X-ray Production Cross Sections Research Articles

New experimental measurements of X-ray emissions induced by protons of several tens of MeV on elements with Z=22 to Z=79: Toward quantitative high-energy PIXE

K-shell X-ray production cross-sections measurement campaigns were carried out at the ARRONAX cyclotron with titanium, chromium, copper, molybdenum, silver and gold targets for different energies from 15 to 68 MeV. These measurements, carried out using three detectors (SDD, CdTe and HPGe), complete the database with 66 new values. Our different measurements agree with previously published data and are consistent for all three detectors, confirming the absence of experimental bias. The universal ionisation cross-section representation allows an optimisation of the data using a 3rd-order polynomial function. This function can be used for HE-PIXE quantification for elements with atomic numbers between 22 (Ti) and 79 (Au) in the studied energy region.

X-ray production cross sections for Ir and Bi M-subshells induced by electron impact

M-subshell X-ray production cross sections were indirectly measured for Ir and Bi targets irradiated with monoenergetic electron beams. The projectile energy range ran from 2.2 to 28 keV, impinging on Ir and Bi pure bulk targets in a scanning electron microscope. The resulting X-ray emission spectra were acquired with an energy dispersive spectrometer, and processed afterwards by means of a robust parameter optimization procedure developed previously. X-ray production cross sections were finally obtained through an approach involving an analytical prediction for the emission spectra, which relies on the ionization depth distribution function. The values obtained by this approach were compared with empirical and theoretical predictions, appealing to different relaxation data taken from the literature.

Semi-empirical parameterization of HI/p L-shell X-ray production cross section ratios in Bi for Heavy Ion PIXE

Quantitative analysis of materials from Heavy Ion PIXE spectra remains impeded by the lack of reliable X-ray production cross section (XPCS) data. Although efforts at experimental Heavy Ion induced XPCS measurements still continue, Multiple Ionisation (MI) effects, which are not fully described by theory, render simulations of heavy ion PIXE data unreliable for large Z1/Z2 collisions, especially at low energies. This is also exacerbated by the random selection of projectile-target combinations for measured and reported experimental data available to validate theory. This study explored heavy ion induced X-ray production cross section deviations from those induced by protons at the same ion velocity. This enabled evaluations of the degree to which cross sections are enhanced through MI effects, with the aim of predicting XPCS due to heavy ion impact. The evaluation was carried out through the scaling of experimental heavy ion to theoretical proton cross section ratios (R), which were then used for the interpolation of XPCS in the same target element for ‘missing’ projectiles within the range of evaluation. Here we present measurements of heavy ion induced total L-shell XPCS in Bi, carried out to determine HI/p MI induced deviations due to C, F, Cl and Ti projectiles at an ion velocity range of (0.2–1.0) MeV/nucleon.

Experimental low velocity proton and 28Siq+ induced X-ray production cross sections for select elements within 24 ≤ Z ≤ 83

Particle Induced X-ray Emission (PIXE) spectroscopy is an effectively well-established analytical technique in the low projectile mass (Z < 3) regime. This is in part due to the availability of fairly accurate theoretical models of fundamental interaction parameters such as the X-ray production cross section (XPCS). Continual development of widely used theoretical models such as the ECPSSR theory with adapted corrections in the United Atom limit (UA), Electron Capture (EC) and Multiple Ionisation (MI); requires a rich database of experimental X-ray production cross sections. Beyond the scope of proton PIXE, validated reliable theoretical models may be useful for the accurate approximation of heavy ion induced X-ray production cross sections for Heavy Ion PIXE. This requires persistent efforts aimed at contributing to the currently sparse heavy ion induced X-ray production cross section database. In this work, we report on a new experimental dataset of low energy XPCS in the 0.3 MeV/u – 1.0 MeV/u ion velocity range in Cr, Ni, Ge, Mo, Sn, W, Au and Bi due to proton and 28Siq + ion impact, with an aim at enriching and updating the current database.

MEASUREMENT OF THE CROSS SECTIONS FOR THE YIELD OF CHARACTERISTIC X-RAY RADIATION FROM 1-MeV PROTONS

This article presents the results obtained by measuring the characteristic x-ray production cross sections arising from the interaction of accelerated protons with the target atoms (PIXE). The PIXE production data were measured at the excitation of the K-, L-, and M-shells of target atoms in the mass range from Mg to Bi by 1 MeV protons. We use the approach based on the calculation of the PIXE production cross sections through the Rutherford backscattering cross section, which can be calculated from the Rutherford formula with high accuracy. This approach makes it possible to reduce the errors in measuring of the PIXE production cross sections and, thus, to improve the accuracy of the data obtained. Further, it is planned to expand the research area including protons of other energies and heavy charged particles in the energy range of 0.5–1.7 MeV/nucleon.

K-shell X-ray production cross sections of Ti, Cr, Ni and Zn induced by chlorine ions

In this work we report on the results of the total K-shell X-ray production cross sections of Ti, Cr, Ni and Zn induced by Cl4+ and Cl5+ ions with energies ranging from 4 MeV to 10 MeV. The experimental results were compared with Atomic Orbitals Coupled-Channels (CC) calculations based on the independent electron model. The experimental X-ray production cross sections vary from about 10−2 barns for Zn up to 102 barns for Ti. The results obtained for Ti indicate that the present CC calculations underestimate the experimental cross sections up to two orders of magnitude at 10 MeV chlorine bombarding energy. However, the discrepancy between CC calculations and experimental results decreases as both bombarding energy and the atomic number of the target species increase. The dependency of the experiment-theory agreement on the asymmetry and adiabaticity parameters α and η respectively is discussed.

X-ray production cross sections induced by 0.8–1.6 MeV/amu 56Fe ions in collision with selected elements from aluminum to bismuth

The K X-ray productions for the Mg, Al, Ti, Cr, Cu, Zn, Zr, Nb, Mo, Ag, Cd, In, Sn, Sb thin films, the L X-ray productions for the Zr, Nb, Mo, Ag, Cd, In, Sn, Sb, Ta, W, Pb, Bi targets and the M X-ray productions for the Ta, W, Pb, and Bi films were investigated using 44.8 MeV, 56 MeV, 67.2 MeV, 78.4 MeV and 89.6 MeV 56Feq+ accelerated beams. The obtained experimental data were compared with the PWBA and ECPSSR theoretical values calculated with the ISICS11 code. A sharp increase in the cross sections for the target elements close to iron is observed. In this way, the X-ray production cross section for the selected chemical element in the PIXE analysis can be maximized with the irradiation mode selection – the energy and species of the incident ion.

Application of spectrum smoothing to improve the accuracy of atomic inner-shell ionization cross sections impacted by electron near the threshold energy

In this study, the X-ray spectrum smoothing is applied to improve the reading precision of the experimental X-ray peak net counts. The experimental Sn L-shell X-ray production cross sections (XRPCSs) and Bi-Mαβ XRPCSs before and after smoothing are compared, respectively. The result shows that spectrum smoothing effectively improves the accuracy of the experimental XRPCSs. The after-smoothing present XRPCSs agree well with the distorted wave Born approximation (DWBA) theoretical XRPCSs and are consistent with the previously published XRPCSs within the experimental uncertainty. Finally, the factors affecting the comparison between the experimental and DWBA theoretical XRPCSs are analyzed.

Accuracy of three-dimensional proton imaging of an inertial confinement fusion target assessed by Geant4 simulation

The Geant4 toolkit was used to perform benchmark Monte Carlo simulations of proton micro-tomography imaging. A phantom of an inertial confinement fusion (ICF) target was designed, based on experimental data. Simulations of STIM (Scanning Transmission Ion Microscopy) and PIXE (Particle Induced X-ray Emission) tomography were performed. Quantitative images were obtained from the TomoRebuild and JPIXET software packages, chosen for their ability to handle large solid angles of X-ray detection. The tomographic images were compared with the original phantom, used as a reference. For STIM-T, the accuracy of the calculated mass density was ≤ 2 % for TomoRebuild and ≤ 14 % for JPIXET. Corrections of X-ray production cross section and X-ray absorption were tested for the quantification of Ge, used as a dopant in the ICF target. The accuracy on the obtained Ge density was ≤ 2.9 % for TomoRebuild and ≤ 6.4 % for JPIXET, whereas the error was about 40 % without correction.

M-subshell X-ray production cross sections of Re and Os by electron impact

X-ray production cross sections of Re and Os M subshells were measured using an electron beam.

Experimental determination of total M shell and subshell X-ray production cross sections for uranium by proton impact

X-ray production cross sections for total and subshell M uranium by proton impact are measured and compared with other studies.

Au L-shell x-ray emission induced by 154.3–423.9 MeV/u C6+ ions

The L-shell x-ray emissions of gold are investigated for the bombardment of high energy C6+ ions in the high energy region of 154.3–423.9 MeV/u. Due to the multiple ionization of outer-shell electrons at the movement of L x-ray emission, the blue shift of the experimental x-ray energy and an enhancement of the relative intensity ratios of Lι, Lβ–Lα x rays are observed. Using the improved thin target formula and considering the effect of multiple ionization on atomic parameters, the L-subshell x-ray production cross sections are extracted from the counts and compared with the theoretical estimations of BEA, PWBA and ECPSSR. It is found that the relative corrections of ECPSSR on PWBA can be ignored in the present experimental energy region. The calculations of PWBA and ECPSSR are almost identical and both are larger than the experimental results. The BEA is in better agreement with the experiment as a whole.

Computed corrections for recollision effects on ionization and x-ray production cross sections obtained in positron-impact studies

The accurate experimental measurement of inner-shell ionization cross sections induced by positrons near the threshold energy is of great significance both for theory and practical application. So far, there are few published experimental data in this field, most of which involve a slow positron beam device and acceleration fields to achieve the desired collision energies. Most previous experimental studies, in which a negative acceleration potential was applied to the target, neglected to consider how backscattered positrons might be accelerated back to the target, generating surplus characteristic x-rays and inflating the cross-section estimates derived therefrom. Using Geant4 and Ansys Maxwell to simulate charged-particle transport, the experimental collision process in the negative high-voltage electromagnetic field of the target chamber is simulated realistically in this paper. Through the simulation process, the effect of the negative high-voltage electromagnetic field on backscattered positrons, hence on ionization and characteristic x-ray production cross sections, is obtained. We then estimate corrections for previously published experimental Ti K-shell ionization cross sections and Ag-Lαβγ, Bi-Mαβ, Pb-Mαβ x-ray production cross sections obtained by positron impact. In addition, we use simulation to demonstrate that such undesired effects can be suppressed by adjusting the size of the target and the tilt angle between the target normal and the positron beam axis.

L-Shell Ionization Cross Sections for Silver by Low-Energy Electron Impacts

The L-subshell ionization cross sections and total L–X-ray production cross sections for the Ag atom by the electron impact near the ionization threshold were calculated with a classical-trajectory Monte Carlo method. The results were compared with experimental data, quantum mechanical calculations, and the cross sections by positron impact. It was demonstrated that the classical treatments are useful for electron–atom collisions at energies higher than about six times the binding energies of target electrons but overestimate L-shell ionization and L–X-ray production cross sections at low energies near the threshold. Possible reasons for this discrepancy are discussed.

Measurement of X-ray production cross sections for lower-energy (0.7-3 MeV) proton induced Cu_K, Ag_L and Au_M X-rays from thick samples

We conducted a series of fundamental research-based experimentations to measure the X-ray production cross sections of K-, L-, and M-shells from thick samples of Cu, Ag and Au, respectively, for proton beam in a lower energy range of 0.7 - 3.5 MeV utilizing particle induced X-ray emission (PIXE) analysis. The measurement theories based on the Merzbacher-Lewis (ML) relationship and procedure for thick samples are described. The detector efficiency and system calibration were first measured from Fe-55 and Am-241 X-ray sources and the standard sample, respectively. The X-ray yields as a function of the proton energy were measured and fitted for finding the derivatives which were used for the cross section measurement. The obtained results were compared with published data and predictions from the theoretical models of Plane Wave Born Approximation (PWBA) and the advanced ECPSSR. The measured results from Cu were in good agreement with the theoretical predictions, especially in the lower energy regime, and most of the reported data, while for the higher energy regime deviated by a few times but still in the same order of magnitude with the theoretical data. The Ag and Au results were in excellent agreement with published and theoretical values.

L-shell ionisation and X-ray production cross-sections for some low Z-elements by proton impact

L-shell ionisation and x-ray production cross-sections of various targets are useful in many Proton Induced X-ray Emission (PIXE) applications. Generally, x-ray production cross sections are measured directly but ionisation cross sections are only evaluated using theoretical models. The use of ionisation models has been instrumental in the ion-atom description of the subshells which are then converted to x-ray production cross sections, however, certain limitations exist for currently available models. For instance, at extremely low energy and high energy of the incident particle, some modifications are made to these models to correctly obtain these values. While existing ionisation theory coupled with associated computed codes or data tables have been used successfully in determining cross-sections of medium Z and high Z-elements, targets of low atomic number have not been fully studied, especially when bombarded with proton energy less than 1 MeV. In this study, a revised model using computer codes and algorithm are used in obtaining cross-sections of some light elements (Neon, Magnesium and Argon) whose experimental values are difficult to measure. To verify the certainty of these values, a comparison was made with some experimental values.

Measurements of L-shell X-ray production cross sections for Sn and Sb using 6–14 keV synchrotron radiation

The synchrotron radiation induced Lkk=l,η,α,β1,3,4,6,β2,15,9,10,γ1,5,γ2,3,4 X-ray production cross-sections (XRPCS) have been measured for Sn and Sb at energies ranging 6–14 keV. These present measured Lk XRPCS have been compared with different sets of theoretical cross sections calculated using the Dirac-Fock (DF) model based X-ray emission rates, the non-relativistic Hartree-Fock-Slater (HFS) model based photoionization cross-sections and three sets of fluorescence and Coster-Kronig (CK) yields based on the Dirac-Hartree-Slater (DHS) model, the semi-empirical values tabulated by Krause, and the recently reported experimental values. The present measured Lk XRP cross sections for Sn and Sb are found to differ by up to 25% from different sets of presently calculated values. Further, the average L-shell fluorescence yields (ω¯L) have been deduced from the present measured total L XRPCS using the theoretical photoionization cross sections and are compared with the values available in literature.

Understanding the mechanisms of L-shell x-ray emission from Os atoms bombarded by 4–6 MeV/u fluorine ion

The L-subshell ionization mechanism is studied in an ultra-thin Os target bombarded by 4–6 MeV/u fluorine ions. Multiple ionization effects are considered through the change of fluorescence and Coster-Kronig yields while determining L-subshell ionization cross sections from L x-ray production cross sections. The present experimental values are compared with various theoretical approximations: (i) the relativistic semi-classical approximation (RSCA), (ii) the shellwise local plasma approximation (SLPA), and (iii) the ECUSAR theory. We also take into account the vacancy sharing among the subshells by the coupled-states model (CSM) and the electron capture (EC) by a standard formalism. We find that the ECUSAR-CSM-EC describes the measured excitation function curves the best. However, the theoretical calculations are still about a factor of two smaller than the measured values even though the recent fluorescence and Coster-Kronig yields are considered. Hence, a re-evaluation of these parameters is a challenge for the theoretical works. Whatsoever, this work leads to demonstrate that in the present energy range the heavy-ion induced inner-shell ionization of the heavy atoms can be understood by combining the direct Coulomb ionization, the electron capture, and the vacancy sharing among subshells, together with optimizing the atomic parameters. Optimization of the atomic parameters shows that our experimental results agree with theoretical vacancy production theories if the L1 fluorescence yield is nearly doubled. Such a optimization is validated by the proton induced L-shell ionization data of uranium atoms.

A Geant4 simulation of X-ray emission for three-dimensional proton imaging of microscopic samples.

Proton computed microtomography is a technique that reveals the inner content of microscopic samples. The density distribution of the material (in g·cm-3) is obtained from proton transmission tomography (STIM: Scanning Transmission Ion Microscopy) and the element content from X-ray emission tomography (PIXE: Particle Induced X-ray Emission). A precise quantification of chemical elements is difficult for thick samples, because of the variations of X-ray production cross-sections and of X-ray absorption. Both phenomena are at the origin of an attenuation of the measured X-ray spectra, which leads to an underestimation of the element content. Our aim is to quantify the accuracy of a specific correction method that we designed for thick samples. In this study, we describe how the 3D variations in the mass density were taken into account in the reconstruction code, in order to quantify the correction according to the position of the proton beam and the position and aperture angle of the X-ray detector. Moreover, we assess the accuracy of the reconstructed densities using Geant4 simulations on numerical phantoms, used as references. The correction process was successfully applied and led, for the largest regions of interest (little affected by partial volume effects), to an accuracy ≤ 4% for phosphorus (compared to about 40% discrepancy without correction). This study demonstrates the accuracy of the correction method implemented in the tomographic reconstruction code for thick samples. It also points out some advantages offered by Geant4 simulations: i) they produce projection data that are totally independent of the inversion method used for the image reconstruction; ii) one or more physical processes (X-ray absorption, proton energy loss) can be artificially turned off, in order to precisely quantify the effect of the different phenomena involved in the attenuation of X-ray spectra.

Experimental and theoretical L -subshell ionization cross sections for 83Bi by electron impact from the L3 threshold to 100 keV

We report experimental and theoretical Bi ${L}_{1}$, ${L}_{2}$, and ${L}_{3}$ subshell ionization cross sections by the impact of electrons with energies from the Bi ${L}_{3}$ ionization threshold to 100 keV. The x-ray spectra have been acquired with two Si drift detectors placed in vacuum, which allowed us to better evaluate the peak fit procedure in the $L$ multiplet. The $L\ensuremath{\alpha}$, $L\ensuremath{\beta}$, $L\ensuremath{\gamma}$, $L\ensuremath{\ell}$, and $L\ensuremath{\eta}$ x-ray production cross sections, measured with relative uncertainties ranging from $5%$ to $9%$, and two sets of atomic relaxation parameters have been used to derive the Bi ${L}_{1}$, ${L}_{2}$, and ${L}_{3}$ ionization cross sections. Although the experimental uncertainties of the subshell ionization cross sections are smaller than those of the few previous measurements, they remain large due to the uncertainties associated with the relaxation parameters. Furthermore, ionization cross sections have been calculated for the three $L$ subshells with the subconfiguration average distorted-wave (SCADW) formalism, which includes the full two-body retarded electromagnetic interaction between the projectile and target electrons. These theoretical cross sections are $15%$ to $30%$ lower than the measured values, but the agreement is reasonable given the aforementioned high uncertainties. We have also found that the simpler distorted-wave Born approximation yields subshell ionization cross sections that match those computed with the SCADW method.