Reverse Monte Carlo iterative algorithm for quantification of X-ray fluorescence analysis based on MCNP6 simulation code

Reverse Monte Carlo iterative algorithm has been developed for quantification of energy-dispersive X-ray fluorescence analysis in order to calculate the concentrations of the elementary composition in solid substances. The core of the simulation code was the MCNP6 that is a well-established and widely applied software package in the nuclear research and practice for simulation of nuclear systems or the full process of gamma- or X-ray spectrometry. The reverse Monte Carlo algorithm and the full analytical procedure was tested by quantitative XRF analysis of reference alloy samples. The atomic compositions of the reference samples were determined by reverse Monte Carlo technique and also fundamental parameter method and by spark emission atomic spectroscopy. The agreement between the results of these three analytical methods was found within the standard deviations of the major elements of the samples. The total duration of the reverse Monte Carlo numerical computation was minimized to a few minutes using the variance reduction procedures available in the MCNP6.     

Analytical formulas for calculating photoelectric attenuation coefficients

Photoelectric absorption is an interaction in which an incoming gamma ray virtually transfers all of its energy to an atomic electron, usually the most tightly bound K-shell electron of an atom. This paper uses the Win XCOM computer code as a reference base. We found analytical photoelectric attenuation coefficients for researchers using the Monte Carlo simulation program for Z∈ [1; 100] and E∈[10 keV; 3 MeV]. We define a photoelectric effect operator and coefficient operators and a series for photoelectric absorption. We have calculated two polynomial coefficient operators for use with XCOM for photoelectric absorption. We determined 14 energies and atomic number limits for elements, and we find that they are accurate limits of photoelectric absorption for fitting with XCOM.     

Advanced Geometrical Modeling of Focused Beam Reflectance Measurements (FBRM)

In the past decade the use of focused beam reflectance measurements (FBRM) has been established as an on line and in situ particle characterization technique. However, a model is required to obtain full information from the FBRM signal and to compare the results to other measurement techniques. Different modeling approaches can be found in the literature. All of these assume a laser focus of zero extension, motionless particles and fully opaque particles. It is shown in this work that these assumptions do not hold even for ideally spherical particles. For large, opaque particles, the particle velocity and a depth dependent laser velocity have to be considered. For highly transparent particles, backscattering only occurs near the edges of a crystal. Consequently, two more refined modeling approaches – the velocity model and the edge scattering model – based on Monte‐Carlo techniques are developed and verified in this work.     

Single particle size and fluorescence spectra from emissions of burning materials in a tube furnace to simulate burn pits

A single-particle fluorescence spectrometer (SPFS) and an aerodynamic particle sizer were used to measure the fluorescence spectra and particle size distribution from the particulate emissions of 12 different burning materials in a tube furnace to simulate open-air burning of garbage. Although the particulate emissions are likely dominated by particles <1 μm diameter, only the spectra of supermicron particles were measured here. The overall fluorescence spectral profiles exhibit either one or two broad bands peaked around 300–450 nm within the 280–650 nm spectral range, when the particles are illuminated with a 263-nm laser. Different burning materials have different profiles, some of them (cigarette, hair, uniform, paper, and plastics) show small changes during the burning process, and while others (beef, bread, carrot, Styrofoam, and wood) show big variations, which initially exhibit a single UV peak (around 310–340 nm) and a long shoulder in visible, and then gradually evolve into a bimodal spectrum with another visible peak (around 430–450 nm) having increasing intensity during the burning process. These spectral profiles could mainly derive from polycyclic aromatic hydrocarbons with the combinations of tyrosine-like, tryptophan-like, and other humic-like substances. About 68 % of these single-particle fluorescence spectra can be grouped into 10 clustered spectral templates that are derived from the spectra of millions of atmospheric aerosol particles observed in three locations; while the others, particularly these bimodal spectra, do not fall into any of the 10 templates. Therefore, the spectra from particulate emissions of burning materials can be easily discriminated from that of common atmospheric aerosol particles. The SFFS technology could be a good tool for monitoring burning pit emissions and possibly for distinguishing them from atmospheric aerosol particles.     

The symmetric heavy-light ansatz

The symmetric heavy-light ansatz is a method for finding the ground state of any dilute unpolarized system of attractive two-component fermions. Operationally it can be viewed as a generalization of the Kohn-Sham equations in density functional theory applied to N -body density correlations. While the original Hamiltonian has an exact Z₂ symmetry, the heavy-light ansatz breaks this symmetry by skewing the mass ratio of the two components. In the limit where one component is infinitely heavy, the many-body problem can be solved in terms of single-particle orbitals. The original Z₂ symmetry is recovered by enforcing Z₂ symmetry as a constraint on N -body density correlations for the two components. For the 1D, 2D, and 3D attractive Hubbard models the method is in very good agreement with exact Lanczos calculations for few-body systems at arbitrary coupling. For the 3D attractive Hubbard model there is very good agreement with lattice Monte Carlo results for many-body systems in the limit of infinite scattering length.     

Electron probe microanalysis (EPMA) measurement of aluminum oxide film thickness in the nanometer range on aluminum sheets

By using Monte Carlo simulation, the thickness of an aluminum oxide film in the nanometer range on aluminum sheets given different heat treatments was determined by electron probe microanalysis (EPMA) and compared with transmission electron microscopy (TEM). The film thickness was ≤50 nm. As a result, although the same analysis areas were not measured, similar deviations between EPMA and TEM were found. Consequently, we found that the Monte Carlo method was useful for measuring the oxide film thickness in the nanometer range on aluminum sheets. Copyright © 2004 John Wiley & Sons, Ltd.     

Magnetar crust electron capture for $$^{}$$Co and $$^{56}$$56Ni

Based on the relativistic mean-field effective interaction principle and random phase approximation theory in superstrong magnetic fields (SMFs), we present an analysis of the influence of SMFs on the electron Fermi energy, nuclear blinding energy, single-particle level structure and electron capture for \(^{55}\)Co, and \(^{56}\)Ni by the shell-model Monte Carlo method in the magnetar’s crust. The electron capture rates increase by two orders of magnitude due to an increase in the electron Fermi energy and a change in single-particle level structure by SMFs. Then the rates decrease by more than two orders of magnitude due to an increase in the nuclear binding energy and a reduction in the electron Fermi energy by SMFs.     

Elemental analysis by high‐energy electron excitation

The possibility of using high‐energy β‐particles (10²–10³ keV) to induce the emission of characteristic x‐rays from pure chemical elements, with important improvements with respect to conventional excitation methods, has been recently reviewed. An excitation procedure named BIXE (β‐induced x‐ray emission) is used for implementing a spectrometric technique along the lines developed for EPMA (electron probe microanalysis). We have found that by using BIXE it is possible to determine binary sample compositions of elements present at concentrations higher than 1%, by comparisons with reference samples to obtain calibration curves. Experience with EPMA shows that when ternary and higher order samples are analyzed, the use of reference samples is not enough and it is necessary to perform theoretical corrections to the relationship between the line intensity and the corresponding concentrations, as a suitable complement to the analytical procedure. Semi‐quantitative results are thus obtained with corrections applied through the ZAF method usually used in EPMA. In this work we concentrated in finding whether calibration curves as used in EPMA (where the electron beam is monochromatic) can be used in BIXE, where the electron beam is polychromatic (the β spectrum). We expect that BIXE can be developed as a spectrometric technique whose main advantages are that it is a low‐cost technique suitable for in situ studies and that the experimental arrangement and data acquisition and its evaluation are comparatively simple. Copyright © 2004 John Wiley & Sons, Ltd.     

Investigation of radiological properties of some shielding materials on charged and uncharged radiation interaction for neutron generator

Radiation interaction parameters such as total stopping power, projected range (longitudinal and lateral) straggling, mass attenuation coefficient, effective atomic number (Z_eff) and electron density (N_eff) of some shielding materials were investigated for photon and heavy charged particle interactions. The ranges, stragglings and mass attenuation coefficients were calculated for the high-density polyethylene(HDPE), borated polyethylene (BPE), brick (common silica), concrete (regular), wood, water, stainless steel (304), aluminum (alloy 6061-O), lead and bismuth using SRIM Monte Carlo software and WinXCom program. In addition, effective atomic numbers (Z_eff) and electron densities (N_eff) of HDPE, BPE, brick (common silica), concrete (regular), wood, water, stainless steel (304) and aluminum (alloy 6061-O) were calculated in the energy region 10?keV–100?MeV using mass stopping powers and mass attenuation coefficients. Two different methods namely direct and interpolation procedures were used to calculate Z_eff for comparison and significant differences were determined between the methods. Variations of the ranges, longitudinal and lateral stragglings of water, concrete and stainless steel (304) were compared with each other in the continuous kinetic energy region and discussed with respect to their Z_effs. Moreover, energy absorption buildup factors (EABF) and exposure buildup factors (EBF) of the materials were determined for gamma rays as well and were compared with each other for different photon energies and different mfps in the photon energy region 0.015–15?MeV.     

Formation of plasma dust structures at atmospheric pressure

The formation of strongly coupled stable dust structures in the plasma produced by an electron beam at atmospheric pressure was detected experimentally. Analytical expressions were derived for the ionization rate of a gas by an electron beam in an axially symmetric geometry by comparing experimental data with Monte Carlo calculations. Self-consistent one-dimensional simulations of the beam plasma were performed in the diffusion drift approximation of charged plasma particle transport with electron diffusion to determine the dust particle levitation conditions. Since almost all of the applied voltage drops on the cathode layer in the Thomson glow regime of a non-self-sustained gas discharge, a distribution of the electric field that grows toward the cathode is produced in it; this field together with the gravity produces a potential well in which the dust particles levitate to form a stable disk-shaped structure. The nonideality parameters of the dust component in the formation region of a highly ordered quasi-crystalline structure calculated using computational data for the dust particle charging problem were found to be higher than the critical value after exceeding which an ensemble of particles with a Yukawa interaction should pass to the crystalline state.     

Quantitative elemental analysis of individual particles with the use of micro‐beam X‐ray fluorescence method and Monte Carlo simulation

The aim of the work was to develop a Monte Carlo (MC) method and combine it with micro‐beam X‐ray fluorescence (XRF) technique for determination of chemical composition of individual particles. A collection of glass micro‐spheres, made of NIST (National Institute of Standards and Technoly) K3089 material of known chemical composition, with diameters in the range of 25–45 µm was investigated. The micro‐spheres were measured in a scanning micro‐beam XRF spectrometer utilising X‐ray tube as a source of primary radiation. Results obtained for low Z elements showed high dependence on particle size. It was found that the root mean square of concentration uncertainty, for the all elements present in the particle, increases with growing sample size. More accurate results were obtained for high Z elements such as Fe–Pb, as compared to others. The elemental percentage uncertainty did not exceed 14% for any particular sample and 6% for the whole group of the measured micro‐spheres as an average. Results obtained by the Monte Carlo method were compared with other analytical approaches. Copyright © 2009 John Wiley & Sons, Ltd.     

Bohr-Coster diagrams for multiply ionized states of light elements in the rangeZ = 10 to 20

Calculations in the L-S coupling approximation of the average total energies of various defect electron configurations with single or doubleK shell and varying number ofL shell vacancies for some light elements in the rangeZ = 10 to 20 are reported. The calculations show that the linear trend observed for normal Bohr-Coster diagrams (√E vsZ curves for the usual X-ray energy states) persists in the case of multiply ionized atomic states as well.     

Phase coexistence and critical point determination in polydisperse fluids

Phase equilibria of fluids with variable size polydispersity have been investigated by means of Monte Carlo simulations. In the models, spherical particles of different additive diameters interact through Lennard-Jones and hard sphere Yukawa intermolecular potentials and the underlying distribution of particle sizes is a Gaussian. The Gibbs ensemble Monte Carlo technique has been applied to determine the phase coexistence far below the critical temperature. Critical points have been estimated by finite-size scaling analysis using histogram reweighting for NpT simulation data. In order to achieve efficient sampling in the vicinity of the critical points, the hyper-parallel tempering scheme has been utilized.     

Extending the quantitative analytical capabilities of the EDXRF technique for plant‐based samples

The energy‐dispersive x‐ray fluorescence (EDXRF) technique has limitations in the quantitative analysis of light elements (low‐Z analytes with Z < 10), for many reasons. This work, however, circumvents the problem through an a priori determination of low‐Z analytes, representative of plant‐based samples. The main purpose of this work was to characterize the major elements in the dark matrix of some plant‐based samples (including biomonitors) using Rutherford backscattering spectrometry (RBS), and the results provided as a generalized input for EDXRF analysis. The derived stoichiometry and mass ratio for the moss, lichen, and cotton cellulose samples analyzed were found to be similar and close to C₇H₁₀O₅, with an average matrix of C = 49.8%, H = 4.0% and O = 45.8%. Quantitative analysis of plant‐based reference material IAEA‐336 (lichen) was subsequently carried out. Use of the a priori determined dark matrix elements (from one‐time RBS spectrometry) extended the scope of applicability of the EDXRF quantitative methods used, and improved accuracy in the elemental analysis of plant‐based samples. The results obtained were in good agreement with the reference values. Copyright © 2004 John Wiley & Sons, Ltd.     

6s and 8d state self-energy for hydrogen-like ions and new results on the self-energy screening

We use a recently published method for the renormalization of the self-energy to calculate the self-energy of 6s and 8d levels to all orders in Zα. We demonstrate the accuracy of the method and its potential for high-n, low-Z applications. We also show that this method is perfectly suited for the evaluation of the two-electron self-energy (self-energy screening). For the first time, evaluation of the screening of the 1s electron by a second one in either the 1s,2s, 2p_1/2 or 2p_3/2 shells has been performed, for 30 ⩽ Z ⩽92. This revised version was published online in July 2006 with corrections to the Cover Date.     

Experimental confirmation of the EPES sampling depth paradox for overlayer/substrate systems

Elastic-peak electron spectroscopy (EPES) has been one of the main tools for obtaining the inelastic mean free path of electrons in solids. Recently it has become clear that, if this type of experiment is done using an energetic electron beam (20-40 keV) and large scattering angles, then the recoil energies of the elastic scattering event for different elements can be resolved. This recoil energy is mass dependent and this fact makes it possible to separate the elastic-peak contributions due to electrons scattered from light and heavy elements. Here we use this energy separation to determine experimentally the sampling depth for an overlayer/substrate system. The sampling depth for a (high-Z) Au overlayer on a (low-Z) C substrate is found to be about two orders of magnitude smaller than for a C overlayer on a Au substrate, whereas the inelastic mean free path of electrons in both materials differ much less. This effect is shown to be a consequence the strong Z dependence of the elastic scattering cross section. The dependence of the spectra on the electron kinetic energy and sample rotation is also dramatically different for both sample geometries.     

Decays of Z Bosons into Triple-Quark and Double-Quark Structures

This paper presents a mechanism of decay of elementary particles, which has been developed based on a new approach. The results obtained may be of interest to experimenters engaged in the decay of Z ⁰ bosons. Schemes and modes of the structural decay of gamma structures, one of which is the Z ⁰ boson, are given. Analysis of the schemes and modes of the structural decay has shown that the decays of the product triple-quark particles (products of the decay of a Z ⁰ boson into triple-quark particles) result in the occurrence of a new mode of decay – the decay of one triple-quark particle into three triple-quark particles. According to the proposed mechanism of the decay of particles, an electron, a muon, a triton, and a gamma photon are particles consisting of a quark–antiquark pair and having a spin equal to unity.     

Mass bounds in a Z 2 scalar-fermion model

The lattice regularized Z ₂ scalar-fermion model using staggered fermions in four dimensions is investigated in the broken symmetry phase. The coupling between the fermion and scalar fields is realized with the overlapping hypercubic type of Yukawa interaction. Triviality upper bound and vacuum stability lower bound on the mass of the scalar particle are numerically estimated. Qualitative agreement between Monte Carlo data and one-loop perturbative results is obtained. Systematic errors of the upper bound are estimated. At strong Yukawa coupling, we see some quantitative disagreements due to finite cutoff effects. We also find the nondecoupling of heavy fermions as predicted from one-loop calculation.     

The fluctuation kinetics of formation of nanoparticles: Particle-size distribution

A stochastic simulation of the growth of particles on a uniform cubic lattice was performed by the Monte Carlo method. Changes in the width of the distribution (M _w /M _n ) as the size of particles increased were extremal in character. Distribution narrowing occurred much more slowly than in classic polymerization. An empirical equation relating the number of free vacancies of a growing particle and its mean size was obtained. The introduction of a stabilizer deactivating free vacancies of a growing particle caused the appearance of a critical phenomenon. At stabilizer concentrations higher than critical, large-sized particles could not form. At stabilizer concentrations close to critical, the particle-size distribution was bimodal. This resulted in an anomalously larger distribution width.