K-shell Ionization Cross Sections Research Articles

Neural-network–based algorithm for the inverse problem of measuring K-shell ionization cross-sections of Si induced by 3–25 keV electrons and 4.5–9 keV positrons using the thick-target method

In this study, a neural network method is proposed for solving the inverse problem in the measurement of inner-shell ionization cross-sections using the thick-target method. It was applied to calculate the K-shell ionization cross-section of silicon (Si) from positron impacts in the energy range from 4.5 to 9 keV, using a Monte Carlo simulation program called PENELOPE to construct a comprehensive characteristic X-ray yield and cross-section database, serving as a foundation for training the neural network. The experimental values are compared with those obtained using regularization, yield differential, and distorted-wave Born approximation (DWBA) theoretical models. Our findings reveal that the cross-section results obtained from all three algorithms are in good agreement with the theoretical DWBA values within the error range. Moreover, our study highlights the superiority of the neural network algorithm in solving ill-posed problems, compared with traditional regularization algorithms and the yield differential method. Furthermore, we re-analyse the experimental data of electron-induced ionization cross-sections on a pure thick Si target in the energy range from 3 to 25 keV, which were originally obtained by Zhu et al. who used a regularization method. The reprocessed cross-sections obtained in this study exhibit good agreement with the reported results within the error range. To the best of our knowledge, this is the first experimental report of the K-shell ionization cross-sections of Si from positron impact.

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.

K X-ray Emission for Slow Oxygen Ions Approaching a Copper Metal Surface

We report on the K X-ray emission for 9–140 keV oxygen ions with initial charge states from 3 to 7 approaching a copper surface. The peak center of the measured X-ray spectrum slightly shifts towards higher energies with the increasing of the initial charge state of the incident ions. For the collisions of oxygen ions with no K-vacancies (q = 3–6), the X-ray yield per incident ion increases gradually with the projectile’s kinetic energy, while for the O7+ ions (with a K-vacancy) it is nearly independent of the energy. The K-shell ionization cross-sections for the oxygen ions with no K-vacancies obtained from the experiments are well consistent with the calculations of the binary encounter approximation model when the collision energy is larger than 30 keV, whereas they are several times larger than the theoretical values at collision energies of less than 30 keV.

Measurements of K-shell ionization cross sections and L-shell X-ray production cross sections of Al, Ti, Cu, Ag, and Au thin films by low-energy electron impact

The K-shell ionization cross sections of Al, Ti, Cu and L-shell characteristic X-ray production cross sections of Cu, Ag and Au (Lα, Lβ and Lγ subshells for Au) by electron impact at incident energy of 5–27 keV are determined experimentally. Thin films of the studied elements, deposited on thin carbon substrates, are employed as targets in the experiments. The thickness of the thin carbon substrate is 7 μg/cm<sup>2</sup>, the targets are Al, Ti, Cu, Ag and Au and their thickness values are 5.5 μg/cm<sup>2</sup>, 28 μg/cm<sup>2</sup>, Cu 35.5 μg/cm<sup>2</sup>, 44 μg/cm<sup>2</sup> and 44 μg/cm<sup>2</sup>, respectively. The target thickness values are checked by using Rutherford Backscattering Spectrometry (RBS). The electron beam is provided by a scanning electron microscope (KYKY-2800B). The characteristic X-rays produced are recorded by a silicon drifted detector (XR-100SDD, Amptek), which has a C2 ultrathin window and can detect the low-energy X-rays down to boron Kα line (0.183 keV). The detector efficiency is calibrated by using the standard sources (<sup>55</sup>Fe, <sup>57</sup>Co, <sup>137</sup>Cs and <sup>241</sup>Am) for X-ray energy larger than 3.3 keV while using the characteristic peak method (i.e. by measuring characteristic X-ray spectra produced by 20 keV electron impacting various thick solid targets) for X-ray energy less than 3.3 keV. The experimental results are corrected by the Monte Carlo code PENELOPE for the effects of target structure and Faraday cup. Meanwhile, the electron escape rates obtained from the Faraday cup and the signal pile-up effect are also considered. The results show that when the incident electron energy is low, the influences of electron energy loss and target thickness are significant. The thinner the target , the smaller the correction is. Experimental uncertainties for K-shell ionization cross sections of Al, Ti and Cu are about 5.0%, 5.6% and 5.1%, respectively; experimental uncertainties for L-shell X-ray production cross sections for Cu and Ag are about 5.3% and 4.0%, and for Lα,Lβ,and Lγ of Au are about 6.1%, 8.9% and 11.0%, respectively. The experimental L-shell characteristic X-ray production cross sections of Cu are given for the first time. Compared with the theoretical values of the semi-relativistic distorted-wave Born approximation (DWBA), most of the experimental values in this work are in good agreement within 7% deviation. The best agreement between the experimental results and the theoretical values is obtained for the K shell ionization cross section of Al, and the deviation is less than 1.7% for the data where the incident energy is above 10 keV. The least consistency with the theoretical values is the experimental L shell characteristic X-ray production cross sections of Cu, with a deviation being about 5–22%. The comparison of the experimental L shell characteristic X-ray production cross sections of Cu (including Ga and As elements) with those from the DWBA theory indicates that the theoretical calculations of L shell ionization cross sections of medium heavy elements and the corresponding atomic parameters (such as fluorescence yields and Coster-Kronig transition probabilities) need to be more accurately determined. According to the present results, the ionization cross sections or characteristic X-ray production cross sections measured by the thin target thin substrate, the thin target thick substrate and the thick target methods are equivalent to each other within the uncertainties.

K-shell ionization cross sections of Cu, Zn and Ge by 3–5 MeV/u Si-ion bombardment

The K x-ray spectra of different targets (Cu, Zn, and Ge) induced by 3 to 5 MeV/u Si projectile ions have been measured to determine the K-shell ionization cross-section. A significant difference is observed between the measurements and theoretical estimates, where the theoretical ones are about 28–35% of the experimental results. Such difference is reduced to a good extent 51%–56% if multiple ionization effects are taken into account. Remaining discrepancy may be attributed to the electron capture contribution.

K-shell ionization cross section of Ti and Cu atoms by 1 and 2 GeV electrons

The K-shell ionization cross sections of titanium and copper atoms were determined by analyzing the spectra of characteristic X-ray radiation generated by an electron beam with energies of 1 and 2 GeV in metal foils. New data obtained for these energies demonstrate the influence of the density effect on the ionization cross sections values. The results were compared with previous experimental data and calculations based on pure theoretical and semi-empirical models.

Measurement of K-Shell ionization cross sections of Al by 4–9 keV positron impact

In this paper, the K-shell ionization cross sections of Al by 4–9 keV positron impact have been measured for the first time. Firstly, the K-shell characteristic X-ray yields produced by positron collision with thick Al target were measured. In this process, online monitoring technology was developed to obtain the accurate number of incident positrons that collided with the thick Al target, and spectrum smoothing technology was introduced to obtain the accurate Kαβ characteristic peak net counts generated by positron collision with the thick Al target. Next, combined with Monte Carlo (MC) simulation and theoretical calculation, the contributions of the multiple scattering of incident positrons, from the bremsstrahlung and annihilation photons and other secondary particles to the experimental characteristic X-ray yields were corrected. Finally, the corrected experimental characteristic X-ray yields were converted into K-shell ionization cross sections by the numerical calculation method. The theoretical values of the distorted wave Born approximation (DWBA) were compared with the experimental results of the Al K-shell ionization cross sections by 4-9 keV positron impact. The result shows that the predicted values of DWBA theory slightly overestimate the experimental results, but the trend is basically consistent with them.

K -shell ionization and characteristic x-ray radiation by high-energy electrons in multifoil targets

Processes of K-shell ionization and accompanying characteristic x-ray radiation (CXR) by high-energy electrons moving through a multifoil copper target are considered. Expressions describing the main characteristics of these processes are derived. It is shown that the average K-shell ionization cross section in the target is not defined just by the target material and the electron energy, but also depends on the number of foils in the target, their thickness and separation between them. The corresponding CXR yield is therefore not unambiguously defined by the aggregated target thickness, but depends on the above parameters as well. It is demonstrated that the average K-shell ionization cross section in a multifoil target can be several times larger than the conventional cross section of this process without the density effect impact. This results in a considerable enhancement of CXR yield from the multifoil target compared to the case of electron incidence upon a single foil of the same aggregated thickness. Comparison of CXR yield in the considered case with the yields of some other types of x-ray emission in multifoil targets is made.

Measurements of K-shell ionization cross sections of Fe, Ni, and Zn by 7–29 keV electron impact using the thick-target method

The measurements of K-shell ionization cross sections for Fe, Ni, and Zn were performed using 7–29 keV electron impact on thick targets. Monte Carlo simulations were employed to correct the effects due to the multiple-scattered electrons and bremsstrahlung photons as well as other secondary particles within the thick targets. The so-called Tikhonov regularization method was adopted to deal with the ill-posed inverse problem involved in the thick-target method. The experimental results were compared with the DWBA and PWBA-C-Ex predictions as well as existing experimental data from the literature. It is observed that our experimental data are in better agreement with the theoretical results based on the DWBA model developed by Bote et al.

High energy PIXE: New experimental K-shell ionization cross sections for silver and gold and comparison with theoretical values from ECPSSR/RECPSSR models

In high energy PIXE, a high energy ion beam, up to several tens of MeV, is used to analyze heavy elements in a thick sample. The knowledge of the interaction cross-section with the atoms is essential to perform quantitative analysis. As measured data in this range of energy are scarce, an experimental campaign was conducted at the C70 cyclotron of the GIP ARRONAX to measure the K-X-ray production cross-sections for silver and gold with proton energies 30, 42, 54 and 68 MeV. The detector efficiency, the beam intensity, and the target thickness were measured accurately to produce precise data. To convert the K-X-ray production cross-sections into the K-shell ionization cross-sections, an average value of the K-shell fluorescence yield, calculated from a compilation of existing data, was used. The outcomes of the campaign are in good agreement with the few existing data and the theoretical prediction of the RECPSSR model.

Employing [formula omitted] elastic scattering for determination of K-shell ionization cross section of 58Ni19+ in collisions with hydrogen gas target at 95 MeV/u

We present a new experimental method for measuring inner-shell ionization cross sections of low-charged ions colliding with hydrogen gas target in a storage ring. The method is based on a calibration by the well-known differential cross sections of proton elastic scattering on nuclei. K-shell ionization cross section of 1047(100) barn for the 95 MeV/u 58Ni19+ ions colliding with hydrogen atoms was obtained in this work. Compared to the measured ionization cross section, a good agreement is achieved with the prediction by the Relativistic Ionization CODE Modified program (RICODE-M).

Target K-shell X-ray emission associated with single and double electron capture for [formula omitted] + Ar collisions

Cross sections for target Ar K-shell ionization associated with single and double electron capture, as well as the same cross sections corresponding to projectile F K X-rays and the total cross sections for single and double capture, were determined for 1.8–2.2 MeV/u F9+,8+,7+ projectiles. This work was performed at Western Michigan University using the tandem Van de Graaff accelerator. Coincidences between emitted X-rays and their corresponding charge-changed particles were detected. The Ar K X-ray coincidence cross section ratios for double to single capture are found to depend strongly on the incident charge state, with the ratios for F9+ well exceeding unity. Possible explanations for this anomalous behavior are discussed but a conclusive explanation is not found. The results are compared to previous experiments using fully-stripped fluorine where coincidence techniques were not employed.

X-ray Photoionization Cross Section Spectra of Water and Ammonia Bonded on Polycyclic Aromatic Hydrocarbons: A Quantum Mechanical Interpretation to the Absorption Spectra on Graphene.

A theoretical study of the K-shell total photoabsorption and photoionization cross section spectra of water and ammonia bonded to benzene (C6H6) and the polycyclic aromatic hydrocarbons (PAHs) naphthalene (C10H8), coronene (C24H12) and circumcoronene (C54H18) by van der Waals (vdW) forces is presented. The discretized electronic pseudospectra at the oxygen and nitrogen K-edges, covering the discrete and the continuum spectral regions, were obtained at the time-dependent density functional theory (TDDFT) level with dispersion correction. An analytic continuation procedure based on the Padé approximants was used in order to obtain the K-shell cross sections of the structures at the discrete and the continuum regions of the spectra. By examining the electronic spectra of water and ammonia bonded to coronene and circumcoronene, we observed that our results agree well with the experiments performed with graphene. This work provides a quantum mechanical interpretation to the NEXAFS experiments of water and ammonia adsorbed on graphene in terms of a physisorption model of these molecules by van der Waals forces.

Characteristic X-ray yields and cross sections of thick targets of Al, Ti, Zr, W and Au induced by keV-electron impact

In this paper, pure thick Al (Z = 13), Ti (Z = 22), Zr (Z = 40), W (Z = 74) and Au (Z = 79) targets are bombarded by electrons in an energy range of 5–27 keV, and the experimental thick-target characteristic X-ray yields of K-shell and L-shell, the X-ray production cross sections and the ionization cross sections of inner shells are presented. The present experimental setup and data processing are improved, specifically, a deflection magnet is installed in front of the X-ray detector to prevent the backscattered electron from entering into the X-ray detector, and the bremsstrahlung background spectra calculated from PENELOPE Monte Carlo simulations are used to deduce the net peak areas. The X-ray detector used in this experiment is the XR-100SDD manufactured by Amptek Inc. with a 25 mm<sup>2</sup> C2 ultra-thin window which can detect the low-energy x-rays down to boron Kα line (0.183 keV). Standard sources (<sup>55</sup>Fe, <sup>57</sup>Co, <sup>137</sup>Cs and <sup>241</sup>Am) with an activity accuracy range of 1%–3% (<i>k</i> = 2), supplied by the Physikalisch-Technische Bundesanstalt, Germany (PTB), are used to perform the detector’s efficiency calibration, and in a low-energy range (< 3.3 keV) the efficiency calibration is accomplished by measuring characteristic X-ray spectra produced by 20 keV electron impacting various thickness solid targets (i.e. by the characteristic peak method). The uncertainty of the detector’s efficiency calibration obtained in this paper is ~1.6%. The experimental thick-target characteristic X-ray yield data with an uncertainty of 1.7%–6.2% are compared with the PENELOPE Monte Carlo simulations, in which the inner-shell ionization cross sections are based on the distorted-wave Born approximation (DWBA) calculations, and they are in good agreement with a difference of less than or ~10%. According to the measured thick-target characteristic x-ray yields, the K-shell ionization cross sections for Al, Ti and Zr and the L-shell X-ray production cross sections for Zr, W and Au are also obtained with an uncertainty of 5%–8% (except for Al due to large K-shell fluorescence yield uncertainty), the difference between the experimental and theoretical data is also less than or ~10%. Moreover, by comparing the thick-target characteristic X-ray yields obtained from the analytical model and the PENELOPE Monte Carlo simulations at the electrons’ incident angles of 45° and 90°, it is found that the degree of agreement between the results from the analytical model and the Monte Carlo simulations at the incident angle of 90° is better than at the incident angle of 45°. Moreover, the contributions of the secondary electrons and bremsstrahlung photons to the characteristic X-ray yield are also given based on the PENELOPE Monte Carlo simulations. As for the elements studied in this paper, for the low ionization threshold energy, the contribution of the secondary electrons is ~2%, and however, for the high ionization threshold energy, the contribution is ~10%–20%. These contributions depend weakly on the energy of the incident electrons and show that these contributions are closely correlated with atomic number.

1s-1s electron transfer in collisions of fast C and O ions with adenine

1s-1s electron transfer and K-shell ionization cross sections of adenine (C5H5N5) molecule have been measured in collisions with C and O ions in the energy range of 2.5–5.3 MeV/u. These cross sections have been measured from the study of KLL Auger electron yields as a function of projectile charge state. The K-ionization cross section data have been compared with the ECUSAR calculations [ECPSSR model with the perturbed stationary state (PSS) effect calculated in a united and separated atom (USA) approximation]. The K-ionization data shows a good agreement with the model whereas the K-K transfer cross section is underestimated by the same model. Energy dependence of the K-K transfer cross section for adenine is found to be flat compared to that for N2 gas molecules. The values of the K-K e− transfer and the K-ionization cross sections are found to be comparable in this energy range.

K-shell ionization cross sections of atoms by muons and pions

The K-shell ionization cross sections of copper and silver atoms by muons and pions with negative and positive charge have been calculated with the classical trajectory Monte Carlo method and the plane-wave Born approximation with corrections for the Coulomb-deflection and binding-energy effects. Both results are in good agreement with each other. The obtained cross sections for muons on copper are also compared with the coupled-channels calculations. The dependence of the K-shell ionization cross sections on the sign of the projectile as well as on the projectile mass is discussed.Graphical abstract

Charge state effect on K-shell ionization of silicon induced by iodineq+ ions

In near Bohr velocity ion-atom collisions, a dependence of target K-shell ionization cross sections upon the ionic charge states has been observed. Experiments were performed in silicon solid target with 2–5 MeV iodineq+ ions incident in charge states +20 to +25. K-shell ionization cross section of silicon for q = 20 and 22 iodine ions impact with the same incident energy are almost equal, and are well described by the theory of binding-energy-modified BEA. However, for q = 25 iodine ions collisions, 3d vacancies of projectile transfer to the 1s orbit of target atom via rotational coupling of 3dπ, δ-3dσ molecular orbits in the framework of quasi-molecular model, which results in an increase of the K-shell ionization cross section of silicon.

K-Shell Ionization Cross Sections of Arsenic and Yttrium by electron impact

K-Shell Ionization Cross Sections of Arsenic and Yttrium by electron impact

K-Shell Ionization Cross Sections of Chromium and Cobalt by electron impact

K-Shell Ionization Cross Sections of Chromium and Cobalt by electron impact

Feasibility study of thin films deposited on a self-supporting carbon grid substrate target on the measurement of atomic inner-shell ionization cross-sections impacted by 3–30 keV electrons

In this paper, we have measured the , and X-ray production cross-sections of the W element and the K-shell ionization cross-sections of the Al element impacted by 3–30 keV electrons. A new kind of target consisting of a thin film deposited on a self-supporting carbon grid substrate has been used in this work. The self-supporting carbon grid substrate is made of several layers of super-aligned carbon nanotube arrays (the mass thickness of each layer of super-aligned carbon nanotube arrays is 20 μg/cm2). As a comparison, three kinds of targets consisting of a) the studied element deposited onto four layers of super-aligned carbon nanotube arrays and separated from each other by one layer of single carbon atoms, b) the studied element deposited directly onto four layers of super-aligned carbon nanotube arrays, and c) the studied element deposited directly onto two layers of super-aligned carbon nanotube arrays, were respectively prepared to figure out which type is fit for the measurement of inner-shell ionization cross-sections induced by 3–30 keV electrons. The experimental data are compared with the distorted-wave Born approximation (DWBA) theoretical predictions and with the available experimental data from other references. The results show that the first and the second targets are both suitable for the inner-shell ionization cross-section measurements by 3–30 keV electrons, but the third target is not. Besides, we present the M-shell X-ray production cross-sections of the W element by 5–30 keV electrons in this paper for the first time.