Shell Ionization Cross Sections Research Articles

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 AND X-RAY PRODUCTION CROSS SECTIONS BY PROTONS IN VACUUM AND GASEOUS ENVIRONMENT

The Κα ionization and x-ray production cross sections from the bombardment of three metal targets with protons were measured in vacuum and in gaseous environment (external beam technique). Proton energies between 1.5 and 8 MeV were used. The experimental Κ shell ionization and x-ray production cross sections were calculated for the same targets and com­ pared with three theoretical and two semiempirical approxima­ tions. For the measurements in gaseous environment the influ­ence of the secondary electrons (delta electrons) emitted from the gas, to the x-ray yields was investigated. For this pur­ pose a suitable model was introduced and tested experimen­tally.

Experimental and theoretical cross sections for K -shell ionization of 52Te , 73Ta , and 83Bi by electrons with energies up to 100 keV

In this work we present a combined experimental and theoretical study of $K$-shell ionization by electrons with energies close to the threshold. The ionization cross sections of the $K$ shells of Te, Ta, and Bi atoms have been measured up to 100 keV with uncertainties ranging from 4% to 8%. In turn, calculations have been done using the subconfiguration average distorted-wave (SCADW) method, which includes the full two-body retarded electromagnetic interaction between the projectile and target electrons. The predictions of the SCADW method are in good agreement with the experimental data. In contrast, theoretical cross sections based on first-order perturbation theory where the transverse interaction is computed with plane waves instead of distorted waves underestimate the SCADW values as well as the experimental data. The difference between the two investigated ab initio formalisms grows with atomic number, being 3% for Te, 15% for Ta, and 25% for Bi. An additional comparison of both theoretical approaches with recent measurements for Au $K$ supports the conclusion that the SCADW method reproduces well the experimental $K$-shell ionization cross section of atoms with intermediate to large $Z$ near the threshold.

Hypersatellite x-ray decay of 3d hollow- K -shell atoms produced by heavy-ion impact

We report on the radiative decay of double $K$-shell vacancy states produced in solid Ca, V, Fe, and Cu targets by impact with about 10 MeV/amu C and Ne ions. The resulting $K$ hypersatellite x-ray emission spectra were measured by means of high-energy-resolution spectroscopy using a von Hamos bent crystal spectrometer. The experiment was carried out at the Philips variable energy cyclotron of the Paul Scherrer Institute. From the fits of the x-ray spectra the energies, line widths, and relative intensities of the hypersatellite x-ray lines could be determined. The fitted intensities were corrected to account for the energy-dependent solid angle of the spectrometer, effective source size, target self-absorption, crystal reflectivity, and detector efficiency. The single-to-double $K$-shell ionization cross-section ratios were deduced from the corrected relative intensities of the hypersatellites and compared to theoretical predictions from the semiclassical approximation model using hydrogenlike and Dirac-Hartree-Fock wave functions and from classical trajectory Monte Carlo calculations.

The [formula omitted] beam line of the São Paulo Microtron electron accelerator

The São Paulo Microtron 10−100keV electron beam-line described here was designed to allow precise measurements of the electron-atom interaction cross-sections using reproducible arrangements. The irradiation chamber has thirteen spectroscopy windows for x-ray detectors and a multi-target ladder. The photon background on the target was reduced by using a large and deep Faraday cup, lining the chamber's interior with plastic, and mounting the targets in carbon fiber frames. The current research plan includes measurements of: electron doubly differential bremsstrahlung cross sections; inner shell ionization cross sections; angular distributions of L X-rays, and the angular distribution of scattered electrons.

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).

Multiple ionization of argon by helium ions

We apply the continuum distorted-wave eikonal initial state and the independent electron model to describe the multiple ionization of Ar by He2+ and He+ in the energy range 0.1–10 Mev amu–1. Auger-like post collisional processes are included, which enhance the high energy multiple ionization cross sections via ionization of the inner shells. All Ar electrons (K, L and M-shells) have been included in these calculations. The results agree well with the experimental data at high energies, where the post-collisional ionization is the main contribution. At intermediate impact energies the description is also good though it tends to overestimate the triple and quadruple ionization data at intermediate energies. We analyze this by comparing the present results for He+2 in Ar, with previous ones for He+2 in Ne and Kr. It was found that the theoretical description improves from Ne to Ar and Kr, with the latter being nicely described even at intermediate energies. The present formalism is also tested for Ar inner shell and total ionization cross sections. In all the cases the results above 0.1 MeV amu–1 are quite reasonable, as compared with the experimental data available and with the ECPSSR values.

Subshell resolved inner shell ionization cross-sections of High Z elements by electron impact

SynopsisWe have obtained the L sub-shell resolved electron impact ionization cross sections for high Z elements in the energy range 15-45 keV. The experimental results are compared with the DWBA and PWBA (Distorted/Plane Wave Born Approximation) based theoretical predictions and MRBEB (Modified Relativistic Binary Encounter Bethe) theory. Good agreement is found between DWBA based results and experiment for L3 sub-shell of all the elements studied.

Relativistic calculations of doubleK-shell-photoionization cross sections for neutral medium-Zatoms

Fully relativistic calculations are presented for the double $K$-shell photoionization cross section for several neutral medium-$Z$ atoms, from magnesium ($Z = 10$) up to silver ($Z = 47$). The calculations take into account all multipoles of the absorbed photon as well as the retardation of the electron-electron interaction. The approach is based on the partial-wave representation of the Dirac continuum states and uses the Green-function technique to represent the full Dirac spectrum of intermediate states. The method is strictly gauge invariant, which is used as an independent cross check of the computational procedure. The calculated ratios of the double-to-single $K$-shell ionization cross sections are compared with the experimental data and with previous computations.

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.

Determination of subshell-resolvedL-shell-ionization cross sections of gold induced by 15–40-keV electrons

The $L$-subshell specific electron impact ionization cross sections, near the ionization threshold ($15<E<40$ keV) of gold are calculated from the measured production cross sections in this collaborative work between an experimental and a theoretical group. Calculations are performed using the distorted wave Born approximation formalism, and the modified relativistic binary encounter Bethe model to understand the data. The observed agreements and discrepancies between the two theoretical formalisms considered and the experimental data are reported.

A suitable analytical formula for the K shell ionization cross section of carbon and potassium atoms by electron impact

A suitable analytical formula for the K shell ionization cross section of carbon and potassium atoms by electron impact

Electron impact ionization cross-section of K-shell and H- to Be-isoelectronic series: An empirical model

The model of Cengiz (2002) [Approximate inelastic scattering cross sections of electrons. Rad. Phys. Chem. 65, 33–44] has been modified by incorporating both the ionic and relativistic corrections due to Uddin et al. (2006) [Modified Kolbensvedt model for the electron impact K-shell ionization cross-sections of atoms and ions. Eur. Phys. J. D 37, 361–369.] to investigate the electron impact s-orbital ionization in the K- and L-shells. With a single set of species independent parameters our evaluated inner shell ionization cross section of atomic targets from H to U over incident energies up to 2GeV and of H- to Be-isoelectronic series reproduce the experimental findings nicely.

Electron correlations in cross sections for ionization of heliumlike ions by high-energy particle impact

We have evaluated the dominant contribution of the electron correlations to the single $K$-shell ionization cross section of heliumlike atomic systems by impact of high-energy electrons. This study is performed consistently within the framework of nonrelativistic perturbation theory. The results obtained are also applicable for the case of high-energy collisions with arbitrary charged particles whose mass is much less than that of the target. The formula for cross section is represented in the form of a universal scaling. A comparison of our numerical calculations with available experimental data is made.

Experimental determination of cross sections forK-shell ionization by electron impact for C, O, Al, Si, and Ti

Cross sections for $K$-shell ionization by electron impact were determined from films of Al, Si, and Ti and their oxides deposited on carbon substrates, for incident energies between 2.5 and 25 keV. The spectral processing of the x-ray emission spectra took into account corrections due to the presence of a spontaneous oxide layer formed on the monoelemental films and to the supporting material. Carbon $K$-shell ionization cross sections were determined from the contribution of the substrate to the measured spectra, while for oxygen, data from the three oxide films were taken. The mass thickness of the coatings was characterized by x-ray reflectivity. The results obtained were compared with other experimental data sets, semiempirical approaches, and theoretical models.

Validation of Proton Ionization Cross Section Generators for Monte Carlo Particle Transport

Three software systems, ERCS08, ISICS 2011 and Šmit's code, that implement theoretical calculations of inner shell ionization cross sections by proton impact, are validated with respect to experimental data. The accuracy of the cross sections they generate is quantitatively estimated and inter-compared through statistical methods. Updates and extensions of a cross section data library relevant to PIXE simulation with Geant4 are discussed.

Measurements of theK-shell ionization cross sections of Si by 3–25-keV electron impact using the thick-target method

In this paper, the $K$-shell ionization cross sections of Si element in the threshold energy region of 3--25 keV have been measured by using the thick-target method. With the Monte Carlo simulations, the effects of multiple scattering of incident electrons and from the bremsstrahlung photons and other secondary particles in the thick-target method have been discussed. The detection efficiency calibration in the lower-energy region has been performed by using the bremsstrahlung spectra of thick carbon target by electron impact in combination with the use of standard x-ray sources, and the detector thickness parameters have also been determined by a nonlinear least-squares fit. The ill-posed inverse problem involved in the thick-target method has been dealt with by the Tikhonov regularization method. The experimental $K$-shell ionization cross sections for Si element obtained in this paper have also been compared with some theoretical models, and it has been observed that the experimental data in this paper are in good agreement with the theoretical values based on the distorted-wave Born approximation model developed most recently.

Photoionization of the outer electrons in noble gas endohedral atoms

We suggest a prominent modification of the outer shell photoionization cross section in noble gas (NG) endohedral atoms NG@C n under the action of the electron shell of fullerene C n . This shell leads to two important effects: a strong enhancement of the cross section due to fullerene shell polarization under the action of the incoming electromagnetic wave and to prominent oscillation of this cross section due to the reflection of a photoelectron from the NG by the fullerene shell. Both factors lead to powerful maxima in the outer shell ionization cross sections of NG@C n , which we call giant endohedral resonances. The oscillator strength reaches a very large value in the atomic scale, 25. We consider atoms of all noble gases except He. The polarization of the fullerene shell is expressed in terms of the total photoabsorption cross section of the fullerene. The photoelectron reflection is taken into account in the framework of the so-called bubble potential, which is a spherical δ-type potential. It is assumed in the derivations that the NG is centrally located in the fullerene. It is also assumed, in accordance with the existing experimental data, that the fullerene radius R C is much larger than the atomic radius r A and the thickness ΔC of the fullerene shell. As was demonstrated recently, these assumptions allow us to represent the NG@C n photoionization cross section as a product of the NG cross section and two well-defined calculated factors.

Projectile atomic number dependence of the relativistic effect on theK-shell ionization of highZelements under heavy-ion impact

Absolute $K$-shell ionization cross sections of Sb, Au, and Bi have been measured in collisions with highly charged C, O, and S ions having energies between 2 and $6.25\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕u$. The data are presented along with the earlier results with F and Si ions as projectiles. The measured data have been compared with theoretical models based on the semiclassical approximation including relativistic effect and perturbed stationary state approximation including the corrections for energy loss, Coulomb deflection, and relativistic effects. The data were analyzed in term of relativistic effect on $K$-ionization: its dependence on the projectile atomic number, target atomic number and projectile energy. The present data set along with our recently measured similar data for F and Si ions show that the relativistic effect increases with projectile atomic number and decreases with projectile velocity. A comparison of the experimental data and relativistic calculations, both normalized to nonrelativistic model, show the inadequacy of the theoretical models in describing the relativistic correction on $K$-shell ionization. For example, the theoretical predictions agree with experimental findings for O ions on Bi while the same theoretical predictions deviate from the experimental results by about a factor of 2 for Si and S on Bi, the theory being higher.

K-shell ionization cross sections following0.6–4‐keVe−+H2Ocollisions

Collisions between electrons and a ${\mathrm{H}}_{2}\mathrm{O}$ vapor target at projectile energies ranging from $600\phantom{\rule{0.3em}{0ex}}\mathrm{eV}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}4\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ have been investigated experimentally and theoretically, in order to determine cross sections for the production of a $K$-shell vacancy of the ${\mathrm{H}}_{2}\mathrm{O}$ molecule. The electrons originating from direct ionization and from autoionization were detected at angles in the range 30\ifmmode^\circ\else\textdegree\fi{}--130\ifmmode^\circ\else\textdegree\fi{} with respect to the incident beam direction. From the spectra, cross sections for the emission of a target electron following the production of a $K$-shell vacancy in oxygen are determined as a function of the projectile energy. The present experimental results are compared with semiempirical formula that have been extensively used previously for electron-atom collisions, and with model calculations using plane wave Born approximation. The ratio between $K$-shell and total ionization cross sections is found to be similar to that determined for an O atomic target, except at the highest projectile energies, for which it is equivalent to that determined for Ne. We show that this ratio is essentially governed, for sufficiently high collision energies, by the ratio between the outer- and inner-shell ionization potentials.