Projectile Electron Research Articles

Scale transformations in model exchange potentials in low energy electron-atom scattering

Model exchange potentials are particularly interesting to account for the indistinguishability between the projectile and target electrons in electron-atom scattering in vacuo and plasma environments. It is well known that their performance is pretty satisfactory in the high energies but also that discrepancies from the results obtained with exact exchange are found toward the zero energy limit. In this article, we examine how well established model exchange potentials based on the free electron gas approach compare to phase shifts calculated considering exchange in exact form. In particular, we show that the Hara and the semiclassical exchange potentials are able to reproduce reference low energy phase shifts through a simple scale transformation, in opposition to the previous approaches where energy dependent corrections to the local momentum were adopted. We provide the scale factors and phase shifts for electron scattering by He, Ne and Ar atoms for k< 1,0 a0−1. Such scaling factors can be determined reproducing the scattering length and the number of s-wave bound states from exact exchange calculations. We also show that the scaling procedure works for electronic densities that present the physically correct asymptotic behavior. The present results are important to the research field, since they form the basis to construction of scattering models based on optical potential approaches.

Virtual photon exchange vs electron transfer in interparticle Coulombic electron capture.

We have investigated Interparticle Coulombic Electron Capture (ICEC) using an abinitio approach for two systems, H+ + H2O and H + H2O+. In this work, we have determined the contribution of virtual photon exchange and electron transfer to the total ICEC cross section as a function of the distance between the charged and neutral particles. Furthermore, we have shown that the relative orientation of the electron acceptor and neighbor systems affects the magnitude of the ICEC cross sections by at least two orders at relatively small distances. This geometry dependence, present even for distances as large as 10 a0, is due to the electron transfer contribution. The relative magnitude of each contribution to ICEC seems to depend on the system studied. By replacing the projectile electron with a positron, we have confirmed that electron transfer also takes place in positron collisions and that the charge of the projectile has a noticeable effect on the process, particularly at low scattering energies.

Differential Cross Section With Volkov-Thermal Wave Function in Coulomb Potential

Laser-assisted thermal electron-hydrogen atom elastic scattering was studied in the first-born approximation. The initial and final states of the projectile electron are described by the modified Volkov wavefunctions known as Volkov-Thermal wavefunctions. The laser-assisted thermal electron with energy ranges from 0.511 MeV to 4 MeV was considered to study the differential cross section (DCS) at azimuthal angles 30° and 14.7°, and laser-assisted field photon energy 1 eV to 3 eV are very weak at room temperature is around the room temperature 280 K to 300 K. The destructive interference was observed when a thermal electron absorbed a single photon from the laser field but no interference was found when a thermal electron emitted an electron to the laser field at a scattering angle . The DCS with eT scattering was found to be greater than a nonthermal electron in presence of laser field with scattering angle and incidence energy of the electron.

Fine structure resolved excitation cross sections of singly ionized Ga for the modeling and diagnostics of Ga plasmas

Calculation of electron impact excitation cross sections for singly charged Ga ions plays a crucial role in plasma modeling, facilitating the comprehension of plasma behavior, characteristics, and dynamics in diverse domains, such as astrophysics, fusion research, the semiconductor industry, etc. In the available literature, there is a notable scarcity of, or even a complete absence of, these cross sections. Hence, in the present work, electron impact excitation cross sections are calculated for the transitions from the fine structure resolved energy levels of the configurations 4s2 and 4s4p to the fine structure resolved energy levels of the configurations 4s4p , 4s5s , 4p2 and 4s4d of the singly charged Ga ion (Ga+) using the relativistic distorted wave approximation theory with the target states represented by multi configurational Dirac Fock wavefunctions. The cross sections are calculated for projectile electron energy varying from threshold to 500 eV. Furthermore, the electron impact excitation rate coefficients for all the transitions under investigation are also calculated for electron temperatures ranging from 0.5 to 5 eV. In addition, analytic fitting of the rate coefficients is also performed, providing a practical resource for directly utilizing in plasma modeling applications.

Electron impact triple differential cross sections of Xe atoms for coplanar to perpendicular plane single ionisation at 60 eV, 80 eV and 100 eV above ionisation

The evolution of the triple differential cross section (TDCS) for the electron impact ionisation of xenon atoms is reported for the variation of momentum of the projectile electron from a coplanar geometry to a perpendicular plane through intermediate angles with the detection plane. The TDCSs have been calculated for the Xe atoms at 60 eV, 80 eV and 100 eV above the ionisation potential. We have calculated the TDCS using distorted wave Born approximation, utilising both the first and second Born terms. Effects of target polarisation and post-collision interaction have also been included in the complete description of the collision dynamics. The TDCS results are compared with recent measurements by Patel et al (2022 Phys. Rev. A 105 032818) showing a dependence between the TDCS and the scattering geometry and kinematics of the collision. Second-order effects have been found significant, particularly in the description of perpendicular plane ionisation at a low energy and the effect of target polarisation has been found important in describing the coplanar ionisation of the xenon target. With an overall good agreement with the recent measurements, there are points of disagreement which are the motivation for further theoretical effort in the near future, as the present attempt is the first of its kind to analyse these measurements.

A Critical Analysis of Target Ionization and Projectile Electron Loss in Neutral– and Ion–Atom Collisions

Electron removal (target ionization and/or projectile electron loss) in neutral–atom collisions is theoretically studied for the impact of H0, He0 and He+ beams on noble gases (He, Ne and Ar). These reactions are investigated theoretically within the Continuum Distorted Wave-Eikonal Initial State model. New features have been included in the theoretical model: (i) a scaled projectile charge depending on its velocity and charge, (ii) a dynamic projectile-effective-charge depending on the momentum transfer, and (iii) a dynamic target-effective-charge depending on the kinematics of the emitted electron. The energy and angular spectra of emitted electrons from the target and from the projectile are calculated and compared with the available experimental data. Also, the influence of each one of the corrections on the resulting spectra will be studied.

Relativistic calculation of electron impact excitation of tin: cross sections of importance in plasma modeling

The present work includes the calculation of electron impact excitation cross sections for the fine structure resolved transitions in Sn I and Sn II, using the relativistic distorted wave approximation with the aid of Dirac-Fock multiconfigurational wavefunctions. For Sn I, the cross sections are calculated for the excitations from the fine structure resolved energy levels of the manifolds, , , , and including the ground state, to the fine structure resolved levels of , , , , and manifolds for a wide range of projectile electron energy from 0 to 500 eV. Further, the cross sections are also calculated for the excitations of Sn II from the fine structure resolved energy levels of the manifolds, , , , and including the ground state, to the fine structure resolved levels of , , , , and manifolds. All the cross sections for Sn I except for the excitation from the ground state to the fine-structure resolved excited states of , and manifolds and all the cross sections for Sn II are reported for the first time. In order to ensure the consistency of the present calculations, a comparison of the oscillator strengths and transition probabilities is carried out with the available calculations and measurements. The present cross sections are also compared with previous calculations and observed to be in reasonable agreement. The calculated cross sections are of great interest in the modeling and diagnostic of various plasmas such as laser induced plasma, fusion plasma, etc. Further, to ease the use of calculated cross sections, the analytic fitting of the cross sections is also provided.

Electron impact excitation of Sn^{2+}

The relativistic convergent close-coupling method is applied to calculate integrated cross sections for the electron-impact excitation of Sn^{2+}. Cross sections have been calculated for excitations to all states in the 5s5p, 5p^2, 5s6s and 5s5d manifolds from the ground state for projectile electron energies ranging from 24 eV to 500 eV. The total discrete inelastic scattering cross section is also presented.Graphical abstract

Determination of the ion beam energy width in tandem Van de Graaff accelerators via Auger projectile spectroscopy

Fast ion beams delivered by tandem Van de Graaff accelerators intrinsically have an energy width, ΔEP/EP, due to the voltage ripple of the accelerator, the production mechanism of the highly charged ions inside the tank of the accelerator, as well as geometrical considerations related to the propagation of the ion beam. The ion beam energy width directly affects the experimental resolution and thus its value should be considered in experiments and the corresponding data analysis. Here, we present a method for determining the energy width of ion beams delivered by tandem Van de Graaff accelerators, based on high resolution Auger projectile electron spectroscopy combined with data analysis via Monte Carlo simulations within the SIMION ion optics package.

Antiproton impact ionization of hydrogen atom: Differential cross sections computed by Coulomb wave function discrete variable representation method

Our aim is using the Coulomb wave function discrete variable representation method (CWDVR) for the calculation of collision problem in first time. Nonrelativistic collision of antiproton with hydrogen atom is described by solving the time-dependent Schrodinger equation numerically. Two collision amplitudes are used for calculation of the differential cross sections, one of them corresponds to impact parameter of the projectile while other one is determined by projectile momentum transfer and found by Fourier transform of the first one. The ionization amplitude calculated by projecting of the wave function onto continuum wave function of the ejected electron. The differential cross sections calculated depending on projectile impact energy, scattering angle and electron ejection energy and angles, which is a result that can be measured experimentally. Our results are in good agreement with the relativistic calculation results.

Electron Capture on Nuclei in Stellar Environment

The stellar electron capture on nuclei is an essential, semi-leptonic process that is especially significant in the central environment of core-collapse supernovae and in the explosive stellar nucleosynthesis. In this article, on the basis of the original (absolute) electron-capture cross-sections under laboratory conditions that we computed in our previous work for a set of medium-weight nuclear isotopes, we extend this study and evaluate folded e−-capture rates in the stellar environment. With this aim, we assume that the parent nuclei and the projectile electrons interact when they are in the deep stellar interior during the late stages of the evolution of massive stars. Under these conditions (high matter densities and high temperatures of the pre-supernova and core-collapse supernova phases), we choose two categories of nuclei; the first includes the 48Ti and 56Fe isotopes that have A&lt;65 and belong to the iron group of nuclei, and the second includes the heavier and more neutron-rich isotopes 66Zn and 90Zr (with A&gt;65). In the former, the electron capture takes place mostly during the pre-supernova stage, while the latter occurs during the core-collapse supernova phase. A comparison with previous calculations, which were obtained by using various microscopic nuclear models employed for single-charge exchange nuclear reactions, is also included.

Comparing different charge-state models with experimental data of ion beams penetrating fully and partially ionized plasmas

In the present work, we have conducted a study to investigate the validity of three different charge-state models of ion beams penetrating plasma targets through a comparison with a total of five experiments from the literature. We have applied two alternative theoretical approaches. On the one hand, we have used a further extension of our cross-sectional model (CSM) code based on projectile electron loss and capture cross sections (rate equations) that was developed previously [Morales et al., Phys. Plasmas 24, 042703 (2017); R. Morales, Ph.D. thesis (Universidad de Castilla-La Mancha, 2019)]. On the other hand, we also used two charge-state models based on a semi-empirical formalism adapted to the plasma case: the Kreussler model [Kreussler et al., Phys. Rev. B 23, 82 (1981)] and the Gus'kov model [Guskov et al., Plasma Phys. Rep. 35, 709 (2009)]. Specifically, we present the predictions and the interpretation of the charge state of light to heavier ions at high, intermediate, and low velocities in Z-pinch and laser-produced partially and fully ionized plasmas. We are showing that experimental data support our new CSM code based on the cross-sectional formalism. In contrast, the framework based on semi-empirical formulas is less accurate for a precise charge-state prediction, but it can be applied for a reasonable stopping power calculation. Overall, results denote that the Gus'kov model is better suited to stopping power calculations at low projectile velocities and the Kreussler model fits better the energy loss data at intermediate velocities. Additionally, we propose a simple non-equilibrium charge model, derived from the semi-empirical framework, as a function of the ion path and equilibrium charge state.

Channeling electronic stopping power of lithium ions in diamond: Contribution of projectile inner-shell electrons

The electronic energy loss of Li ion in diamond under a channeling condition is studied using real-time time-dependent density functional theory. Simulations with and without inner-shell electrons explicitly considered in describing the electron configuration of projectile Li ions are performed to understand their contribution to the dissipation mechanism. It is found that the explicit involvement of inner-shell electrons is particularly important in describing the charge state of the projectile during collision, especially in the high velocity regime where the inner-shell orbital is indeed far from fully occupied during collision. Due to the overestimate of the electronic screening, Li ions with inner-shell electrons that are frozen show only a reduced and hydrogenlike capability in perturbing the host electronic system.

Projectile electron loss, excitation and de-excitation cross section database in a collision between two hydrogen atoms in the impact energy range between 50 keV–5.0 MeV, Part I: Target is in ground state

We present projectile electron loss, excitation, and de-excitation cross-sections database for H(nl)+H(1s) collision system. A four-body classical trajectory Monte Carlo (CTMC) and a quasi-classical trajectory Monte Carlo (QCTMC) methods were employed in the projectile energy range between 50 keV to 5.0 MeV.

Experimental and theoretical L -subshell ionization cross sections for 83Bi by electron impact from the L3 threshold to 100 keV

We report experimental and theoretical Bi ${L}_{1}$, ${L}_{2}$, and ${L}_{3}$ subshell ionization cross sections by the impact of electrons with energies from the Bi ${L}_{3}$ ionization threshold to 100 keV. The x-ray spectra have been acquired with two Si drift detectors placed in vacuum, which allowed us to better evaluate the peak fit procedure in the $L$ multiplet. The $L\ensuremath{\alpha}$, $L\ensuremath{\beta}$, $L\ensuremath{\gamma}$, $L\ensuremath{\ell}$, and $L\ensuremath{\eta}$ x-ray production cross sections, measured with relative uncertainties ranging from $5%$ to $9%$, and two sets of atomic relaxation parameters have been used to derive the Bi ${L}_{1}$, ${L}_{2}$, and ${L}_{3}$ ionization cross sections. Although the experimental uncertainties of the subshell ionization cross sections are smaller than those of the few previous measurements, they remain large due to the uncertainties associated with the relaxation parameters. Furthermore, ionization cross sections have been calculated for the three $L$ subshells with the subconfiguration average distorted-wave (SCADW) formalism, which includes the full two-body retarded electromagnetic interaction between the projectile and target electrons. These theoretical cross sections are $15%$ to $30%$ lower than the measured values, but the agreement is reasonable given the aforementioned high uncertainties. We have also found that the simpler distorted-wave Born approximation yields subshell ionization cross sections that match those computed with the SCADW method.

Relativistic Study on the Scattering of e± from Atoms and Ions of the Rn Isonuclear Series

Calculations are presented for differential, integrated elastic, momentum transfer, viscosity, inelastic, total cross sections and spin polarization parameters S, T and U for electrons and positrons scattering from atoms and ions of radon isonuclear series in the energy range from 1 eV–1 MeV. In addition, we analyze systematically the details of the critical minima in the elastic differential cross sections along with the positions of the corresponding maximum polarization points in the Sherman function for the aforesaid scattering systems. Coulomb glory is investigated across the ionic series. A short range complex optical potential, comprising static, polarization and exchange (for electron projectile) potentials, is used to describe the scattering from neutral atom. This potential is supplemented by the Coulomb potential for the same purpose for a charged atom. The Dirac partial wave analysis, employing the aforesaid potential, is carried out to calculate the aforesaid scattering observables. A comparison of our results with other theoretical findings shows a reasonable agreement over the studied energy range.

Correct calculation of nitrogen charge state passing through highly ionized carbon plasmas.

In the present work, we reanalyze the energy loss experimental data from Cayzac etal. [Nat. Commun. 8, 15693 (2017)10.1038/ncomms15693] using our successful ion charge state theoretical model. We predict lower nitrogen charge values, from 3.5+ to 5.0+, than the ones calculated by Cayzac etal., fitting better to their data. For energy loss estimations, we use the same stopping model, so our predictions agree better with the experimental data only due to our charge state model. Different projectile electron loss and capture processes are taken into account to estimate the projectile charge state. The projectile electron loss, or ionization, with plasma ions and free electrons are considered. On the other hand, the projectile electron capture, or recombination, with plasma free or bound electrons are also considered. The projectile ionization with plasma ions is shown as the main factor that modifies the mean charge of the projectile. Here, the new Kaganovich fitting formula for this projectile ionization is used because it seems to be more accurate than Gryzinsky's fitting in the low energy range. Our charge state model fits better with experimental data than any other model in the bibliography. Thus, it should be considered in any charge state and any energy loss estimation to obtain reliable results in future work.

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.

Role of the variable charge in (e,3e) processes on argon

SynopsisThe differential fivefold cross section for the double ionization of argon by electron impact is calculated taking into account the variations of the effective charges describing each ejected electron during the reaction; the energy of the electron projectile is fixed in the intermediate range, and the ejected electrons have low energies. The initial state is described by the Clementi wavefunction, and the ejected electrons in the final state by Coulomb waves. A comparison is made with the measurements of Jia et al [1].

Effect of Projectile Charge State on Electron Emission Spectra from He Atom

The single ionization of He atom by the impact of highly charged dressed projectile nucleus is investigated by applying the three-body formalism of three-Coulomb wave (3CW) model and the first Born approximation (FBA). In the 3CW formalism, the interaction between the dressed projectile and the active electron is represented by a model potential containing both the long-range and short-range part of the Coulomb potential. The target is treated as a one-electron atom, where the interaction of the active electron with the rest of the target is represented by a similar type of model potential. The correlated motion of each pair of particles, interacting through long-range Coulomb potential, is taken into account in the final state. In addition, an independent particle model and a single-zeta Roothaan-Hartree-Fock 1s wavefunction, describing helium in its ground state, is used to carry out the calculations, where the effective charge of the target nuclei is obtained from the initial orbital energy. The energy distributions of the double-differential cross sections (DDCS) at low and intermediate energy electron emission from helium atom have been investigated. Our theoretical results are compared with both the available experimental measurements and theoretical calculations using other methods. There is good overall agreement of the present calculations with experimental data except for low-energy electron emission (less than 10 eV). For target ionization by a dressed projectile, we find that the cross sections depend on the projectile charge. For distant collisions involving high energy ions, the primary effect of bound projectile electrons is to screen the projectile nuclear charge, thereby reducing the strength of the interaction potential. Finally, the energy distribution of DDCS ratio at different angles has also been studied.