented by direct spectra acquired with an HPGe detector in a laboratory facility, not applicable for on-field measurements.     

Cu-Ni和Fe-Cu合金中Cu含量与康普顿散射光子数的关系

从理论上推导了康普顿散射光子数与合金中某成分含量间的关系表达式,经分析可近似为线性关系。然后,按一定成分制备好Cu-Ni和Fe-Cu两组合金,从实验上验证了Cu-Ni和Fe-Cu两组合金中Cu含量和康普顿散射光子数间的线性关系。最后作了详尽讨论,拟进一步开拓康普顿散射的应用领域。     

The effect of an external electric field on radiation transmission and Compton scattering in plexiglass

The effect of an external electric field on radiation transmission of a plexiglass sample has been studied by using an extremely narrow-collimated-beam transmission method. Also, the photon scattering properties of the charge centers have been determined by changing the charge density distributions of the plexiglass sample with an external electric field having an intensity in the range 0-1000 V/cm. The plexiglass sample was bombarded by 59.5 keV gamma rays emitted from an Am-241 point source. The transmitted and Compton scattered photons were detected by a Si(Li) detector. Appreciable variations were observed in the transmission factors of the plexiglass sample as a function of applied field. The results show that the electrical properties of the plexiglass sample changes with the applied electric field and the gamma ray irradiations although it is a dielectric material. Furthermore, the negatively charged scattering centers are slightly more effective than the positively charged scattering centers in the Compton scattering of gamma rays from an insulator sample, similar to result found for conductor and semiconductors.     

碳同素异形体的康普顿轮廓研究

本文介绍了用康普顿散射方法研究碳同素异形体的电子动量密度分布。实验中得到了碳不同结构材料的康普顿轮廓,发现由于晶体结构、成键方式的不同,它们的核外电子动量有着较显著的区别,纳米材料的表面效应表现明显。     

A closed-form solution for the two-dimensional Fokker–Planck equation for electron transport in the range of Compton Effect

In this paper we solve the Fokker–Planck (FP) equation, an alternative approach for the Boltzmann transport equation for charged particles in a rectangular domain. To construct the solution we begin applying the P_N approximation in the angular variable and the Laplace Transform in the x-variable, thus obtaining a first order linear differential equation in y-variable, which the solution is straightforward. The angular flux of electrons and the parameters of the medium are used for the calculation of the energy deposited by the secondary electrons generated by Compton Effect. The remaining effects will not be taken into account. The results will be presented under absorbed energy form in several points of interested. We present numerical simulations and comparisons with results obtained by using Geant4 (version 8) program which applies the Monte Carlo’s technique to low energy libraries for a two-dimensional problem assuming the screened Rutherford differential scattering cross-section.