Inner-shell Ionization Cross Sections Research Articles

Inner-shell ionization cross sections of atoms by positron impact

The relativistic binary-encounter-Bethe model with Wannier-type threshold law is employed to obtain the inner-shell ionization cross sections of multi-electron atoms (Ni, Cu, Y, Ag, Au, Yb, Ta, and Pb) for positron impact energies from the thresholds up to 105 keV. There is good agreement between the present calculations and the experimental data. The constant in the acceleration term derived from the Wannier law is determined to be 0.2 and 0.5 for the K- and L-shells, respectively.

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.

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.

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.

Calculating the Atomic electron impact Ionization Cross Section for some elements

Inner-shell ionization cross section (ICS) by electron impact are of interest not only to the basic collision physics for complex atoms, but also to various practical applications in material science and electron microscopy. Theoretical difficulties in the past were between the threshold and the peak, which occur usually four to five times the threshold energy. Theories based on classical mechanics are somewhat better than on Born cross section, but such theories usually requires adjustable parameters. We used the Gryzinski formalism to calculate atomic electron impact ionization cross sections for the elements (Fe, Co, Mn, Ti, Zn, and Nb). Good to satisfactory agreement was found for all atoms with the exception of (Nb), where the distance between our cross section and Deutsch-Mark formula become larger at the high values of the overvoltage (U). Moreover, when compared to other to available ionization cross sections for these atoms, calculated using other methods and semiempirical formula, the Gryzinski formalism achieved a level of agreement with experimental data that is as good better than the predictions from the other methods.

X-ray emission for Ar11+ ions impacting on various targets in the collisions near the Bohr velocity* *Project supported by the National Key R&D Program of China (Grant No. 2017YFA0402300), the National Natural Science Foundation of China (Grant Nos. 11505248, 11775042, 11875096, and 11605147) the Scientific Research Program Funded by Shaanxi Provincial Education Department, China (Grant No. 20JK0975), the Scientific Research

X-ray emission from the collisions of 3 MeV Ar11 + ions with V, Fe, Co, Ni, Cu, and Zn is investigated. Both the x-rays of the target atom and projectile are observed simultaneously. The x-ray yield is extracted from the original count. The inner-shell ionization cross section is estimated by the binary encounter approximation model and compared with the experimental result. The remarkable result is that the Ar K-shell x-ray yield is diminished with the target atomic number increasing, which is completely opposite to the theoretical calculation. That is interpreted by the competitive consumption of the energy loss for the ionization of inner-shell electrons between the projectile and target atom.

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).

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.

RBED cross sections for the ionization of atomic inner shells by electron-impact

The relativistic binary-encounter-dipole (RBED) model for electron-impact ionization of atoms combines classical binary-encounter theory and the asymptotic dipole interaction, which is based on the plane-wave Born approximation, with the only non-trivial ingredient being the optical oscillator strength (OOS). Due to the difficulty of obtaining accurate OOSs, the performance of the RBED model has so far not been fully assessed. In the present work we compare RBED inner-shell ionization cross sections (total and differential) of neutral atoms evaluated using three types of OOSs, namely an empirical power-law OOS, analytical hydrogenic OOSs and ab initio OOSs calculated numerically from self-consistent atomic potentials. We find that, compared to the distorted-wave Born approximation (DWBA), the RBED with either hydrogenic or numerical OOSs generally yields more accurate total cross sections (TCSs) than the RBED with the power-law OOS, especially for the most tightly bound shells. In the highly relativistic limit the RBED model does not recover the Bethe asymptotic behavior because of its different energy-dependent prefactor, hence we investigate an alternative prefactor which restores the correct Bethe asymptote. Finally, we suggest multiplying the RBED differential cross sections (DCSs) by the ratio of DWBA to RBED TCSs and verify that this renormalization improves the agreement with the DWBA DCSs.

Reprint of: Ionization probabilities of Ne, Ar, Kr, and Xe by proton impact for different initial states and impact energies

In this contribution we present ab initio results for ionization total cross sections, probabilities at zero impact parameter, and impact parameter moments of order +1 and −1 of Ne, Ar, Kr, and Xe by proton impact in an extended energy range from 100 keV up to 10 MeV. The calculations were performed by using the continuum distorted wave eikonal initial state approximation (CDW-EIS) for energies up to 1 MeV, and using the first Born approximation for larger energies. The convergence of the CDW-EIS to the first Born above 1 MeV is clear in the present results. Our inner-shell ionization cross sections are compared with the available experimental data and with the ECPSSR results. We also include in this contribution the values of the ionization probabilities at the origin, and the impact parameter dependence. These values have been employed in multiple ionization calculations showing very good description of the experimental data. Tables of the ionization probabilities are presented, disaggregated for the different initial bound states, considering all the shells for Ne and Ar, the M-N shells of Kr and the N-O shells of Xe.

Experimental study on Ti K shell ionization cross sections induced by 8-9.5 keV positrons

Due to lack of experimental data of the inner shell ionization cross sections induced by low-energy positron, advanced theoretical models developed in recent years cannot be correctly evaluated, and the application of slow positron beam technique is greatly limited. Here we present the method of obtaining reliable experiment data of atomic inner-shell ionization cross section by positron impact. In this work, the slow positron beam device is used to generate 8-9.5 keV positron beams impacting on a pure thick Ti target, and the silicon drift detector (SDD) is adopted to collect the X-ray spectra produced by positrons impacting on thick Ti target, and the incident positron numbers are obtained by applying an HPGe detector to on-line collect annihilation photons. Then the experimental characteristic X-ray yields of Ti K shell impacted by 8-9.5 keV positron could be acquired. Meantime, the simulated characteristic X-ray yields are acquired by the PENELOPE program simulating the experiments. In the comparison between the experimental yields and the simulated yields based on two sets of different inner shell ionization cross section database in the PENELOPE code, i.e. the optical data model (ODM) and the distorted-wave Born approximation model (DWBA), there is a large difference between the simulated data from the ODM theoretical model and the experimental values, while the simulated yields from the DWBA theoretical model are in good agreement with the experimental results. Accordingly, a correction factor is introduced to modify the DWBA theoretical model database which is used in the PENELOPE, and then the experimental process is re-simulated. When the simulated yields and the experimental yields are in the highest consistence, the reliable Ti K shell ionization cross sections impacted by 8-9.5 keV positron could be obtained. The biggest advantage of using this method to obtain atomic inner-shell ionization cross section impacted by positron is that the effects of the multiple scattering of incident positrons in the thick target, from the bremsstrahlung and annihilation photons, and other secondary particles on the experimental characteristic X-rays do not need calculating (the calculation method that has been developed previously cannot give the more correct result about the contribution of the multiple scattering of incident positrons, from the bremsstrahlung and annihilation photons, and other secondary particles to characteristic X-rays).

Ionization probabilities of Ne, Ar, Kr, and Xe by proton impact for different initial states and impact energies

In this contribution we present ab initio results for ionization total cross sections, probabilities at zero impact parameter, and impact parameter moments of order +1 and −1 of Ne, Ar, Kr, and Xe by proton impact in an extended energy range from 100keV up to 10MeV. The calculations were performed by using the continuum distorted wave eikonal initial state approximation (CDW-EIS) for energies up to 1MeV, and using the first Born approximation for larger energies. The convergence of the CDW-EIS to the first Born above 1MeV is clear in the present results. Our inner-shell ionization cross sections are compared with the available experimental data and with the ECPSSR results. We also include in this contribution the values of the ionization probabilities at the origin, and the impact parameter dependence. These values have been employed in multiple ionization calculations showing very good description of the experimental data. Tables of the ionization probabilities are presented, disaggregated for the different initial bound states, considering all the shells for Ne and Ar, the M-N shells of Kr and the N-O shells of Xe.

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.

Evaluation of computational models and cross sections used by MCNP6 for simulation of characteristic X-ray emission from thick targets bombarded by kiloelectronvolt electrons

This paper evaluates the accuracy of the single-event (SE) and condensed-history (CH) models of electron transport in MCNP6.1 when simulating characteristic Kα, total K (=Kα+Kβ) and Lα X-ray emission from thick targets bombarded by electrons with energies from 5keV to 30keV. It is shown that the MCNP6.1 implementation of the CH model for the K-shell impact ionization leads to underestimation of the K yield by 40% or more for the elements with atomic numbers Z<15 and overestimation of the Kα yield by more than 40% for the elements with Z>25. The Lα yields are underestimated by more than an order of magnitude in CH mode, because MCNP6.1 neglects X-ray emission caused by electron-impact ionization of L, M and higher shells in CH mode (the Lα yields calculated in CH mode reflect only X-ray fluorescence, which is mainly caused by photoelectric absorption of bremsstrahlung photons). The X-ray yields calculated by MCNP6.1 in SE mode (using ENDF/B-VII.1 library data) are more accurate: the differences of the calculated and experimental K yields are within the experimental uncertainties for the elements C, Al and Si, and the calculated Kα yields are typically underestimated by (20–30)% for the elements with Z>25, whereas the Lα yields are underestimated by (60–70)% for the elements with Z>49. It is also shown that agreement of the experimental X-ray yields with those calculated in SE mode is additionally improved by replacing the ENDF/B inner-shell electron-impact ionization cross sections with the set of cross sections obtained from the distorted-wave Born approximation (DWBA), which are also used in the PENELOPE code system. The latter replacement causes a decrease of the average relative difference of the experimental X-ray yields and the simulation results obtained in SE mode to approximately 10%, which is similar to accuracy achieved with PENELOPE. This confirms that the DWBA inner-shell impact ionization cross sections are significantly more accurate than the corresponding ENDF/B cross sections when energy of incident electrons is of the order of the binding energy.

Multiple ionization of Ar by alpha particles

SynopsisWe present theoretical results on multiple ionization of Ar by He2+ by employing the continuum distorted-wave eikonal initial state together with photoionization branching ratios to include Auger-type contributions. We also analyze the inner-shell ionization cross sections (K and L-shells of Ar). The high energy experimental data is correctly described, showing differences with proton impact tendency in the post-collisional region. At intermediate impact energies (direct ionization region) the single and double ionization are described rather well, but we note certain overestimation for higher final charge states.

Measurements of L shell X-ray yields of thick Ag target by 6–29keV electron impact

Abstract In this paper, the L shell X-ray yields for a thick Ag target have been measured at incident electron energies of 6–29 keV. The experimental values are compared with the Monte Carlo simulation results that are obtained by using the PENELOPE code, in which the inner-shell ionization cross sections by electron impact calculated in the theoretical frame of distorted wave Born approximation are used. The experimental and simulation values are in agreement with ~10% difference. Meanwhile, the L shell X-ray production cross sections are also obtained based on the measured L shell X-ray yields for a thick Ag target in this paper, and are compared with other experimental Ag L shell X-ray production cross section data by electron and positron impact measured previously and some theoretical models. Some factors that could affect these comparisons are also discussed in this paper.

Inner-shell ionization cross section of Gold by electron and positron impact

The theoretical modified Khare (BEB) model has been used to calculate the total cross sections for L1, L2 and L3-subshells ionization of gold atom due to electron and positron impact for projectile energy varying from the threshold of ionization to 60 times the threshold energy For L subshells the present cross section due to electron and positron impact cross sections are in remarkable agreement with available experimen- tal data and other theoretical cross sections. Total L shell ionization cross sections have been also calculated in the energy varying from the threshold of ionization to several MeV by electron impact. It is found good agreement with available experimental data. The investigation for other atoms is in progress.

Energy loss in the ECPSSR theory and its calculation with exact integration limits

ECPSSR cross sections for inner-shell ionization are compared with numerical calculations that use correct and wrong expressions for exact limits of momentum transfer. For very adiabatic collisions, the employment of the wrong expression, as done in several popularly utilized computer codes, overestimates the cross sections up to two orders of magnitude. By contrast, even in such collisions the original ECPSSR approach of Brandt and Lapicki that approximates the effect of projectile energy loss by a multiplicative correction function fS and the relativistic effects by a relativistically corrected electron mass yields cross sections that are in agreement within a factor of two with respect to the calculation with hydrogenic Dirac wavefunctions and exact limits of integration with no relativistic correction. For plane-wave Born approximation calculations, the relativistic corrected expressions of the exact limits of integration are presented. The cross section calculated with such limits differs from the ECPSSR calculation using the fS-function by less than 2% in the region of lowest collision velocities covered by experiments. A straightforward modification of the existing computer codes with the correct expression for exact momentum transfer is suggested.

Cross Sections for Inner-Shell Ionization by Electron Impact

An analysis is presented of measured and calculated cross sections for inner-shell ionization by electron impact. We describe the essentials of classical and semiclassical models and of quantum approximations for computing ionization cross sections. The emphasis is on the recent formulation of the distorted-wave Born approximation by Bote and Salvat [Phys. Rev. A 77, 042701 (2008)] that has been used to generate an extensive database of cross sections for the ionization of the K shell and the L and M subshells of all elements from hydrogen to einsteinium (Z = 1 to Z = 99) by electrons and positrons with kinetic energies up to 1 GeV. We describe a systematic method for evaluating cross sections for emission of x rays and Auger electrons based on atomic transition probabilities from the Evaluated Atomic Data Library of Perkins et al. [Lawrence Livermore National Laboratory, UCRL-ID-50400, 1991]. We made an extensive comparison of measured K-shell, L-subshell, and M-subshell ionization cross sections and of Lα x-ray production cross sections with the corresponding calculated cross sections. We identified elements for which there were at least three (for K shells) or two (for L and M subshells) mutually consistent sets of cross-section measurements and for which the cross sections varied with energy as expected by theory. The overall average root-mean-square deviation between the measured and calculated cross sections was 10.9% and the overall average deviation was −2.5%. This degree of agreement between measured and calculated ionization and x-ray production cross sections was considered to be very satisfactory given the difficulties of these measurements.

Werner Brandt legacy to PIXE: Past and present perspectives

Inner-shell ionization cross sections used in Particle-Induced X-ray Elemental (PIXE) analyses are routinely calculated in the ECPSSR [W. Brandt, G. Lapicki, Phys. Rev. A 23 (1981) 1717–1729] theory and/or semiempirical formulas scaled to that theory. Thirty years after the passing of Werner Brandt, with recognition of his seminal contributions to other research on positron physics and stopping power problems, the work and articles that progressed into the ECPSSR theory for inner-shell ionization by protons and heavier ions are recalled as Brandt’s past legacy to the PIXE community. Applications of the ECPSSR and its evolution into the ECUSAR [G. Lapicki, Nucl. Instr. Meth. B 189 (2002) 8–20] theory over the last three decades are reviewed with perspectives on Brandt’s present legacy.