Distorted-wave Method Research Articles

Electron-impact ionization of Si IV-VIII in hot plasmas

Abstract In this work, we investigate the ionization of silicon by electron impacts in hot plasmas. Our calculations of the cross sections and rates rely on the Coulomb-Born-Exchange, Binary-Encounter-Dipole and Distorted-Wave methods implemented in the Flexible Atomic Code (FAC), and are compared with measurements and other theoretical values. We use a semi-empirical formula for the cross section, which involves a small set of adjustable parameters. The rate coefficient is then expressed in terms of these parameters and is represented in a large temperature interval, up to 108 K. As expected, the agreement with measurements improves for increasing ion charges, confirming the applicability of our approach to hot plasma studies such as inertialconfinement fusion, and its reliability. Configuration interaction is taken into account and is shown to affect the cross section at low energy, in particular for Si3+.

Integration of ML methods with CR model-based optical diagnostic for the estimation of electron temperature in Ga laser produced plasma

Accelerated diagnostic of plasma plays a significant role in controlling and optimizing plasma-mediated processing, particularly for plasma with higher temporal and spatial gradients, such as laser produced plasma (LPP). In the present work, two advanced machine learning (ML) algorithms, random forest regression, and gradient boosting regression are integrated with noninvasive collisional radiative (CR) model-based optical diagnostics to facilitate accurate diagnostics. A comprehensive fine-structure resolved CR model framework is developed by incorporating our consistent cross section data obtained from the Relativistic Distorted Wave method [Suresh et al., “Fully relativistic distorted wave calculations of electron impact excitation of gallium atom: Cross sections relevant for plasma kinetic modelling,” Spectrochim. Acta B: At. Spectrosc. 213, 106860 (2024)]. An extensive dataset of CR model simulated intensities is created to train and test the ML methods. The present CR model is applied to characterize the Gallium LPP coupling with the optical emission spectroscopic measurements of Guo et al. [“Time-resolved spectroscopy analysis of Ga atom in laser induced plasma,” Laser Phys. 19, 1832–1837 (2009)] at different delay times. Further, a detailed correlation study of the line intensity ratios is performed to observe the qualitative behavior of the plasma parameters. The electron temperature results obtained from the CR model, ML, and line ratio methods were compared and found to be in excellent agreement. Overall, the present study demonstrates diagnostic approaches that can benefit the LPP community significantly by providing a rapid understanding of the plasma behavior across various operating conditions.

Measurement of differential collisional excitation cross sections for the Kα emission of He-like oxygen

We measure the energy-differential cross sections for collisional excitation of the soft x-ray electric-dipole Kα (x+y+w) emission from He-like oxygen (O ), using an electron beam ion trap. Values near their excitation thresholds were extracted from the observed emissivity by rapidly cycling the energy of the exciting electron beam. This allows us to subtract time-dependent contributions of the forbidden z-line emission to the multiplet. We develop a time-dependent collisional-radiative model to further demonstrate the method and predict all spectral features. We then compare the extracted x+y+w cross sections with calculations based on distorted-wave and R-matrix methods from the literature and our own predictions using the . All R-matrix results are validated by our measurements of direct and resonant excitation, supporting the use of such state-of-the-art codes for astrophysical and plasma physics diagnostics. Published by the American Physical Society 2024

Study of the electronic structure and electron impact excitation cross section of helium impurities in spherical quantum dots

This manuscript is devoted to explore the atomic structure and electron impact excitation process of atom impurities in quantum dots. To achieve this goal, a method that solves the fully relativistic Dirac equation within the framework of relativistic configuration interaction is proposed. The Gaussian potential is used, which can accurately describe the location of impurities in quantum dots and their local effects on the surrounding electron cloud. The coupled Dirac equation is modified to include a new central potential, providing solutions that include both the continuous and bound state wave functions. The process of electron impact excitation is elucidated using the distorted wave method, all within the framework of relativistic Dirac theory. For illustrative purposes, a detailed investigation of the excitation energies, transition rates, wave functions, and excitation cross sections is carried out for a wide range of confinement strengths of the potential and quantum dot radii, using the helium impurities in spherical quantum dots as an example. Our results reveal that for a given confinement strength of the potential, the bound state wave functions are initially pulled into the inner region by the attractive Gaussian potential well, but eventually reflect the free atom scenario at large quantum dot radii. In contrast, the continuous electron wave functions exhibit monotonic variations as a function of the quantum dot radii. Such behavior of the wave functions gives rise to distinctive phenomena in the variation of excitation energies, transition rates, and excitation cross sections in relation to the potential parameters. Good agreement between the present results and existing data, where available, is obtained. This work holds importance not only for basic research in atomic physics but also for the optical and electronic applications of quantum dots. I.e., in the design and optimization of quantum dot lasers and quantum dot sensors.

Electron-impact double ionization cross sections and rate coefficients for Be-like ions: B+ to Ne6+

We report a detailed analysis of the electron-impact double ionization process for Be-like ions, spanning charge states from B+ to Ne6+. We considered both direct and indirect double ionization processes. For direct double ionization, we calculated the cross sections by considering three different processes: ionization-ionization (II), excitation-ionization-ionization (EII), and ionization-excitation-ionization (IEI). Our results show excellent agreement between the measured cross sections for Be-like-B and Be-like-O ions. The agreement is slightly weaker for Be-like-Ne ions when we take the potential of ionized ions in the distorted-wave method. For other ions for which experimental data are not available, our calculations should provide the missing data. We have summarized the trends of electron-impact double ionization cross sections with atomic number for isoelectronic sequences. Finally, we have provided the Maxwellian and non-Maxwellian rate coefficients for these Be-like ions. The data obtained should be useful for both equilibrium and non-equilibrium charge-state distributions in astrophysical research.

Electron–ion collision and polarization of X-ray fluorescence radiation under hot quantum plasma conditions

In the current article, the spectral properties and electron collision (total and magnetic) excitation cross sections of ions taking placed in quantum plasmas are investigated. These cross sections are further used to study the polarization and angular distribution characteristics of the de-excitation radiation X-ray spectra, which play an important role in basic theoretical research, the diagnosis of the plasma environment, and the design of optical devices. To do so, a distorted wave method within the relativistic Dirac–Coulomb atomic structure scheme is suggested. The effective interaction potential between electrons and particles in hot quantum plasmas in the method is determined using a quantum approach that incorporates the influence of effective plasma screening effects caused by collective plasma oscillations. This potential replaces the traditional Coulomb interaction potential and is used in solving the modified Dirac equation to obtain the bound and continuum electron wave functions. Higher-order relativistic effects, such as the Breit interaction and the dominant quantum electrodynamics corrections, are added to enhance the accuracy of the method. Detailed calculations for the relativistic atomic structure and collision excitation dynamics process are carried out, taking the highly stripped H-like O7+ ion of astrophysical importance as an illustrative example. Detailed investigations are also conducted on the variation of energies, collision cross sections, and fluorescence polarizations as functions of the plasma parameters. Our results suggest that the joint effects of shielding and plasma coupling lead the energies, cross sections and fluorescence polarizations decrease (compared with the isolated case). The angular distribution of the X-ray fluorescence emission shows large change, suggesting their sensitivity to these effects. This study not only offers a valuable approach to investigating the plasma shielding and plasmon coupling effects in quantum plasmas but also holds significant relevance for applications in controlled nuclear fusion, astrophysical plasmas and so on.

Experimental and theoretical total cross sections for single and double ionization of the open-4d-shell ions Xe12+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{12+}$$\\end{document}, Xe13+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{13+}$$\\end{document}, and Xe14+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{14+}$$\\end{document} by electron impact

We present new experimental and theoretical cross sections for electron-impact single ionization of Xe12+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{12+}$$\\end{document} and Xe13+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{13+}$$\\end{document} ions, and double ionization of Xe12+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{12+}$$\\end{document}, Xe13+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{13+}$$\\end{document} and Xe14+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{14+}$$\\end{document} ions for collision energies from the respective ionization thresholds up to 3500 eV. The calculations use the fully relativistic subconfiguration-averaged distorted-wave approach and, partly, the more detailed level-to-level distorted wave method. We find that, unlike in previous work, our theoretical cross sections agree with our experimental ones within the experimental uncertainties, except for the near-threshold double-ionization cross sections. We attribute this remaining discrepancy to the neglect of direct-double ionization in the present theoretical treatment.Graphical abstractExperimental and theoretical cross sections for electron-impact single ionization of Xe12+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{12+}$$\\end{document}.

Cross section sensitivity to perturbation strengths in distorted waves for double electron capture by alpha particles from helium targets

Computer experiments are performed on total cross sections for capture of both electrons from helium targets at 100-10000 keV. Employed are four quantum-mechanical perturbative four-body distorted wave methods (one of the first and three of the second order). The goal is to determine the cross section sensitivity to the perturbation strengths in distorted waves from the second-order methods. The perturbation strength is parametrized by the Sommerfeld factor (the quotient of the nuclear charge and the relative velocity of the colliding particles). At each fixed impact energy, the sought sensitivity is monitored by gradually modifying the nuclear charges in the Sommerfeld factors. These factors reside in the Coulomb distortions of the unperturbed channels states. The focus is on the electronic distortions through the eikonal Coulomb logarithmic phases and the full Coulomb waves. The logarithmic phases are the constituents of the compound phases for the net charges of the two heavy scattering aggregates in relative motions. A striking perturbation strength sensitivity of the obtained total cross sections is recorded.

Theoretical analysis of the electronic structure and electron collision ionization process in a strongly coupled semi-classical plasma environment

In this work, we propose a distorted wave method in the relativistic framework to analyze the electron collision ionization process under the influence of strongly coupled semi-classical plasmas. A pseudopotential is used to represent the screened interactions between the core and outer electron, together with solving the Dirac equation to take care of the relativistic effects. This potential characterizes the plasma in terms of the Debye screening length and the de Broglie wavelength, which takes into account both the quantum mechanical effects of diffraction (short distance) and the collective effects (long distance). With this method, the traditional central-field potential is modified, the bound- and continuum-electron wavefunctions and the collision matrix elements are estimated under a relativistic Dirac–Coulomb framework. The strongly coupled semi-classical plasma effects on the energies, transition rates, and the electron impact ionization cross sections are investigated in detail, using the hydrogen atom as an example. Our results agree well with other available theoretical data. The reported results and the computational scheme are not only of interest to the communities such as atomic and plasma physics, but also have implications for many other areas, including astrophysical objects, inertial confinement fusion plasmas, etc.

Theoretical investigation of electron-impact ionization of W<sup>6+</sup> ion

<sec>Due to its unique characteristics, metal tungsten has been selected as the wall material for the tokamak magnetic confinement fusion device. The wall material directly interacts with the plasma for a long time, thus causing tungsten atoms and ions to be sputtered and ionized into different charge states, which then enter the tokamak device as plasma impurities. To ensure stable plasma combustion conditions, highly complex model is currently being used to evaluate the behavior of tungsten impurities and their influence on the tokamak plasma. This requires various high-precision atomic data for tungsten atoms and different ionized states of tungsten ions. Electron collision ionization, as a fundamental atomic physical process, is widely encountered in laboratory and astrophysical plasma environments. The parameters such as electron collision ionization cross-sections and rate coefficients are crucial for plasma radiation transport simulations and state diagnostics.</sec><sec>Electron-impact single-ionization (EISI) cross sections of the ground state and metastable state for W<sup>6+</sup> ions are calculated by using the level-to-level distorted-wave (LLDW) method. The contributions of direct ionization (DI) cross section and excited autoionization (EA) cross section to the total EISI cross section are primarily considered.</sec><sec>Comparison of our calculation results with the experimental data from Stenke et al. (Stenke M, Aichele K, Harthiramani D, Hofmann G, Steidl M, Volpel R, Salzborn E <ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://iopscience.iop.org/article/10.1088/0953-4075/28/13/021">1995 <i>J. Phys. B: At. Mol. Opt. Phys.</i> <b>28</b> 2711</ext-link>) reveals that the EISI cross section considering only the ground state is significantly smaller than the experimental result. Therefore, it is imperative to take into account the contribution from the metastable state. To determine the fraction of ions in long-lived energy levels within the parent ion beam, three models are employed.</sec><sec>Our results, which include the contribution of metastable states, accord well with the experimental results of Stenke et al. Compared with the theoretical calculation result of Pindzola et al. our calculaiton provides a more comprehensive understanding of the electron-impact single-ionization process for W<sup>6+</sup> ions. The comparison is illustrated in the attached figure.</sec>

Study of Electron Impact Excitation of Na-like Kr Ion for Impurity Seeding Experiment in Large Helical Device

In this work, a krypton gas impurity seeding experiment was conducted in a Large Helical Device. Emission lines from the Na-like Kr ion in the extreme ultraviolet wavelength region, such as 22.00 nm, 17.89 nm, 16.51 nm, 15.99 nm, and 14.08 nm, respective to 2p63p(2P1/2o)−2p63s(2S1/2), 2p63p(2P3/2o)−2p63s(2S1/2), 2p63d(2D3/2)−2p63p(2P3/2o), 2p63d(2D5/2)−2p63p(2P3/2o), and 2p63d(2D3/2)−2p63p(2P1/2o) transitions, are observed. In order to generate a theoretical synthetic spectrum, an extensive calculation concerning the excitation of the Kr25+ ion through electron impact was performed for the development of a suitable plasma model. For this, the relativistic multiconfiguration Dirac–Hartree–Fock method was employed along with its extension to the relativistic configuration interaction method to compute the relativistic bound-state wave functions and excitation energies of the fine structure levels using the General Relativistic Atomic Structure Package-2018. In addition, another set of calculations was carried out utilizing the relativistic many-body perturbation theory and relativistic configuration interaction methods integrated within the Flexible Atomic Code. To investigate the reliability of our findings, the results of excitation energies, transition probabilities, and weighted oscillator strengths of different dipole-allowed transitions obtained from these different methods are presented and compared with the available data. Further, the detailed electron impact excitation cross-sections and their respective rate coefficients are obtained for various fine structure resolved transitions using the fully relativistic distorted wave method. Rate coefficients, calculated using the Flexible Atomic Code for population and de-population kinetic processes, are integrated into the collisional-radiative plasma model to generate a theoretical spectrum. Further, the emission lines observed from the Kr25+ ion in the impurity seeding experiment were compared with the present plasma model spectrum, demonstrating a noteworthy overall agreement between the measurement and the theoretical synthetic spectrum.

Electron-impact Excitation of Pt i–iii: The Importance of Metastables and Collision Processes in Neutron Star Merger and Laboratory Plasmas

The detection of a gravitational-wave signal and subsequent electromagnetic transient from a neutron star merger in 2017 is consistent with expectations of neutron star mergers as an r-process element production site. Within the first few days post-merger, the kilonova spectra are consistent with a blackbody illuminating a mix of heavy, r-process elements. With increasing time, the kilonova transitions to the non-LTE regime where the level populations and ionization balance are determined by both collisional and photoprocesses. Detailed cross section data for electron-impact processes involving the relevant species are often not available. In such circumstances, it is reasonable to use approximate methods as baseline data for use in spectral modeling, and it is useful to evaluate the accuracy of such methods against more sophisticated collision calculations when possible. We describe new calculations of the electron-impact excitation cross sections of Pt i–iIi using the DARC R-matrix codes. Using collisional-radiative models, we show that, at plasma conditions expected in kilonovae, the expressions of van Regemorter and Axelrod are insufficient for producing electron-impact excitation data for complex, heavy species such as the low charge states of Pt. Through comparisons with data generated with the relativistic distorted wave approach, as implemented in the Flexible Atomic Code, we show the distorted wave method produces cross section data that, when incorporated into spectral models, predicts strong spectral feature distributions similar in intensity to those from models built on data computed with the R-matrix approach for the considered ions and plasma conditions.

Maxwellian and non-Maxwellian rate coefficients of the tungsten ions: W46+–W55+

This study focuses on the significance of suprathermal (‘hot’) electrons in the tokamak device. Hot electrons, which follow a non-Maxwellian energy distribution, are high-energy electrons that exert a substantial influence on various processes taking place within the plasma. Our aim was to investigate the influence of non-Maxwellian distribution on the rate coefficients of highly charged tungsten ions. This paper presents Maxwellian and non-Maxwellian electron impact ionization rate coefficients for W46+ to W55+ ions. The cross sections were calculated using the fully relativistic flexible atomic code with level-to-level distorted-wave method. We found that even for a small fraction of hot electrons, the contribution of hot electrons to the rate coefficients is still dominant at low bulk temperature.

Modeling the Mg I from the NUV to MIR

Context. Reliable atomic data are mandatory ingredients to obtain a realistic semiempirical model of any stellar atmosphere. Due to their importance, we further improved our recently published Mg I atomic model. Aims. We tested the new atomic model using atmospheric models of stars of different spectral types: the Sun (dG2), HD 22049 (dK2, Epsilon Eridani), GJ 832 (dM2), and GJ 581 (dM3). Methods. Significant improvements have been included in the atomic model, mainly to the electron impact excitation (ϒij) values. We used new Breit-Pauli distorted-wave (DW) multiconfiguration calculations, which proved to be relevant for many transitions in the mid-infrared (MIR) range. The new atomic model of Mg I includes the following: (i) recomputed (ϒij) data through the DW method, including the superlevels. (ii) For the nonlocal thermodynamic equilibrium (NLTE) population calculations, 5676 theoretical transitions were added (3001 term-to-term). (iii) All of these improvements were studied in the Sun and the stars listed above. Comparisons for the distribution of magnesium among the first ionization states and the formation of molecules, as well as for the population of the different energy levels and atmospheric heights, were carried out. Several lines, representative of the spectral ranges, were selected to analyze the changes that were produced. In particular, we exemplify these results with the problematic line 2853.0 Å, a transition between the third level and the ground state. Results. The magnesium distribution between ionization states for stars with different effective temperatures was compared. For the Sun and Epsilon Eridani, Mg II predominates with more than 95%, while for GJ 832 and GJ 581, Mg I represents more than 72% of the population. Moreover, in the latter stars, the amount of magnesium forming molecules in their atmosphere is at least two orders of magnitude higher. Regarding the NLTE population, a noticeable lower variability in the departure coefficients was found, indicating a better population coupling for the new model. Comparing the synthetic spectrum calculated with the older and new Mg I atomic model, these results show minimal differences in the visible range but they are stronger in the infrared (IR) for all of the stars. This aspect should be considered when using lines from this region as indicators. Nevertheless, some changes in the spectral type were found, also emphasizing the need to test the atomic models in different atmospheric conditions. The most noticeable changes occurred in the far-ultraviolet (FUV) and near-ultraviolet (NUV), obtaining a higher flux for the new atomic model regardless of the spectral type. The new model did not prevent the formation of the core emission in the synthetic NUV line 2853.0 Å. However, by including other observations, we could note that the emission indeed exists, although with a much lower intensity. Further tests have shown that to reduce the emission, the population of its upper level (3s3p 1P) should be reduced by a factor of about 100.

Theoretical study of (e,2e) triple differential cross section of 1b3g orbital of ethylene by vibrational multi-center distorted-wave method

The vibrational motions are usually neglected when calculating (e,2e) triple differential cross sections (TDCSs) of molecules. Here, multi-center distorted-wave method (MCDW) has been modified by including molecular vibrations. This vibrational MCDW method is employed to calculate the TDCSs of 1b3g orbital of ethylene at low (100 eV) and medium (250 eV) incident electron energies in coplanar asymmetric kinematic condition. The results show that molecular vibrations significantly influence the angular distributions of the TDCSs, especially in the binary region along momentum transfer near the Bethe ridge.

Influence of plasma fluctuation on the electronic structures and electron collisional excitation and ionization processes

Studies demonstrated significant discrepancies between the experimental observations of Stillman et al. [Phys. Rev. E 95, 063,204 (2017)] and almost all recent state-of-the art theoretical predictions for the He-α (1s2p→1s2) line shift of Al11+ ions placed in a hot dense plasma environment. Here, we suggest a new distorted wave method to determine the electronic structure and collision dynamics of highly stripped ions placed in plasmas. The method incorporating the plasma fluctuation, which yields modification term to the calculation of the central-field potential, is applied to the above problem. By adjusting the parameter q, which characterizes the intensity of the plasma fluctuation, we reproduce the experimental line shifts well over the whole range (of temperature and density) measured. In addition, we perform a calculation by incorporating the screened potential of Stanton and Murillo [Phys. Rev. E 91, 033,104 (2015)] and the current results (from ab-initio calculations) are in much better agreement with the experimental data than most previous theoretical results. Finally, we perform the calculation of electron collisional excitation and ionisation dynamic processes, where the continuous electron wave function is obtained by numerically solving the modified coupled Dirac equation. A careful investigation of the effect of plasma fluctuation on the integrated cross sections is made. The present work not only leads to further stimulation of the development of shielding models in extreme conditions, but also has important applications in laboratory and space plasmas.

Electron impact ionization cross sections of highly charged open L-shell tungsten ions

L-shell electron-impact ionization (EII) cross sections for highly charged tungsten ions were measured at incident electron energies of 29.10 and 38.92 keV using the Shanghai-EBIT. Resolved x-rays from radiative recombination (RR) processes were recorded with a high-purity Ge detector in a static electron energy scanning mode. Absolute EII cross sections were obtained by normalizing to the theoretical RR cross sections. The experimental results were compared with the calculated results using the relativistic distorted-wave method implemented in the flexible atomic code and the relativistic Lotz semi-empirical equation. The measurements showed general agreement with the calculated results by two theoretical methods for Li- to N-like W ions. The experimental uncertainties are not sufficiently small to discern the two theoretical results. Furthermore, the influence of Breit interaction on the EII cross sections of open L-shell tungsten ions was studied, and the effect is small but non-negligible. The measured EII cross sections of open L-shell tungsten ions would contribute to fusion plasma studies.

Electron impact elastic scattering by a calcium atom using the first order distorted wave method with a complex potential

Electron-atom scattering data is required in diverse fields of physics. In particular, inelastic collision cross sections data are needed in photonics and radiation physics. Elastic collision data, on the other hand, are useful in material science for surface analysis. There is a lack of accuracy and completeness of atomic data obtained using theoretical methods relative to experimental techniques. Furthermore, the distorted wave Born approximation method with a complex potential is yet to be applied in calculating cross sections. Differential and total cross sections have been calculated for electron-calcium scattering in the impact energy range 10 – 100 eV. There is good shape resonance between the present results with a complex potential and experimental values as well as other theoretical results

Electron-impact ionization of the tantalum atom

Electron-impact ionization cross sections for the ground configuration of the tantalum (Ta) atom are calculated using a combination of non-perturbative time-dependent close-coupling and perturbative distorted-wave methods. Direct ionization of the 6s and 5d subshells leading to single ionization are presented. The inclusion of a polarization potential in the 6s direct ionization leads to a small reduction in the cross section. Angular factors are included that allow the configuration-average direct ionization cross sections to be split into LS term resolution. The magnitude of the ionization cross section suggests that the ionization mean free path for neutral Ta will be similar to that for tungsten (W) plasma facing components in fusion experiments, leading to similarly large fractions of prompt redeposition.

Electron-impact ionization of W9+ and W10+

Electron-impact single-ionization (EISI) cross sections for W q+ (q = 9, 10) ions have been calculated by using the level-to-level distorted-wave (LLDW) method with emphasis on the contribution of metastable states to the total ionization cross sections. Contributions from direct-ionization (DI) and excitation-autoionization (EA) processes are taken into account. The calculated cross sections include the contributions from both the ground configuration and the long-lived metastable states with lifetimes exceeding 10−6 s. Calculated cross sections are in good agreement with experimental measurements when the influence of metastable states on the total ionization cross section are well considered.