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.     

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.     

Compton scattering of 59.5 keV gamma rays from p-Si sample in an external electric field

This study is related to Compton scattering of photons from a p-Si sample whose surface charge density distributions are changed by an external electric field. The external electric field intensity in the range 0-75 kV/m was used to change the surface charge density distributions of the sample. The sample surface perpendicular to the electric field was selected as the scattering surface. The p-Si sample was bombarded by 59.5 keV γ-photons emitting from an Am-241 point source. The Compton scattered photons at an angle of 90^o were detected by an Si(Li) detector. The Compton scattering intensity suddenly increased with the application of the electric field since the applied electric field distorts both the negatively charged scattering center (free electron, bound electron, ionized acceptor) and the positively charged scattering center (hole) and their momentum distribution in the sample. There is a good third-order polynominal relation between the Compton scattering intensity and the increasing (or decreasing) electric field intensity. The results show that the positively charged scattering centers behave like negatively charged scattering centers, but the latter are slightly more effective than the former in the Compton scattering of γ-rays from the sample in the electric field.     

A gamma-ray scattering technique for estimation of density and moisture content of wood

A densitometer system, operating in a non-destructive and non-invasive way, is presented to investigate the density and moisture variation in wood samples of Pinus roxburghii (known as chir pine). The inherent ability of Compton scattering can ascertain quantitative information of electron density of the target material. A well collimated beam of 662?keV gamma rays from ¹³⁷Cs radioactive source has been used to extract the information of density from interior of sample by recording scattered spectra with NaI(Tl) scintillation detector. An inverse matrix approach for unfolding of observed pulse-height distribution to a true photon spectrum is used, by choosing bin mesh (E^1/2) of 0.025 (MeV)^1/2, for the measurements of scattered spectra. The regression lines, obtained from data of scattered spectra, provide the density and moisture content of selected wood sample. The adjusted R² value 0.984 for fitted curve, justifies the linear dependence of scattered intensity upon wood density. Also, Compton scatter measurements results that the technique is less sensitive beyond wood thickness of ～110?mm due to overlying scatter components in the measured spectrum.     

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.     

Untersuchung der Polarisationsebene von Photonen nach Compton-Streuung an polarisierten Elektronen

Two polarization phenomena in Compton scattering by polarized electrons were investigated. In the first experiment, the rotation of the polarization plane of photons passing through magnetized iron and gadolinium was measured. This effect arises from a spin dependence of the Compton forward scattering amplitude. For 228 and 333 keV photons and iron absorbers, the observed rotation angles areφ ₀=(3.90±0.57) ×10^?3 rad · cm^?2 and (4.75±0.58)×10^?3 rad · cm^?2, respectively. Secondly, the orientation of the photon polarization plane after scattering of unpolarized photons by polarized electrons was measured. This experiment tests time reversal invariance in quantum electrodynamics. No dependence of the polarization plane on the direction of the electron spin was found within 2×10^?3.     

激光-电子康普顿散射物理特性研究

对激光-电子康普顿散射物理特性即能量特性和微分截面角分布进行了仔细的研究.计算结果显示出光子能量和微分截面角分布的简单结构.康普顿散射X射线光源具有散射光子的能量易调节、方向性好等特点.在入射电子束能量很高时,X射线近乎单向出射.光源色散度较大,但实验上可以获得色散（带宽）小的X射线.对于各种波长的激光,在很宽的电子束能量范围（1 MeV—10 GeV）内,散射X射线光子的总截面和前向发射圆锥内（半圆锥角1/γ,其中γ=E/m₀ 关键词： 康普顿散射 能量特性 微分截面 角分布     

Monte Carlo calculation of electron spectra produced in water phantoms by 20 keV-1 GeV photons

Abstract

A Monte Carlo calculation for the energy spectra of electrons and positrons produced in infinite and semiinfinite water phantoms by photons ranging in energies from 20 keV to 1 GeV are presented. The dominant processes considered are the photoelectric effect, Auger effect, Compton effect, pair, and triplet production. Bremsstrahlung produced by electrons and positrons with energies greater than 1 MeV is also included. The effect of multiple Compton scattering, not considered in the earlier calculation, for the infinite phantom for photon energies higher than 2 MeV has been incorporated. For a semi-infinite phantom, multiple Compton scattering and backscattering through the top are considered. The results are compared with the earlier calculations for the first-collision spectrum. It is found that the inclusion of multiple Compton scattering significantly increases the average number of electrons/cm³ per photon/cm² at all energies considered whereas bremsstrahlung reduces the number of high energy electrons and produces more low energy electrons in the spectrum.     

Relativistic double differential cross sections for Compton scattering by bound electrons: Test at low photon energies and predictions at intermediate photon energies

Cross section profiles d²σ/dΩdω′ for Compton scattering of photons by bound electrons are calculated for all subshells of the atom. Results obtained from the form factor approximation and from a relativistic version of the impulse approximation are compared with experimental data for Cu and Pb at a scattering angle ofθ=145° and a photon energy of 662 keV. The impulse approximation proves to be superior to the form factor approximation and is used to predict cross section profiles for a primary energy of 50 MeV and different scattering angles and charge numbers. It is shown that only for the heaviest atoms and scattering angles belowθ=5° there is a non-negligible contribution of Compton scattering to the elastic peak.     

Differential cross sections of proton compton scattering at photon laboratory energies between 700 and 1000 MeV

Differential cross sections of proton Compton scattering have been measured at the Bonn 2.5 GeV synchrotron. 78 data points are presented as angular distributions at photon lab energies of 700, 750, 800, 850, 900, and 950MeV. The c.m. scattering angle ranges from 40°–130°, corresponding to a variation of the four momentum transfer squared betweent=?0.10 tot=?0.96 GeV² at 700 and 950 MeV, respectively. Two additional differential cross sections have been measured at 1000MeV, 35.6° and 47.4°. The angular distributions show forward peaks whose extrapolations to 0° are consistent with calculated forward cross sections taken from literature. The small angle data (|t| ?0.2 GeV²) together with the calculated cross sections at 0° are also consistent with the assumption of a slope parameterB of 5 GeV^?2. For the first time a rerise of the angular distributions towards backward angles has been observed. It becomes less steep with increasing energy. The most interesting feature of the angular distributions is a sharp structure which appears betweent=?0.55 GeV² at 700MeV andt=?0.72 GeV² at 950 MeV. Such a rapid varation of the differential cross section witht has never been ovserved in elastic hadron-hadron scattering or photoproduction processes. It indicates the existence of a dynamical mechanism which could be a peculiarity of Compton scattering.     

Protein dynamics studied on myoglobin

Two methods of inelastic scattering of synchrotron radiation were used to measure the dynamics of myoglobin in the temperature range from T = 60 K to 300 K. The inelastic Rayleigh scattering of metmyoglobin was analyzed by delayed elastic nuclear forward scattering of an iron foil. This yields averaged information on all phonons within the sample. The mean square displacement of the atoms due to this dynamics is 〈x〉 ²/T = 2.1 · 10^—4 Ų K^—1 on average. Complementary information was obtained by phonon assisted nuclear scattering on deoxymyoglobin. This method selects the phonons coupling to the iron atom in the active center of the protein. The mean square displacement of the iron was measured to be 〈x〉 ²/T = 0.6· 10^—4 Ų K^—1. The results are in agreement with Mössbauer absorption experiments in the low temperature range. Above 200 K the results allow one to distinguish between harmonic and quasidiffusive dynamics within the protein. A comparison with Raman spectroscopy is made.

     

Dependence of the Compton to Rayleigh intensity ratio on the scatterer atomic number in the range of 4(Be) to 31(Ga)

Compton to Rayleigh scattering intensity ratios (I_C/I_R) have been measured using X-rays with energy 17.44 keV for single-component materials with atomic number Z from 4 (Be) to 31 (Ga) and binary compounds of stoichiometric composition. The measurements have been performed using two optical schemes: an energy-dispersive X-ray fluorescence scheme with a molybdenum secondary target and wavelength-dispersive X-ray fluorescence one. The processing of the spectra was carried out by fitting with Pearson VII functions. For single-component and binary standards, the experimental dependence of the scattering intensity ratio on the atomic number was found to be the same. This confirms the additivity of the contribution of different atoms to the scattering. The dependence has a complex shape but is well described by the theoretical relationship for I_C/I_R with correction on the difference between Compton and Rayleigh radiation absorption coefficients. Two ranges of atomic number values are defined, in which the effective atomic number Z_eff can be determined by the calibration method using this dependence: for Z from 4 to 7 with low error of ΔZ_eff =±0.15 and for Z_eff from 10 to 18 with low error of ΔZ_eff =±0.69. A change in the shape of the Compton peak and an overestimated value of the of the Compton and Rayleigh peak intensity ratio when passing from a single-component scatterer (Al or Si) to their oxides Al₂O₃ or SiO₂, respectively, have been revealed.     

Analysis of the electronic structure of ZrO2 by Compton spectroscopy

The electronic structure of ZrO₂ is studied using the Compton scattering technique. The first-ever Compton profile measurement on polycrystalline ZrO₂ was obtained using 59.54 keV gamma-rays emanating from the ²⁴¹Am radioisotope. To explain the experimental data, we compute theoretical Compton profile values using the method of linear combination of atomic orbitals in the framework of density functional theory. The correlation scheme proposed by Perdew-Burke-Ernzerhof and the exchange scheme of Becke are considered. The ionic-model-based calculations for a number of configurations, i.e., Zr^+x (O^?x/2)₂ (0 ≤ x ≤ 2), are also performed to estimate the charge transfer on compound formation, and the study supports transfer of 1.5 electrons from Zr to O atoms.     

Nucleon polarizabilities from deuteron Compton scattering within a Green’s function hybrid approach

We examine elastic Compton scattering from the deuteron for photon energies ranging from zero to 100MeV, using state-of-the-art deuteron wave functions and NN potentials. Nucleon-nucleon rescattering between emission and absorption of the two photons is treated by Green’s functions in order to ensure gauge invariance and the correct Thomson limit. With this Green’s function hybrid approach, we fulfill the low-energy theorem of deuteron Compton scattering and there is no significant dependence on the deuteron wave function used. Concerning the nucleon structure, we use the chiral effective field theory with explicit D \Delta(1232) degrees of freedom within the small-scale expansion up to leading-one-loop order. Agreement with available data is good at all energies. Our 2-parameter fit to all elastic g \gamma d data leads to values for the static isoscalar dipole polarizabilities which are in excellent agreement with the isoscalar Baldin sum rule. Taking this value as additional input, we find a_E^s \alpha_{E}^{s} = (11.3±0.7(stat)±0.6(Baldin)±1(theory))^.10^-4 fm^3 and b_M^s \beta_{M}^{s} = (3.2±0.7(stat)±0.6(Baldin)±1(theory))^.10^-4 fm^3 and conclude by comparison to the proton numbers that neutron and proton polarizabilities are the same within rather small errors.     

Compton scattering of 0.279 MeV gamma rays fromK-shell electrons of lead

Differential cross-sections for Compton scatterig of 0.279 MeV gamma rays fromK-shell electrons of lead are measured at scattering angles ranging from 30 to 150° to study the effect of binding on the scattering process. Measurements are made employing two Nal(Tl) scintillation spectrometers and a slow-fast coincidence set-up of 30 nsec resolving time. The experimental results are compared with the available theoretical data. The totalK-shell Compton scattering cross-section is 34% of the free electron Compton cross-section.     

In operando quantitation of Li concentration for a commercial Li‐ion rechargeable battery using high‐energy X‐ray Compton scattering

Compton scattering is one of the most promising probes for quantitating Li under in operando conditions, since high‐energy X‐rays, which have high penetration power, are used as the incident beam and the Compton‐scattered energy spectrum has specific line‐shapes for each element. An in operando quantitation method to determine the Li composition in electrodes has been developed by using line‐shape (S‐parameter) analysis of the Compton‐scattered energy spectrum. In this study, S‐parameter analysis has been applied to a commercial coin cell Li‐ion rechargeable battery and the variation of the S‐parameters during the charge/discharge cycle at the positive and negative electrodes has been obtained. By using calibration curves for Li composition in the electrodes, the change in Li composition of the positive and negative electrodes has been determined using the S‐parameters simultaneously.     

Effects of in‐target Compton‐scattering in lanthanum fluorescence spectra

A study was made of the continuum adjacent to the Kα₁ and Kα₂ peaks (the ‘shoulder’) in lanthanum fluorescence spectra. The fluorescence was induced by 59.537 keV γ‐rays from a ²⁴¹Am source. The spectra were observed with an La₂O₃‐loaded paraffin target (the ‘La target’). To limit the observations to the scattering in the target, a collimator was used in front of the germanium detector, which strongly reduced the near‐detector scattering. Changes in the shoulder spectra were observed on attaching additional mass to the La target and on changing its orientation with respect to the detector‐to‐target centre‐line. The measurements clearly show that the main cause of the shoulder spectra is the in‐target Compton scattering. A different distribution of mass in the vicinity of the fluorescing atoms with respect to the detector‐to‐target centre‐line results in different probabilities of the observed scattering at all angles. Since the energy of secondary Compton photons is directly related to the scattering angles, different distributions of mass cause changes in the shoulder spectra. Comparison of the calculated and measured shoulder spectra shows good agreement on an absolute scale. Copyright © 2006 John Wiley & Sons, Ltd.     

Compton scattering and electron-atom scattering in an elliptically polarized laser field of relativistic radiation power

Presently available laser sources can yield powers for which the ponderomotive energy of an electrons can be equal to or even larger than the rest energy mc ² of an electron. Therefore it has become of interest to consider fundamental radiation-induced or assisted processes in such powerful laser fields. In the present work we consider laser-induced Compton scattering and laser-assisted electron atom scattering in such fields, assuming that the laser beam has arbitrary elliptic polarization. We investigate in detail the angular and polarisation dependence of the differential cross-sections of the two laser-induced or laser-assisted nonlinear processes as a function of the order N of absorbed or emitted laser photons . The present work is a generalization of our previous analysis of Compton scattering and electron-atom scattering in a linearly polarized laser field [Phys. Rev. A 65, 022712 and 033408 (2002)].Received: 3 November 2002, Published online: 29 April 2003PACS: 34.50.Rk Laser-modified scattering and reactions - 34.80.Qb Laser-modified scattering - 32.80.Wr Other multiphoton processes