Binary Encounter Approximation Research Articles

Electron Impact Single Ionization Cross Sections of Ar+ Ion

Binary encounter approximation has been used for theoretical calculations of electron impact single ionization cross sections of singly ionized Ar atom at ground state in the energy range of 29.1eV to 2495.1 eV/amu. The cross sections for energy transfer given by Vriens’ and quantum mechanical Hartree-Fock velocity distributions for target electron have been used in the calculation. The contributions in total single ionization cross sections from 3p and 3s subshells are observed higher than from 2p, and the contributions from 3p first increases with impact energy and then decreases with increase of impact energy whereas the contribution from 3s decreases with impact energy. About 69% of results have ratio factors ≤ 1.5 and 59% have values 1.25. Major contributions to the total ionization cross sections are from 3p and 3s for direct single ionization.

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.

He2+ impact single ionization cross sections of Cu atom

Semi-classical binary encounter approximation has been used for theoretical calculations of single ionization cross sections of Cu atom at ground state by alpha particle impact in energy range varying from threshold 35 keV/amu to 425 keV/amu. An accurate expression of cross section for energy transfer ΔΕ (σΔΕ) as given by Vriens and quantum mechanical Hartree-Fock velocity distributions for target electrons have been used in the calculation. Major contribution to the total single ionization cross sections of Cu are from 4s and 3d subshells. The ionization cross sections decrease with the increase of impact energy same as experimental data reported. The theoretical and experimental results of single ionization cross sections have same trends against the increase of impact energy. The ratio factor falls within 2, varying from 1.26 to 1.86, for given energy range. Theoretical results are under valid range. About 50% of total theoretical results of single ionization cross sections have ratio factor (R) . Major contribution to total ionization cross section is from 3d and 4s subshells-electrons whose contributions varies from 62 to 71% and 41.7% to 23.8% respectively. The higher value of linear correlation coefficient (=0.9647) and lower value of standard deviation (=0.822) shows that results calculated are close to the experimental data in the intermediate and high energy range. BIBECHANA 19 (2022) 111-118

W L-shell X-ray emission induced by C<sup>6+ </sup>ions with several hundred MeV/u

The L-shell X-ray emission of tungsten is investigated under the bombardment of C<sup>6+</sup> ions in a high energy range of 154—424 MeV/u. Compared with the atomic data, the energy of the X-ray is enlarged, and the relative intensity ratio of Lι, Lβ<sub>1,3,4</sub> and Lβ<sub>2,15</sub> to Lα<sub>1,2</sub> X-rays are enhanced. The L-subshell and the total X-ray production cross section are calculated from a well corrected thick target formula and compared with the theoretical estimation of binary encounter approximation (BEA), plane-wave Born approximation (PWBA) and ECPSSR (PWBA theory modified with Energy-loss, Coulomb-repulsion, Perturbed-Stationary-State and Relativistic corrections). On the whole, the experimental cross sections are all smaller than the prediction of PWBA and ECPSSR, but in rough agreement with that of BEA. It is indicated that the inner-shell ionization of W can be considered as a binary process between the high energy C<sup>6+</sup> ions acting as a point charge and the independent target electrons. With the L-shell ionization, the outer-shells are multiply ionized. The multi-ionization degree is approximately regard as a constant in the present work. This leads the X-ray energy to be blueshifted and the relative intensity ratios of Lι and Lβ to Lα X-ray to be enhanced. Using the atomic parameters corrected by multi-ionization, the X-ray production cross section can be estimated by the BEA model.

Application of Binary Encounter Approximation and Electron Impact on Ionization of Atoms

Semi-classical binary encounter approximation has been used for theoretical calculations of electron impact single ionization cross sections of Xe and Kr and double ionization of Fe atom at ground state. An accurate expression of cross section for energy transfer ΔE (σΔE) as given by Vriens and quantum mechanical Hartree-Fock velocity distributions for target electron have been used in the calculation. In the case of single ionization of Xe, 71% theoretical results lies within valid range of ratio factor less than 2 and 55% have valueless than 1.5. In the case of Kr, 97% of results have ratio factor less than 2 and 34% of results have ratio factor less than 1.1. Gryzinski and Kune model of charged particle impact double ionization of atoms found suitable for describing double ionization of atoms and ions. In the case of double ionization of Fe by electron impact 47% of results have ratio factor less than 2 and 18% of results have ratio factor 1.2. At impact 760 eV, 800 eV and 850 eV having ratio factor 1.01, 0.989 and 0.967. Major contribution in double ionization is 60.16% from (4s,3d) and 31% is from (4s,3p).

Study of Alpha Particle Impact Double Ionization Cross Sections of Cu Atom

Semi-classical binary encounter approximation has been used for the study of ionization cross sections of Cu atom at ground state. Projectile, alpha particle, with energy varying from threshold to 360 keV/amu are considered for direct double ionizations cross section. Out of the two path ways of ionization we have ruled out the indirect process (like excitation-auto ionization, Auger effect) of double ionization. We considered direct - ionization of outer shells of Cu atom. Vriens accurate expression of cross section for energy transfer ΔE(σΔE ) and Hertree-Fock velosity distribution function for the target electrons are used. The theoretical value of double ionization cross sections at impact energy 300 keV/amu is 0.98 x 10-16 cm2 which is same as experimental values at that impact energy. Above energy of 300 keV/amu, the calculated results underestimates the experimental data and at 360 keV/amu their magnitude are 0.77 x 10-16 and 1.0 x 10-16 respectively. Above impact energy of 75keV/amu, all the theoretical results have ratio factor within 2. Out of the total number of theoretical data 75% are under valid range of ratio factor 2 and among the valid range 41% have ratio factor below 1.325 and hence calculated results of double ionization cross section lie in the acceptable range. The linear correlation coefficient (R square) and standard deviation (SD) of linear fit are 0.6984 and 0.7883 respectively. In low energy range the theoretical results are more apart from corresponding experimental values and possess relatively more error compared to intermediate and higher energy region. Calculated results are in satisfactory agreement with experiment in intermediate and high energy range.

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.

He2+ Impact Single Ionization Cross Sections of Fe Atom

Binary encounter approximation has been used for theoretical calculations of alpha particle (He2+) impact single ionization cross sections of iron atom at ground state in the energy range of 35 to 360 keV/amu. The cross sections for energy transfer given by Vriens’ and quantum mechanical Hartree-Fock velocity distributions for target electron have been used in the calculation. The contributions in total single ionization cross sections from 4s and 3d subshells are observed to be higher than from 3p, and the contributions from 4s decreases with increase of impact energy whereas the contribution from 3d increases. The total single ionization cross sections decrease gradually with the increase of impact energy similar to experimental results which implies that our results are in satisfactory agreement with the experimental data in the given energy range.

Calculation of secondary electron bremsstrahlung in the binary encounter approximation using Dirac–Hartree–Fock–Slater velocity distributions

One of the main factors that determine the detection limit in particle-induced X-ray emission (PIXE) spectrometry is the continuous X-ray background. In the case of impinging protons, a complete description requires five radiative processes. Among them, secondary electron bremsstrahlung (SEB) is one of the largest contributions and describes the bremsstrahlung radiated by the electrons ejected from the target atoms by proton impact. The calculation of SEB cross sections in the binary encounter approximation (BEA) entails knowledge of the velocity distributions (VDs) of the atomic electrons. For this purpose, analytical hydrogenic VDs are currently used for all the (sub)shells. In the present work, numerical VDs calculated from Dirac–Hartree–Fock–Slater (DHFS) wave functions are employed. Additionally, a compact equation for the SEB differential cross section is derived. Results for the ionisation and SEB cross sections of Al, Ag, and Au calculated from the DHFS and hydrogenic VDs are compared in detail.

Experimental measurements validate the use of the binary encounter approximation model to accurately compute proton induced dose and radiolysis enhancement from gold nanoparticles

In protontherapy, it has been suggested that nanoparticles of high-Z material like gold (GNP) could be used as radiosensitizers. The origin of this enhancement phenomenon for proton radiation is not yet well understood and additional mechanistic insights are required. Previous works have highlighted the good capabilities of TRAX to reproduce secondary electron emission from gold material. Therefore, TRAX cross sections obtained with the binary encounter approximation (BEA) model for proton ionization were implemented within Geant4 for gold material.Based on the TRAX cross sections, improved Geant4 simulations have been developed to investigate the energy deposition and radical species production around a spherical gold nanoparticle (5 and 10 nm in diameter) placed in a water volume during proton irradiation. Simulations were performed for incident 2 MeV proton. The dose enhancement factor and the radiolysis enhancement factor were quantified. Results obtained with the BEA model were compared with results obtained with condensed-history models.Experimental irradiation of 200 nm gold films were performed to validate the secondary electron emission reproduction capabilities of physical models used in Monte Carlo (MC) simulations. TRAX simulations reproduced the experimental backscattered electron energy spectrum from gold film with better agreement than Geant4. Results on gold film obtained with the BEA model enabled to estimate the electron emission from GNPs. Results obtained in our study tend to support that the use of the BEA discrete model leads to a significant increase of the dose in the near vicinity of GNPs (<20 nm), while condensed history models used in Geant4 seem to overestimate the dose and the number of chemical species for increasing distances from the GNP. Based on discrete BEA model results, no enhancement effect due to secondary electron emitted from the GNP is expected if the GNP is not in close proximity to key cellular functional elements (DNA, mitochondria…).

Positronium collisions with molecular nitrogen

Positronium (Ps) collisions with molecular hydrogen are investigated theoretically. Elastic and Ps ionization cross sections are calculated. For elastic scattering the pseudopotential method, previously developed for rare-gas atoms, is applied. Ps ionization cross sections are calculated using the binary-encounter approximation. The results agree with swarm measurements at low collision energies and with beam measurements at higher energies. The total Ps-${\mathrm{H}}_{2}$ cross section when plotted as a function of collision velocity is close to the ${e}^{\ensuremath{-}}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ cross section at velocities above the Ps ionization threshold, confirming earlier observations [Brawley et al., Science 330, 789 (2010)]. However, below the threshold the two sets of cross sections are different because of the different nature of the long-range interaction between the projectile and the target, the polarization interaction in the case of ${e}^{\ensuremath{-}}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ collisions and the van der Waals interaction in the case of Ps-${\mathrm{H}}_{2}$ collisions.

Electronic wave function and binding effects in M-shell ionization of gold by protons

Abstract The measured M-X-ray production cross sections for protons, which are used in the particle induced X-ray emission (PIXE) technique, are systematically underestimated for low impact energies by the ECPSSR and ECUSAR theories. These theories, which are based on the plane wave Born approximation (PWBA) and use the screened hydrogenic wave functions, include corrections for the projectile Coulomb deflection and electron relativistic and binding effects. In the present paper, in order to interpret the observed disagreement at low impact energies, the systematic calculations of the M-shell ionization cross sections for gold were performed using the semiclassical (SCA) and the binary encounter (BEA) approximations in order to identify a role of the electronic wave function and electron binding effects. In these calculations the different wave functions, from nonrelativistic hydrogenic to selfconsistent Dirac-Hartree-Fock, were considered and the binding effect was treated within extreme separated- (SA) and united-atoms (UA) limits. The results are discussed in details and the observed discrepancies are attributed to inadequate description of the electron binding effect at the lowest impact energies for which the molecular approach is required.

M-X-ray production cross sections of heavy elements by charged-particle impact

The M-subshell ionization cross sections of heavy elements by proton and helium-ion impact have been calculated in the binary-encounter approximation. The momentum distribution of target electrons is taken into account by the use of the nonrelativistic and relativistic hydrogenic models and the Hartree–Fock–Roothaan method. The obtained subshell ionization cross sections are converted into the M-X-ray production cross sections and compared with experimental data and other theoretical calculations. The electronic relativistic effect and the wave-function effect on M-shell ionization cross sections are studied and possible reasons for large discrepancy between theory and experiment for Mγ-X-ray production cross section are discussed.

Multiple ionization of Au by fast Sq+ ions of energy 0.4–3.8 MeV/amu

The measurements of the M- and N-shell ionization probabilities in gold bombarded by highly charged Sq+ (q=4–14) ions of energy 0.4–3.8MeV/amu are reported. The ionization probabilities were extracted from the measured L-X-ray spectra which were substantially modified by the multiple ionization effects. The observed L-X-ray line shifts and broadening allowed us (Banaś et al., 2002) to extract both the M- and N-shell ionization probabilities for the zero impact parameter. These ionization probabilities, which correspond to the moment of X-ray emission, were correlated with the ionization probabilities for the moment of ion impact ionization by using the vacancy rearrangement procedure developed here. In this way the ionization probabilities for the moment of ion impact multiple ionization were obtained. By comparing to the theoretical predictions of the semiclassical approximation (SCA) (Trautmann and Kauer, 1989) and the “geometrical model” (GM) (Sulik et al., 1987) based on the binary encounter approximation (BEA), the role of the electronic wave functions and the binding effect is discussed. Generally, the calculations using the hydrogenic wave functions reproduce the measured ionization probabilities.

K-shell X-ray emission from high energy pulsed C6+ ion beam impacting on Ni target

Accurate measurement of the ionization cross section of the target atom induced by collision between ions and atoms is of great significance for studying the atomic shell process and establishing a suitable theoretical model. The experimental data and the theoretical models mostly concentrate on the cases in the low energy region at present. Only a few experimental data of high energy region are reported due to the limitation of experimental conditions. Which theory is more suitable to describe the ionization cross section of the inner shell of the target atom caused by the high energy heavy ions, is necessarily studied experimentally. The C6+ ions provided by the Heavy Ion Research Facility in Lanzhou Electron Cooling Storage Ring, are used to bombard the Ni target, in which the K-shell X-ray of Ni is measured. The incident energies of C6+ ions are 165, 300, 350 and 430 MeV/u respectively. Through analyzing the intensity ratio of K/K X-ray of Ni, it is found that the influence of incident energy on the intensity ratio of K/K X-ray is not obvious. The intensity ratios of this experiment are greater than the experimental values of incident proton and the calculated values based on the Hartree-Slater theory, which may be caused by the multiple-ionization of the L shell. The production cross sections of Ni K-shell X-ray are calculated by the binary encounter approximation (BEA) model, the plane wave Born approximation (PWBA) model and the energy-loss coulomb-repulsion perturbed-stationary-state relativistic (ECPSSR) theory respectively, which are compared with the experimental results in this paper. It is found that the experimental cross section increases with the increasing incident energy, which is consistent with the trend of BEA model estimation, but the experimental value is obviously lower than the theoretical value. We think that BEA model needs to be modified when describing the ionization process in the high energy region.

Study of proton and alpha particle impact double ionization of Fe

Theoretical calculations of H+ and He2+ impact double ionization cross sections for ground state Fe atoms have been performed in the binary encounter approximation(BEA) in the energies region ranging from 80 to 1440 keV/amu for proton impact and from 47 to 360 keV/amu in the case of alpha particle impact. The accurate expression for αδE (cross section for energy transfer ΔE) and Hartree –Fock velocity distributions for the target electrons have been used throughout the calculations. It has been concluded that the calculated results of H+ and He2+ impact double ionization cross sections are in good agreement with the experimental data throughout the given energy range.

Production of projectile and target K-vacancy in near-symmetric collisions of 60–100 MeV Cu9+ ions with thin Zn target**Project supported by the Joint Funds of the National Natural Science Foundation of China (Grant No. U1332122).

We report studies on both target and projectile K-shell ionization by collisions of Cu9+ ions on the thin Zn target in the energy range of 60–100 MeV. In this work, the relative ratio for the production of the target to projectile K-vacancy is measured. The result shows that it almost remains stable over this energy range and has good consistency with the predictions by vacancy transfer via the 2pσ–1sσ rotational coupling, which gives experimental evidence for K-vacancy sharing between two partners. Furthermore, the discussion for comparisons between the experimental ionization cross sections and the possible theoretical estimations is presented. These comparisons suggest that the experimental data agree well with those predicted by the Binary–Encounter approximation (BEA) model but are not in good agreement with the modified BEA calculations. It allows us to infer that the direct ionization (and/or excitation) is of importance to initial K-vacancy production before 2pσ–1sσ transitions in the present collision condition.

X-ray emission from 424-MeV/u C ions impacting on selected target**Project supported by the National Basic Research Program of China (Grant No. 2010CB832902), the National Natural Science Foundation of China (Grant Nos. 11505248, 11375034, U1532263, 11275241, 11205225, 11105192, and 11275238), and the Scientific Research Program of Education Bureau of Shaanxi Province, China (Grant No. 15JK1793).

The K-shell x-rays of Ti, V, Fe, Co, Ni, Cu, and Zn induced by 424-MeV/u C6+ ion impact are measured. It is found that the K x-ray shifts to the high energy side and the intensity ratio of Kβ/Kα is larger than the atomic data, owing to the L-shell multiple-ionization. The x-ray production cross sections are deduced from the experimental counts and compared with the binary encounter approximation (BEA), plane wave approximation (PWBA) and energy-loss Coulomb-repulsion perturbed-stationary-state relativistic (ECPSSR) theoretical predictions. The BEA model with considering the multiple-ionization fluorescence yield is in better consistence with the experimental results. In addition, the cross section as a function of target atomic K-shell binding energy is presented.

Vanadium K-shell X-ray emission induced by xenon ions at near the Bohr velocity

The X-ray emission spectra produced by 2.4-6.0 MeV Xe20+ ions impacting on vanadium surface were measured. The V K-shell X-ray production cross sections were extracted from the experimental yield data and compared with the theoretical predictions of the binary encounter approximation (BEA), the plane wave born approximation (PWBA), and the energy-loss coulomb-repulsion perturbed-stationary-state relativist (ECPSSR). In order to predict reasonably the inner-shell ionization induced by highly charged heavy ions during the asymmetric collisions at near the Bohr velocity, the corrections of BEA model are discussed. It is found that the X-ray production cross section induced by highly charged heavy ions moving at near the Bohr velocity is on the magnitude of 1 barn, which is almost four orders of magnitude larger than that induced by proton. The ECPSSR, which is regarded as the best model to simulate the inner-shell ionization by light ions, may underestimate the experimental data at least three orders of magnitude. The PWBA model presents a prediction to the results on an order of magnitude better than the ECPSSR simulation, but gives a worse tendency than the BEA model. The BEA calculations, corrected both by Coulomb repulsion and effective nuclear charge, present the best agreement with the experimental results. It is proposed, that in the energy region near the Bohr velocity, during the asymmetric collisions of Xe20+ ions with V atoms, the K-shell electron of V is ionized by direct ionization, and that it can be described by the binary encounter process between the xenon ions and the bound electrons. The X-ray production cross section can be simulated by BEA model, but the corrections of Coulomb repulsion and effective nuclear charge must be considered.

Electron impact single and double ionization cross sections of Hg atoms

Theoretical studies of electron impact single and double ionization cross sections of Hg atoms have been performed in the binary encounter approximation. Direct double ionization has been investigated in the modified double binary encounter model. Accurate expression of σ ΔE cross section for energy transfer ΔE and the Hartree–Fock velocity distributions for the target electrons have been used throughout the calculations. The present results of single ionization cross sections are in good agreement with the experimental observations. In the case of double ionization, the theoretical cross sections for direct double ionization show overall satisfactory agreement with the experiment. The calculated single and direct double ionization cross sections substantiate the viewpoint that only the direct processes lead to double ionization of Hg and there is no role of Auger effect concerning the measured data of double ionization.