Electron-impact Excitation Cross Sections Research Articles

Cross sections for valence-shell excitations of H2O in the 9.85–12.15-eV energy-loss range studied by high-energy inelastic electron scattering

The recent measurement of the generalized oscillator strengths (GOSs) for $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{A}\phantom{\rule{0.28em}{0ex}}^{1}B_{1}$ and $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{B}\phantom{\rule{0.28em}{0ex}}^{1}A_{1}$ of ${\mathrm{H}}_{2}\mathrm{O}$ exhibits the apparent deviations from the first Born approximation calculations in the large squared momentum transfer region [W. Q. Xu et al., Phys. Rev. A 103, 032808 (2021)]. Here a simplified theoretical model was proposed to calculate the GOSs of the two excitations at large momentum transfer within the second Born approximation. The accord of the experimental GOSs and the theoretical ones is improved, but the differences still exist. In addition, the GOSs and the integral cross sections for the higher excitations of ${\mathrm{H}}_{2}\mathrm{O}$ in 9.85--12.15 eV are presented, which could be used to complete the database of electron-impact excitation cross sections of ${\mathrm{H}}_{2}\mathrm{O}$ and be beneficial for modeling interaction processes between electrons and ${\mathrm{H}}_{2}\mathrm{O}$ in the earth's atmosphere, plasmas, radiation physics, biology, etc.

Calculations of electron-impact excitation and dielectronic recombination rate coefficients of highly charged silicon ions

The rate coefficients for dielectronic recombination and electron-impact excitation processes with H-like to Be-like silicon ions (${\mathrm{Si}}^{13+}\text{\ensuremath{-}}{\mathrm{Si}}^{10+}$) are calculated using relativistic distorted-wave approach. The prominent $▵n=1$ and the weaker $▵n=2$ and 3 dielectronic recombination (DR) resonances with $K$-shell excitations are presented, and compared with the existing DR experimental rate coefficients of ${\mathrm{Si}}^{13+}, {\mathrm{Si}}^{12+}$, and ${\mathrm{Si}}^{11+}$ ions, it is found that the theoretical DR rate coefficients are in very good agreement with the experimental results. With the same approach, the direct and resonant electron-impact excitation (EIE) cross sections associated with $1s\ensuremath{-}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}$ core excitations are calculated for the ground states of ${\mathrm{Si}}^{13+}\text{\ensuremath{-}}{\mathrm{Si}}^{10+}$ ions and found in excellent agreement with the available experiment. Finally, we present the synthesized DR and EIE rate coefficients for the sum of all detected $(13+\ensuremath{\sim}10+)$ charge states of Si and these agree well with the experimental results.

Development of various methods to the investigation of the spectral properties and collision dynamics of H‐like ions taking place in dense and hot plasma environments

AbstractThe correct understanding of the behavior of highly stripped ions immersed in a dense plasma environment is a hitherto challenge for theory and it is of importance in various applications. Here, we developed four kinds of novel theoretical models to the determination of the spectral properties and collision dynamics of H‐like ions in dense and hot plasmas by employing the analytical potential [Li et al., Phys. Plasmas 2019, 26, 033301] to describe the interactions among the charged particles: (i) The electron photon processes in plasma model within the relativistic scheme; (ii) The multiconfiguration Dirac–Fock model within the framework of relativistic self‐consistent iteration approximation; (iii) The generalized pseudospectral method within the relativistic framework; and (iv) An analytic formula based on the Hartree–Fock method and the irreducible tensor theory within the non‐relativistic regime, derived from a solution of Schrödinger equation. As a typical example, energy eigenvalues, radiative transition properties, spectral line shifts, and electron impact excitation and ionization cross sections of the selected N6+ and Ne9+ ions are determined for several temperature‐density cases, characteristic of inertial confinement fusion plasmas. A comparison of these results with each other and the results from earlier calculations as well as with the available experimental data is provided. Systematic trend is determined for all the properties under study concerning increased screening. The present study not only extends our understanding of the dense plasma shielding effects, but also opens the way for future investigations allowing accurate predictions of spectral properties of ions in dense and hot plasmas aimed at providing precision data for various practical applications.

Debye-screening effect on electron-impact excitation of helium-like Al11+ and Fe24+ ions

Debye-screening effects on the electron-impact excitation (EIE) processes for the dipole-allowed transition 1s2 1 S → 1s2p 1P in He-like Al11+ and Fe24+ ions are investigated using the fully relativistic distorted-wave methods with the Debye–Hückel (DH) model potential. Debye-screening effects on the continuum-bound (CB) interaction and target ion are discussed, both of which result in reduction of EIE cross sections. This reduction due to screening on the CB interaction is dominant. The non-spherical and spherical DH potentials are adopted for considering the screening effect on the CB interaction. It is found that the spherical DH potential could significantly overestimate the influence of plasma screening on EIE cross sections for multielectron He-like ions.

High-resolution Laboratory Measurements of K-shell X-Ray Line Polarization and Excitation Cross Sections in Helium-like S XV Ions

Abstract We report measurements of electron-impact excitation cross sections for the strong K-shell n = 2 → 1 transitions in S xv, using the LLNL EBIT-I electron beam ion trap, two crystal spectrometers, and the EBIT Calorimeter Spectrometer. The cross sections are determined by direct normalization to the well-known cross sections of radiative electron capture, measured simultaneously. Using contemporaneous polarization measurements with the two crystal spectrometers, whose dispersion planes are oriented parallel and perpendicular to the electron beam direction, the polarization of the direct excitation line emission is determined, and in turn the isotropic total cross sections are extracted. We further experimentally investigate various line-formation mechanisms, finding that radiative cascades and collisional inner-shell ionization dominate the degree of linear polarization and total line-emission cross sections of the forbidden line, z.

Effect of plasma screening on electron impact excitation and ionization of Fe16+ in a dense environment

ABSTRACT Electron impact excitation and ionization with atoms and ions within a dense plasma are fundamental microscopic processes that determine the ionization balance, physical properties (such as electron conductive opacity and thermal conductivity) and plasma formation and dynamics. While collision cross-sections and rates are well studied in dilute systems, similar investigations are scarce for dense plasmas under stellar interior conditions using an appropriate plasma-screening potential. Here we investigate the plasma-screening effect on the electron impact excitation and ionization cross-sections, effective collision strengths, and rate coefficients within plasmas under stellar interior conditions in a mass density range of 1–15.748 g cm−3 and a temperature range of 200–1000 eV. These investigations were carried out using our recently developed plasma-screening model, taking Fe16+ as an example. The results show that the cross-sections of the electron impact excitation are generally decreased, whereas they are always significantly increased for the collision ionization due to the plasma screening. In a plasma at a temperature of 200 eV and density of 15.748 g cm−3, the plasma screening causes a decrease in the excitation cross-section of 36 per cent for the dipole-allowed transition $2\mathrm{ s}^22\mathrm{ p}^6~^1\mathrm{ S}_0 \rightarrow 2\mathrm{ s}^22\mathrm{ p}^53\mathrm{ d}~^1\mathrm{ P}^o_1$ and of 50 per cent for the dipole-forbidden transition $2\mathrm{ s}^22\mathrm{ p}^6~^1\mathrm{ S}_0 \rightarrow 2\mathrm{ s}^22\mathrm{ p}^53\mathrm{ d}~^3\mathrm{ D}^o_1$. However, the collision ionization cross-section of a 2p electron from the ground level of Fe16+ is increased by 500 per cent and 100 per cent under an incident electron energy of 1500 and 10 000 eV, respectively. This results in the rate coefficient increasing by a factor of 18.5 at a temperature of 200 eV and density of 15.748 g cm−3.

Diagnostics of laser-produced Mg plasma through a detailed collisional radiative model with reliable electron impact fine structure excitation cross-sections and self-absorption intensity correction

A detailed fine-structure resolved collisional radiative model is developed to investigate the laser-produced Mg plasma. The dominant processes linked with the electron impact excitation and de-excitation have been considered explicitly in a very reliable and consistent manner in the present model. The required electron impact excitation cross-sections of Mg for the large number of transitions from the ground state 3s2 (J = 0) to the 3s3p, 3s4s, 3s3d, 3s4p, 3s5s, 3s4d, 3s5p, 3s6s, 3s5d, and 3s6p excited states and from 3s3p manifolds to the other fine-structure levels of 3s4s, 3s3d, 3s5s, 3s4d, 3s6s, and 3s5d configurations are obtained using the fully relativistic distorted wave approach. To ensure the accuracy of our calculations, where available, the oscillator strengths and cross-sections are compared with previous measurements and other calculations. Further, plasma diagnostics are carried out by coupling the present collisional radiative model with the laser-induced breakdown spectroscopy measurements reported by Delserieys et al (2009 J. Appl. Phys., 106, 083304). Five measured intense emission lines of Mg viz 383.3, 470.3, 517.8, 552.8, and 571.1 nm are used and corrected through the self-absorption to extract the plasma parameters i.e. electron temperature and electron density. The obtained plasma parameters at different delay times ranging from 100–700 ns are compared with the results of Delserieys et al (2009 J. Appl. Phys., 106, 083304) that were estimated using the Thomson scattering and Boltzmann plot approaches.

Electron-impact rotational excitation cross-sections and rate coefficients of molecular ion: HCO+

ABSTRACT HCO+ is one of the most abundant polyatomic ion in the Universe, also its presence in the planetary atmospheres and interstellar medium (ISM) makes it an interesting case to study. Low energy e−-HCO+ collisions result in rotational excitation and other molecular processes. In this study, the cross-sections for rotational transitions in HCO+ are evaluated for four rotational levels (j = 0, 1, 2, and 3) using the UK R-matrix method and the multichannel quantum defect theory (MQDT). The UK R-matrix method used to generate scattering matrices, through which cross-sections are computed. In past two decades, after developments and implementations of different theoretical approaches, the improved channel elimination procedure applied here is more promising to evaluate more accurate results near rotational thresholds important for the analysis of intensities of microwave region in plasma modelling. The rate coefficients are deduced from the computed cross-sections and studied over a wide electron temperature range.

Simple electron-impact excitation cross-sections including plasma density effects

The modeling of non-local-thermodynamic-equilibrium plasmas is crucial for many aspects of high-energy-density physics. It often requires collisional–radiative models coupled with radiative-hydrodynamics simulations. Therefore, there is a strong need for fast and as accurate as possible calculations of the cross-sections and rates of the different collisional and radiative processes. We present an analytical approach for the computation of the electron-impact excitation (EIE) cross-sections in the Plane Wave Born (PWB) approximation. The formalism relies on the screened hydrogenic model. The EIE cross-section is expressed in terms of integrals, involving spherical Bessel functions, which can be calculated analytically. In order to remedy the fact that the PWB approximation is not correct at low energy (near threshold), we consider different correcting factors (Elwert–Sommerfeld, Cowan–Robb, Kilcrease–Brookes). We also investigate the role of plasma density effects such as Coulomb screening and quantum degeneracy on the EIE rate. This requires to integrate the collision strength multiplied by the Fermi–Dirac distribution and the Pauli blocking factor. We show that, using an analytical fit often used in collisional–radiative models, the EIE rate can be calculated accurately without any numerical integration, and compare our expression with a correction factor presented in a recent work.

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: II. Fully vibrationally-resolved electronic excitation of the isotopologues of H2 ([formula omitted

We present a comprehensive set of vibrationally-resolved cross sections for electron-impact electronic excitation of the isotopologues of molecular hydrogen (D2, T2, HD, HT, and DT) initially in the ground electronic state. We apply the adiabatic-nuclei molecular convergent close-coupling (MCCC) method to calculate cross sections from threshold to 500 eV for excitation of all bound vibrational levels and dissociative excitation of the B1Σu+, C1Πu, EF1Σg+, B′1Σu+, GK1Σg+, I1Πg, J1Δg, D1Πu, H1Σg+, b3Σu+, c3Πu, a3Σg+, e3Σu+, d3Πu, h3Σg+, g3Σg+, i3Πg, and j3Δg electronic states from all bound vibrational levels of the ground electronic (X1Σg+) state. Including the previously-published MCCC e-H2 cross sections (Scarlett et al., Atom. Data Nucl. Data Tables 137 (2021) 101361) the data set contains cross sections for over 60,000 electronic and vibrational transitions. The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files. The data can also be downloaded from the MCCC database at mccc-db.org.

Application of molecular convergent close-coupling cross sections in a collisional radiative model for the triplet system of molecular hydrogen

Collisional radiative (CR) models for molecular hydrogen are of high relevance for performing qualitative and quantitative analysis of excited-state population densities measured in plasmas or predicting the dependence of plasma emission on parameter variations. Although the development of such models for H2 started decades ago, major uncertainties still exist regarding the most important set of input parameters, namely the cross sections for electron-impact excitation. The deviations between cross sections from different datasets are particularly pronounced in the energy region close to the threshold energy, strongly increasing the uncertainty of CR models applied to low-temperature plasmas. This paper presents experimental validation of a set of newly calculated non ro-vibrationally resolved electron-impact cross sections calculated for the triplet system of H2 using the molecular convergent close-coupling method in the adiabatic-nuclei formulation. These cross sections are implemented into a CR model based on the flexible solver Yacora. A first comparison of CR calculations with the different datasets to experimentally-determined population densities is performed at a planar ICP discharge for varying pressure (between 1 and 10 Pa) and RF power (between 700 and 1100 W). For the experimentally-accessible electron temperature and density range (2.5–10 eV and 1.8–3.3 × 1016 m−3, respectively), very good agreement between the model and experiment is obtained using the new data set, in contrast to previously used cross sections.

Excitation and ionisation cross-sections in condensed-phase biomaterials by electrons down to very low energy: application to liquid water and genetic building blocks.

Electronic excitations and ionisations produced by electron impact are key processes in the radiation-induced damage mechanisms in materials of biological relevance, underlying important medical and technological applications, including radiotherapy, radiation protection in manned space missions and nanodevice fabrication techniques. However, experimentally measuring all the necessary electronic interaction cross-sections for every relevant material is an arduous task, so it is necessary having predictive models, sufficiently accurate yet easily implementable. In this work we present a model, based on the dielectric formalism, to provide reliable ionisation and excitation cross-sections for electron-impact on complex biomolecular media, considering their condensed-phase nature. We account for the indistinguishability and exchange between the primary beam and excited electrons, for the molecular electronic structure effects in the electron binding, as well as for low-energy corrections to the first Born approximation. The resulting approach yields total ionisation cross-sections, energy distributions of secondary electrons, and total electronic excitation cross-sections for condensed-phase biomaterials, once the electronic excitation spectrum is known, either from experiments or from a predictive model. The results of this methodology are compared with the available experimental data in water and DNA/RNA molecular building blocks, showing a very good agreement and a great predictive power in a wide range of electron incident energies, from the large values characteristic of electron beams down to excitation threshold. The proposed model constitutes a very useful procedure for computing the electronic interaction cross-sections for arbitrary biological materials in a wide range of electron incident energies.

A revised comprehensive approach for determining the H2 and D2 rovibrational population from the Fulcher-α emission in low temperature plasmas

The emission of the Fulcher- transition is well-known for providing access to the rovibrational population of the hydrogen molecule in low temperature plasmas by means of optical emission spectroscopy. A revised comprehensive approach is developed for the evaluation that omits several simplifying assumptions, which are often made. The rovibrational distribution is directly calculated in the state considering the typically observed hockey-stick population. The projection into the d 3Π u state is performed via vibrationally resolved electron impact excitation cross sections and radiative decay into the is considered via vibrationally resolved transition probabilities. The obtained steady-state population is fitted to the experimentally measured one via varying the population parameters in the electronic ground state. The impact of this evaluation routine compared to the simplified ones is demonstrated both for H2 and D2 at two experiments: a standard CW low-power laboratory ICP and the pulsed high-power negative ion source plasma of the Linac4 accelerator at CERN. This assessment demonstrates that especially the simplification of measuring only the first five rotational emission lines (i.e. neglecting the rotational hockey-stick distribution) can affect the evaluation results significantly. In the application example, this leads to an overestimation of the gas temperature up to a factor of nine and to an underestimation of the determined intensity of the full Fulcher-α transition (required for applying collisional radiative models) up to a factor of three.

Electron-impact excitation cross sections for Ar and Ar[formula omitted] by unitarized distorted-wave approximation

Unitarization for a relativistic distorted-wave approximation has been made by using two types of scattering matrix for reactance matrix and the electron-impact excitation cross sections for Ar and Ar+ are calculated by the unitarized relativistic distorted-wave method. The unitarization by using the scattering matrix obtained from diagonalization of the reactance matrix significantly reduces the cross sections rather than by using the scattering matrix given from inversion of matrix related to the reactance matrix which brings out better agreement with other more sophisticated R-matrix prediction and experiments at intermediate electron energies for Ar. The cross sections for Ar+ by the effective unitarization are smaller than those by available other prediction using perturbative relativistic distorted-wave approach.

Resonance scattering of positronium atoms by nitrogen molecules

We study theoretically the resonance scattering of positronium (Ps) atoms by nitrogen molecules and compare it with resonance e–N2 scattering in the Πg symmetry. The velocity positions of the Ps–N2 resonances in Σu, Πu, and Δg symmetries are very close to the velocity position of the e–N2 resonance which leads to the total Ps–N2 cross section being very similar to the e–N2 cross section when both are plotted as functions of the projectile velocity. However, in the Ps–N2 case the resonances are much wider and their positions vary much slower with increasing internuclear separation than in the e–N2 case. This makes the Ps-impact vibrational excitation cross section much smaller than the electron-impact vibrational excitation cross section, and no boomerang oscillations are observed in Ps–N2 scattering. We analyze the role of the static potential in the e–N2 case and compare exchange potentials for e–N2 and Ps–N2 interactions. This analysis allows us to explain the difference in the vibrational dynamics in these two cases.

Electron-impact excitation of the ( 5s25p ) P1/22→(5s26s ) S1/22 transition in indium: Theory and experiment

We present angle-integrated and angle-differential cross sections for electron-impact excitation of the (5s25p)P1/22→(5s26s)S1/22 transition in atomic indium. Experimental data for six incident electron energies between 10 and 100 eV are compared with predictions from semirelativistic and fully relativistic B-spline R-matrix calculations, as well as a fully relativistic convergent close-coupling model. Agreement between our measured and calculated data is, with a few exceptions, found to be typically very good. Additionally, the agreement between the present theoretical predictions is generally excellent, with the remaining small deviations being associated with the slightly different, although still very accurate, descriptions of the target structure. Agreement between the present results and an earlier relativistic distorted-wave computation [T. Das, R. Srivastava, and A. D. Stauffer, Phys. Lett. A 375, 568 (2011)PYLAAG0375-960110.1016/j.physleta.2010.12.037] was, however, found to be marginal, particularly at 10 and 20 eV.

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: I. Fully vibrationally-resolved electronic excitation of H[formula omitted

We present a comprehensive set of vibrationally-resolved cross sections for electron-impact electronic excitation of molecular hydrogen suitable for implementation in collisional-radiative models. The adiabatic-nuclei molecular convergent close-coupling method is used to calculate cross sections for excitation of all bound vibrational levels and dissociative excitation of the B1Σu+, C1Πu, EF1Σg+, B′1Σu+, GK1Σg+, I1Πg, J1Δg, D1Πu, H1Σg+, b3Σu+, c3Πu, a3Σg+, e3Σu+, d3Πu, h3Σg+, g3Σg+, i3Πg, and j3Δg electronic states from all vi=0–14 bound vibrational levels of the ground electronic (X1Σg+) state. The data set consists of cross sections from threshold to 500 eV for over 5000 transitions, representing all possible electronic and vibrational transitions between the X1Σg+ state and the n=2–3 singlet and triplet states (where n refers to the united-atoms-limit principle quantum number). The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files. The data can also be downloaded from the MCCC database at http://mccc-db.org.

Detailed electron impact fine-structure excitation cross-sections of Kr+ and linear polarization of its subsequently emitted photons

An extensive calculation for electron impact excitation cross-sections of Kr+ ion is performed using relativistic distorted wave theory. The transitions considered are from the ground state i.e. 4s24p5 (J=3/2) to the 4s24p5 (J = 1/2), 4s4p6 (J=1/2) levels and fine structure levels of 4s24p45s, 4s24p45p, 4s24p46s, 4s24p46p, 4s24p44d and 4s24p45d excited states. The transition matrix is evaluated using the relativistic multi-configuration Dirac-Fock bound state wave functions of the initial and final states of Kr+ ion obtained from the GRASP2K program. The 4s24p5, 4s4p6, 4s24p45s, 4s24p45p, 4s24p46s, 4s24p46p, 4s24p44d and 4s24p45d configuration state functions are used to calculate the required wave functions. The incident and scattered projectile electron continuum wave functions are calculated numerically by solving the Dirac equations using static potential of the target ion. Oscillator strengths and transition probabilities are calculated and reported for the dipole allowed transitions, making these available to check the accuracy of the bound state wave functions for future comparison purposes. The detailed excitation cross-sections and their corresponding excitation rate coefficients are reported for considered 116 fine-structure excitation transitions from the ground state 4s24p5 (J=3/2). Further, analytic fittings of the obtained cross-sections with respect to incident electron energy are also performed for all the transitions considered in the present work so that these can be directly used in any plasma model for diagnostics purposes. In addition, using the obtained magnetic sub-level cross-sections, the degree of linear polarization of the photon emissions from the decay of electron impact excited anisotropic states of Kr+ ion through the dipole allowed transitions is calculated and reported.

Electron Impact Excitation of 4p5 5p Levels of Krypton Atom from Metastable States

Data on electron impact excitation cross sections of the 4p55p levels of krypton from metastable states 4p55s3P0,2 have been obtained. They reflect the aggregate result of the available data on the specified process including the results of our own measurements.

Electron-impact excitation of ions within a quantum plasma

We develop a new relativistic model which can describe the dynamics on electron-impact excitation (EIE) of ions within a quantum plasma environment. An exemplary excitation 1s1/2 → 2p3/2 of Fe XXVI by electron impact with the exponential cosine-screened Coulomb potential (ECSCP) is presented, i.e., 25 times ionized atoms of Fe, exist in laser-produced plasmas, astrophysical objects, and electron beam ion trap experiments. For the atomic structure of target ion, using the same potential, a Ritz variational method with a trial wave function that contains unknown variational parameters is also proposed for comparison purposes. In this method, an analytical formula of bound energy is derived from the energy equation, and the variational parameters are determined by the minimization of the energy. The energies obtained from our two methods are compared with each other and other theoretical predictions based on the non-relativistic model and found to be in good agreement. For the collision dynamics, the continuum wave function is determined by solving the modified Dirac equations, in which the ECSCP is included for the solution of the continuum orbital. The total cross sections, magnetic sublevel cross sections, and the degrees of linear polarization of emitted x-rays are calculated as a function of the incident energy and screening parameter by using the distorted-wave method in the relativistic frame. Since there are no experiments or other calculations for EIE cross sections on this ion, the obtained results have been compared with those for an isolated ion. The effect of quantum plasma leads to a reduction in the total and magnetic sublevel cross-sections and thus reduces the degrees of linear polarization of emitted x-rays. Comparative analysis allows to estimate the quality of the proposed approximations. Our dynamic model is practicable and easy to apply, which may provide an alternative route towards information with fluorescence polarization in a quantum plasma environment.