Analytical performance of Compton/Rayleigh signal ratio by total reflection X-ray fluorescence (TXRF): A potential methodological tool for sample differentiation

The high sensitivity Compton and Rayleigh X-ray scattering signals can be used to gain valuable information on the chemical composition of various matrices, by exploiting the ratio of those signals as a function of the effective atomic number (Z_eff). Neither total reflection X-ray fluorescence (TXRF) nor the effect of the experimental setup, including sample preparation, X-ray excitation source selection, and band deconvolution procedure, has been assessed in this kind of approach. Here, a Compton/Rayleigh ratio and Z_eff-based TXRF method was set up and tested as an analytical tool for milk samples differentiation. The method was developed using a 90° scattering angle and assessed using different X-ray excitation sources: a molybdenum tube (Mo Kα 17.5 KeV) and a tungsten tube (W Lα 8.5 KeV and W-Brems 35 KeV). The evaluation of independent Compton and Rayleigh signals was performed by non-Gaussian and Gaussian curve resolution methods, and both height and area-based calculations were evaluated. Different sample preparation conditions were assessed. By using 11 standard materials, a calibration curve for Compton/Rayleigh ratio versus Z_eff was established. The method was tested to determine the Z_eff of milk samples, which enabled its use as a parameter to differentiate them. Good precisions were obtained with the Mo excitation source and the area-based calculations, which allowed to differentiate undiluted milk samples by species, treatment, and fat content according to their Compton/Rayleigh ratio. This simple and rapid method has the potential to be used for the differentiation of various types of samples, including liquids, solids, and aerosols.     

Practical method for experimental effective atomic number in the coherent to Compton scattering ratio

A practical method of calculating Z_eff was developed for the coherent to Compton scattering ratio and the method is applicable for any material with known weight percentages of different elements in the compound. The coherent to Compton scattering ratio depends only on the mixture under study and provides a measurement of certain complicated functions of the atomic number Z and Z_eff. In order to measure the effective atomic number of Sb₂O₃, BaO, La₂O₃, CeO₂ and Nd₂O₃, the linear differential scattering coefficients of 59.5 keV γ-rays have been studied using a high-resolution Si(Li) semi-conductor detector. The coherent to Compton scattering ratio R is taken from the linear differential scattering coefficients μ(E, q). The results obtained have been compared with relativistic (RT) and non-relativistic (NRT) theoretical values.     

A comparative study of gamma-ray interaction and absorption in some building materials using Zeff-toolkit

The gamma-ray shielding behaviour of a material can be investigated by determining its various interaction and energy-absorption parameters (such as mass attenuation coefficients, mass energy absorption coefficients, and corresponding effective atomic numbers and electron densities). Literature review indicates that the effective atomic number (Z_eff) has been used as extensive parameters for evaluating the effects and defect in the chosen materials caused by ionising radiations (X-rays and gamma-rays). A computer program (Z_eff-toolkit) has been designed for obtaining the mean value of effective atomic number calculated by three different methods. A good agreement between the results obtained with Z_eff-toolkit, Auto_Z_eff software and experimentally measured values of Z_eff has been observed. Although the Z_eff-toolkit is capable of computing effective atomic numbers for both photon interaction (Z_eff,PI) and energy absorption (Z_eff,En) using three methods in each. No similar computer program is available in the literature which simultaneously computes these parameters simultaneously. The computed parameters have been compared and correlated in the wide energy range (0.001–20?MeV) for 10 commonly used building materials. The prominent variations in these parameters with gamma-ray photon energy have been observed due to the dominance of various absorption and scattering phenomena. The mean values of two effective atomic numbers (Z_eff,PI and Z_eff,En) are equivalent at energies below 0.002?MeV and above 0.3?MeV, indicating the dominance of gamma-ray absorption (photoelectric and pair production) over scattering (Compton) at these energies. Conversely in the energy range 0.002–0.3?MeV, the Compton scattering of gamma-rays dominates the absorption. From the 10 chosen samples of building materials, 2 soils showed better shielding behaviour than did other 8 materials.     

Experimental measurement of effective atomic number of composite materials for Compton effect in the <Emphasis Type="Italic">γ</Emphasis>-ray region 280–1115 keV by a new method

In this paper, we report a new method to determine the effective atomic number, Z _eff, of composite materials for Compton effect in the γ-ray region 280–1115 keV based on the theoretically obtained Klein–Nishina scattering cross-sections in the angular range 50°–100° as well as a method to experimentally measure differential incoherent (Compton) scattering cross-sections in this angular range. The method was employed to evaluate Z _eff for different inorganic compounds containing elements in the range Z = 1–56, at three scattering angles 60°, 80° and 100° at three incident gamma energies 279.1 keV, 661.6 keV and 1115.5 keV and we have verified this method to be an appropriate method. Interestingly, the Z _eff values so obtained for the inorganic compounds were found to be equal to the total number of electrons present in the sample as given by the atomic number of the elements constituting the sample in accordance with the chemical formula of the sample. This was the case at all the three energies.     

Non-destructive evaluation of scientific and biological samples by scattering of 145 keV gamma rays

The objective of present experiment is to assign effective atomic number (Z_eff) to samples of scientific interest (oxides of lanthanoids, also called rare earths, and alloys of lead and tin of known composition) and to measure stable iodine content of tissue (biological sample). An HPGe semiconductor detector, placed at 70° to the incident beam, detects gamma photons scattered from the sample under investigation. The experiment is performed on various elements with atomic number satisfying, 6 ≤ Z ≤ 82, for 145 keV incident photons. The intensity ratio of Rayleigh to Compton scattered peaks, corrected for photo-peak efficiency of gamma detector and absorption of photons in the sample and air, is plotted as a function of atomic number and constituted a fit curve. From this fit curve, the respective effective atomic numbers of the scientific samples are determined. The agreement of measured values of Z_eff with theoretical calculations is found to be quite satisfactory. The measured intensity ratio from phantom (KI solutions, simulating thyroid content of stable iodine) varies linearly with KI concentration and provides stable iodine content of tissue.     

Determination of effective atomic number and electron density of heavy metal oxide glasses

The effective atomic number (Z_eff) and effective electron density (N_eff) of eight heavy metal oxide (HMO) glasses have been determined using the Monte Carlo simulation code MCNP for the energy range of 10?keV–10?MeV. The interpolation method was employed to extract Z_eff and N_eff values from the simulation and that calculated with the help of XCOM program. Comparisons are also made with predictions from the Auto-Z_eff software in the same energy region. Wherever possible, the simulated values of Z_eff and N_eff are compared with experimental data. In general, a very good agreement was noticed. It was found that the Z_eff and N_eff vary with photon energy and do not have extended intermediate regions where Compton scattering is truly dominating; only dips slightly above ～1.5?MeV were recorded. Z_eff and N_eff are found to increase with PbO and Bi₂O₃ contents. It was found that the Z_eff value rather than the N_eff value is a better indicator for PbO and/or Bi₂O₃ contents.     

Determination of effective atomic numbers and mass attenuation coefficients of samples using in‐situ energy‐dispersive X‐ray fluorescence analysis

The matrix effect has a major impact on energy‐dispersive X‐ray fluorescence analysis (EDXRFA) and is difficult to be evaluated due to that the contents of some low‐atomic‐number elements cannot be identified by in‐situ EDXRFA. Up to today, the fundamental parameter algorithm proposed by Rousseau has been widely applied to correct the matrix effect. Accordingly, determining the matrix and mass attenuation coefficient (μ/ρ) of sample is a key issue for the fundamental parameter algorithm. In present work, the method to deduce μ/ρ by effective atomic number (Z_eff) was studied. First, the relationship between Z_eff and coherence to Compton scatting ratio (R) of the incident X‐ray was determined by standard samples. Then, we deduce Z_eff and their μ/ρ. The value of μ/ρ deduced by our method is in good agreement with that calculated by WinXCOM, and the relative change (Δ) is less than 7%. We also deduced Z_eff and their μ/ρ of Chinese national standard soil samples employing our method and good agreement with the calculated values were also obtained. We found that the agreement between experimental values of μ/ρ with theoretical values by WinXCOM still exists when the energy of the incident X‐ray is greater than 4 keV, and the Δ is less than 10%. The result indicates that our method may be applied directly to in‐situ EDXRFA.     

Study of radiation interaction parameters for organic compounds at gamma photon energies different from available standard radioisotopes

The present work emphasizes on the transmission of gamma photons, having energies in the range (241.8–401.8 keV) obtained by Compton scattering technique, to determine mass-attenuation coefficients (μ_m), molar-extinction coefficients (ε), mass-energy absorption coefficient (μ_en/ρ), effective atomic number (Z_eff), mean free path (MFP), half value layer (HVL), total atomic (σ_t.a) and electronic (σ_t.el) cross-sections, and Hounsfield number (H) of various organic compounds like Alcohols, Aldehydes, Ketones, Esters, Amines, Benzene compounds and Water, and further used as radiation shielding. The WinXcom software package is used to compare the experimentally deduced radiation interaction parameters with theory. The theoretical and experimental results are in good agreement within permissible experimental uncertainty. The radiation shielding parameters have been found to vary with gamma-ray energy and effective atomic number for these organic compounds under present investigations.     

Determination of binary systems based on light elements by the ratio of the Compton and Rayleigh scattering intensities

A generalization of the Compton method for determining elements with a low atomic number Z from 1 (H) to 9 (F) by the ratio of the intensities of incoherent (Compton) and coherent (Rayleigh) scattering is proposed. The generalization takes into account not only the dependence of this ratio on the effective atomic number of the scatterer material but also the momentum transfer variable x = . The new method is based on the application of calibration function of obtained by measuring scattering spectra at two values of x₁= 0.831 Å⁻¹ and x₂= 1.297 Å⁻¹ with a WDXRF spectrometer. The elemental atomic numbers and their concentrations of binary compounds with unknown compositions are determined by the solution of a system of linear equations. Coefficients of the equations are calculated from the measured ratios for the test sample and the regularization solution for the corresponding calibration. The experiments have been carried out for standard samples of single-component, binary and triple stoichiometric compounds based on H, Li, Be, B, C, O and F. The identification of these elements was found to be possible in the absence of a relationship between the positions of scattering peaks and the composition of the sample, and a qualitative and quantitative analysis of the composition of the material was carried out as part of the solution of a single inverse problem.     

Temperature dependence of the electrical resistivity of R6(Fe1-xMnx)23 compounds in the temperature range 4.2 to 300 K

The temperature dependence of the electrical resistivity of binary R₆Mn₂₃, R₆Fe₂₃ (R = Y, Dy, Ho, Er, Tm) and pseudobinary R₆(Fe_1-xMn_x)₂₃ (R = Y, Er, Ho) compounds has been determined by a four-probe measuring technique in the temperature range 4 to 400 K.The binary compounds exhibit a prop. T² dependence at low temperatures, while above 100 K a negative curvature of the -T-curves is observed.These experimental results are discussed on the basis of electron-spin wave scattering in the low temperature range and on the basis of s-d scattering in the high temperature range, taking explicitly into account the temperature dependence of the chemical potential.The pseudobinary compounds generally exhibit a decreasing resitivity with increasing temperature, combined with a high residual resistivity. These facts are explained by the so-called strong scattering mechanism and the appearance of “quasilocalized” states.     

Experimental evaluation of effective atomic number of composite materials using back-scattering of gamma photons

A method has been presented for calculation of effective atomic number (Z_eff) of composite materials, by using back-scattering of 662?keV gamma photons obtained from a ¹³⁷Cs mono-energetic radioactive source. The present technique is a non-destructive approach, and is employed to evaluate Z_eff of different composite materials, by interacting gamma photons with semi-infinite material in a back-scattering geometry, using a 3^″?×?3^″ NaI(Tl) scintillation detector. The present work is undertaken to study the effect of target thickness on intensity distribution of gamma photons which are multiply back-scattered from targets (pure elements) and composites (mixtures of different elements). The intensity of multiply back-scattered events increases with increasing target thickness and finally saturates. The saturation thickness for multiply back-scattered events is used to assign a number (Z_eff) for multi-element materials. Response function of the 3^″?×?3^″ NaI(Tl) scintillation detector is applied on observed pulse-height distribution to include the contribution of partially absorbed photons. The reduced value of signal-to-noise ratio interprets the increase in multiply back-scattered data of a response corrected spectrum. Data obtained from Monte Carlo simulations and literature also support the present experimental results.     

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.     

Nonresonance Compton scattering of an X-ray photon by a Ni-like atomic ion

The absolute values and the shape of the double differential cross section for nonresonance Compton scattering of an X-ray photon by an atomic ion with d symmetry in the core are studied theoretically beyond the impulse approximation for the example of the Ni-like atomic ions Zn²⁺, Kr⁸⁺, and Mo¹⁴⁺. It is established that, as the nuclear charge of an ion increases, (a) in all the scattering channels, the leading harmonics of transition to states of the continuous spectrum are concentrated and (b) the integral intensities of nonresonance Compton scattering are increasingly redistributed to the energy region of resonance Lands-berg-Mandelstam-Raman scattering between the threshold of termination of the Compton profile and the line of elastic (Thomson and Rayleigh) scattering. The calculated results are predictive in character.     

Non-evidence for Z 1 oscillations of the nuclear ion-atom interaction in an amorphous target

Periodic variations in the Z ₁ dependence of the interatomic potential has recently bevlen revealed by a channeling technique. To search for oscillations of similar kind in a target of randomly arranged atoms we have made systematic measurements on the scattering distributions of energetic (32–56 keV) ions in amorphous carbon. Our technique was to transmit light mass ions through carbon foils with a thickness of 2–4 μg/cm². The atomic number of the ions, Z, ranged from 3 to 18. The scattering distribution of the transmitted particles was recorded. From these curves the angular halfwidth,ψ ^1/2, and the relative intensity at a scattering angle 2.5 times ψ ^1/2 was determined. The experimental values are in good agreement with theoretical calculations based on the Thomas-Fermi and Lenz- Jensen potentials. Furthermore, the saturation value of the mean nuclear stopping cross sections for ions scattered in the straight forward direction with a mean energy of 50 keV are given. No evidence for a Z ₁ oscillatory behaviour could be found in any of the three parameters investigated.     

Measurement of the effective atomic number of some transition and rare earth compounds using the Rayleigh to Compton scattering ratio of gamma radiation

The effective atomic numbers of some transition and rare earth compounds have been determined by measuring the ratio of Rayleigh to Compton scattering signal using 59.5?keV gamma radiation from americium-241 radioactive source. The scattered gamma photons from the elements and compounds at an angle of 90° were detected using an ORTEC high-purity germanium detector coupled with 16K multi-channel analyzer. By measuring the ratio of Rayleigh to Compton scattered signal (momentum transfer 3.38?Å^?1), the effective atomic numbers of the transition and rare earth compounds have been determined and compared with theoretical values predicted by AutoZeff, power law, and direct method.     

Gamma or X-rays attenuation properties of some biochemical compounds

The probability of gamma or X-ray interactions with important 14 antioxidants have been discussed for total photon interactions in the wide energy range of 1?keV–100?GeV using the WinXCOM code. The variations of mass attenuation coefficient (μ_ρ), effective atomic number (Z_eff) and electron density (N_el) with photon energy were plotted for total photon interactions. It was found that the values of μ_ρ, Z_eff and N_el depend on the incoming photon energy and chemical compositions of antioxidant. The highest values of these parameters were found at a low-energy zone where the photoelectric effect is the dominant interaction process. When antioxidants were compared with each other, it was seen that Z_eff has the highest values for Oenin chloride and Delphinidin chloride which contain the Cl element. This investigation is thought to be useful for medical applications where radiation exposure is present.     

A partial-wave analysis for proton compton scattering in the Δ(1232) energy region

Based on the nowadays available phenomenological multipoles for pion photoproduction, a systematic dispersion theoretic calculation of Compton partial amplitudes has been performed. By comparing with the new experimental data in the Δ(1232) region it is found that the hitherto existing discrepancies between the data and theory remain. Our results allow us to isolate the basis of this problem. It is due to the fact that the imaginary parts of the Compton amplitudes determined already by unitarity, give too large contributions to the cross section thus leaving no space for real parts required by the dispersion integrals.Therefore a simultaneous partial-wave analysis for Compton scattering and pion photoproduction was carried through employing only the unitarity connections between both. The resulting amplitudes give a good fit to the Compton cross section and all photoproduction data; moreover the photoproduction multipoles agree essentially with those of the previous analyses. On the other hand for Compton scattering, phenomenological amplitudes are obtained for the first time and a model independent test of dispersion theoretic amplitudes can be carried out. For the resonating f_MM¹⁺ amplitude which describes the M1 excitation and deexcitation to the Δ-isobar, large discrepancies have been found. Possible consequences especially for the forward scattering amplitude and the validity of the Kramers-Kronig relation are discussed.     

An experimental study on cross-section ratio of coherent to incoherent scattering for 145 keV incident gamma photons

The coherent (Rayleigh) to incoherent (Compton) scattering cross-section ratio of elements, in the range 6 ≤ Z ≤ 82, are determined experimentally for 145 keV incident gamma photons. An HPGe (High purity germanium) semiconductor detector is employed, at scattering angle of 50°, 70° and 90°, to record the spectra originating from interactions of incident gamma photons with the target under investigation. The intensity ratio of Rayleigh to Compton scattered peaks observed in the recorded spectra, and corrected for photo-peak efficiency of gamma detector and absorption of photons in the target and air, along with the other required parameters provides the differential cross-section ratio. The measured values of cross-section ratio are found to agree with theoretical predictions (corresponding to 4.939, 6.704 and 8.264 Å⁻¹ photon momentum transfer) based upon non-relativistic form factor, relativistic form factor, modified form factor and S-matrix theory.