Relativistic Distorted-wave Method Research Articles

R-matrix calculations for opacities: IV. Convergence, completeness, and comparison of relativistic R-matrix and distorted wave calculations for Fe xvii and Fe xviii

To investigate the completeness of coupled channel (CC) Breit–Pauli R-matrix (BPRM) calculations for opacities we employ the relativistic distorted wave (RDW) method to complement (‘top-up’) and compare the BPRM photoionization cross sections for high- nℓ levels of both Fe xvii and Fe xviii . Good agreement is found with background photoionization cross sections using these two methods, which also ensures the correct matching of bound level cross sections for completeness. In order to top-up the CC-BPRM calculations, bound–bound transitions involving additional bound levels, and a large number of doubly-excited quasi-bound levels corresponding to BPRM autoionizing resonances described in the paper RMOPII are calculated using the RDW method. Photoionization cross sections in the high energy region are also computed and compared up to about 500 Ry, and contributions from higher core level excitations than BPRM are considered. The effect of configuration interaction is investigated, which plays a significant role in correctly reproducing some background cross sections. Due to the fact that the additional RDW levels correspond to high- nℓ bound levels that are negligibly populated according to the Mihalas–Hummer–Däppen equation-of-state (paper I), the effect on opacities is expected to be small.

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 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.

On the development of relativistic distorted wave approximation for the energies and collision dynamics of atoms or ions subjected to the outside plasma

In this manuscript, we present the development of a relativistic distorted wave method for determining the energies and collision dynamics of plasma-immersed atoms or ions. The methodology is based on the Dirac–Coulomb Hamiltonian, in which contributions from relativity and higher order effects, such as quantum electrodynamics and Breit interaction, are incorporated. The key element in this method is that a modified Debye–Hückel approximation is employed to represent the effect of plasma screening. In order to correctly describe the (bound and continuous state) wave functions, a self-consistent field calculation incorporating the shielding potential is performed within the fully relativistic framework. The particle interaction within the scattering matrix element of the excitation process is described by the shielded Coulomb interaction. The present technique is illustrated by calculations of energy, line shift, transition probability, electron-impact excitation/ionization cross section, and photoionization cross section of a few-electron system confined in plasma environments. The present model is tested and validated against a number of known cases (simulations are made for the He-like Al11+ ion) in the literatures. Numerical results demonstrate that the modifications to the Coulomb potential proposed in the spatial and temporal criteria of the Debye–Hückel approximation allow us to improve the theoretical description of the plasma shielding and thus the dynamical processes in dense plasmas. Comparisons of our computational predictions and the recent experimental measurements are performed. The current work not only has far-reaching implications for our understanding of the dense plasma screening, but also has potential applications in fusion, laboratory astrophysics, and related disciplines.

Angular and polarization properties of the Lyman- α1 line 2p3/2→1s1/2 following electron-impact excitation of hydrogenlike ions

Electron-impact excitation from the ground state to the excited energy level $2{p}_{3/2}$ of hydrogenlike ions and subsequent Lyman-${\ensuremath{\alpha}}_{1}$ $(2{p}_{3/2}\ensuremath{\rightarrow}1{s}_{1/2})$ radiative decay are investigated using the relativistic distorted-wave method. Special attention is paid to the linear polarization and angular distribution of the Lyman-${\ensuremath{\alpha}}_{1}$ line and also to the effects of the Breit interaction. To this aim, detailed calculations are performed for hydrogenlike ${\mathrm{Ti}}^{21+}$, ${\mathrm{Mo}}^{41+}$, ${\mathrm{Ba}}^{55+}$, and ${\mathrm{Au}}^{78+}$ ions. It is found that the presently obtained (partial cross sections and) linear polarization agree excellently with other theoretical and experimental results available for low-$Z\phantom{\rule{4pt}{0ex}}{\mathrm{Ti}}^{21+}$ ions within the experimental uncertainties. Moreover, the Lyman-${\ensuremath{\alpha}}_{1}$ line is found to be less linearly polarized and less anisotropic due to the contribution of the Breit interaction. Such effects of the Breit interaction behave more prominently for higher-$Z$ ions and higher impact electron energies, respectively. For instance, the Breit interaction qualitatively changes the polarization behavior and angular emission pattern of the Lyman-${\ensuremath{\alpha}}_{1}$ line from high-$Z\phantom{\rule{4pt}{0ex}}{\mathrm{Au}}^{78+}$ ions at the impact energy of about 4.2 times the corresponding excitation threshold.

Electron Impact Excitation of Ge-like Te20+–Cd16+ Ions

We study electron impact excitation of dipole allowed transitions in the extreme ultraviolet range—8–55 nm—for the germanium isoelectronic sequence Te20+–Cd16+. The fine structure transitions between the ground state having configuration 4s24p2 and the excited states with configurations 4s4p3 and 4s24p4d are considered for these ions. We employ the relativistic distorted wave method to calculate the excitation cross sections in the incident electron energy range from the excitation threshold to 5000 eV. To obtain the required ionic bound state wavefunctions we have used the multi-configuration Dirac-Fock method with correlations within the n = 5 complexes as well as performed relativistic configuration interaction calculations to include the quantum electrodynamic effects. The accuracy of these wavefunctions is established by comparing our calculated wavelengths and oscillator strengths of the considered transitions with the previously reported measurements and other available theoretical results. We also provide the fitting parameters of the calculated cross sections and the excitation rate coefficients for their direct applications in plasma modeling.

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.

Electron Impact Excitation of Extreme Ultra-Violet Transitions in Xe7–Xe10 Ions

In the present work, a detailed study on the electron impact excitation of Xe7+, Xe8+, Xe9+ and Xe10+ ions for the dipole allowed (E1) transitions in the EUV range of 8–19 nm is presented. The multi-configuration Dirac–Fock method is used for the atomic structure calculation including the Breit and QED corrections along with the relativistic configuration interaction approach. We have compared our calculated energy levels, wavelengths and transition rates with other reported experimental and theoretical results. Further, the relativistic distorted wave method is used to calculate the cross sections from the excitation threshold to 3000 eV electron energy. For plasma physics applications, we have reported the fitting parameters of these cross sections using two different formulae for low and high energy ranges. The rate coefficients are also obtained using our calculated cross sections and considering the Maxwellian electron energy distribution function in the electron temperature range from 5 eV to 100 eV.

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.

Electron Impact Excitation of Singly Charged Indium Ion

We study electron impact excitation of In\({}^{+}\) using relativistic distorted wave method and report cross sections for 37 transitions among the fine-structure levels of \(5s^2\), \(5s5p\), \(5s5d\), \(5s6s\) and \(5s6p\) configurations at the scattered electron energies upto 200 eV. The bound state wavefunctions of the target ion are obtained within multi-configuration Dirac-Fock approach. Our calculated oscillator strengths are compared with the results from the NIST database and other theoretical calculations. Cross sections are fitted with an analytical formula and the fitting parameters are made available for their possible applications in plasma modeling.

Electron impact excitation of Ge-like to Cu-like xenon ions in the extreme ultraviolet

Electron impact excitation of Ge-like (Xe22+) to Cu-like (Xe25+) highly charged xenon ions are studied and dipole allowed fine-structure transitions in the wavelength range 9–25 nm are considered. We use relativistic distorted wave method to calculate the electron excitation cross sections for the different transitions of the four ions in the scattered electron energy range from excitation threshold to 1500 eV. The ionic bound state wavefunctions have been obtained using multi-configuration Dirac–Fock method. To ascertain the accuracy of the wavefunctions, the wavelengths and oscillator strengths of the considered transitions in these ions are calculated and compared with the previously reported measurements and other theoretical calculations, where available. For plasma diagnostic applications, the obtained cross sections are further used to calculate the rate coefficients of the transitions as well as fitted with an analytical expression which can be used in plasma model conveniently.

Electron impact excitation of the 4 1S0-4 1P1 state of Zn atom

SynopsisThe electron impact excitation total and differential cross sections, Stokes parameters, and coherence pa-rameters of Zn atom from the ground state 41S0 to the excited state 41P1 were systematically calculated using the fully relativistic distorted wave method. The calculated results are compared with the experimental data and other theoretical results, good agreement is obtained.

Electron impact excitation of krypton from the metastable state to the $$4p^{5}5p$$ 4 p 5 5 p levels

Using the fully relativistic distorted-wave method, we calculated electron impact excitation cross sections out of the two metastable levels of $$4p^{5}$$ 5sJ = 0 and J = 2 into the ten levels of the $$4p^{5}$$ 5p configuration of krypton. To obtain accurate results, careful consideration is given to the generation of the target state wave functions through the systematic inclusion of electron correlations. We find that the electron correlation has a large influence on the cross sections. This effect weakens as the incident electron energy increases. Our numerical results are compared with the available experimental data and other theoretical values over the measured energy range, showing a good quantitative agreement. We believe that these accurate results will be useful in plasma modeling studies.

Application of relativistic distorted-wave method to electron-impact excitation of highly charged Fe XXIV ion embedded in weakly coupled plasmas

The process of excitation of highly charged Fe XXIV ion embedded in weakly coupled plasmas by electron impact is studied, together with the subsequent radiative decay. For the target structure, the calculation is performed using the multiconfiguration Dirac-Hartree-Fock method incorporating the Debye-Hückel potential for the electron-nucleus interaction. Fine-structure levels of the 1s22p and 1s2s2p configurations and the transition properties among these levels are presented over a wide range of screening parameters. For the collision dynamics, the distorted-wave method in the relativistic frame is adopted to include the effect of plasma background, in which the interparticle interactions in the system are described by screened interactions of the Debye-Hückel type. The continuum wave function of the projectile electron is obtained by solving the modified Dirac equations. The influence of plasma strength on the cross section, the linear polarization, and the angular distribution of x-ray photon emission are investigated in detail. Comparison of the present results with experimental data and other theoretical predictions, when available, is made.

Angular Distribution and Linear Polarization of X-ray Radiation Resulting from Electron Impact Excitation of Highly Charged Ions in Debye Plasmas

Plasma-screening effects on the $$1s _{1/2} \rightarrow 2l \; (l = s , p )$$ and $$1s _{1/2} \rightarrow 3d _{3/2}$$ electron-impact excitation of highly charged ions are investigated, together with their subsequent radiative decay. The analysis is performed based on the multi-configuration Dirac–Fock method and the fully relativistic distorted-wave method incorporating the Debye–Huckel potential. To explore the nature of the effects, calculations are carried out based on detailed analyses of the integrated total and magnetic sublevel cross sections, the alignment parameters, the linear polarizations, and the angular distribution of the X-ray photoemission, as well as on corresponding data calculated in various Debye lengths/environments, taking the $$2p _{3/2}\rightarrow 1s _{1/2}$$ and $$3d _{3/2}\rightarrow 1s _{1/2}$$ characteristic lines of H-like $$\hbox {Fe}^{25+}$$ ion as an example. The present results are compared with experimental data and other theoretical predictions where available.

Hyperfine structure effect on circular polarization of X-ray radiation

During the last decades, the electron impact excitation (EIE) process has aroused much interest in various research areas. This process is crucial to the diagnoses of astrophysical and laboratory plasmas. Moreover, the EIE studies play an important role in understanding the quantum electrodynamic, many-electron, and hyperfine interaction effects in heavy atomic systems. As is well known, when ions are excited by collisions with a unidirectional beam of electrons, the magnetic sublevels of the excited state may be populated with nonstatistical probability. In the decay of the excited state, the emitted radiation is found to be anisotropic and polarized. From the analysis of the polarization, valuable information can be obtained. These properties have become indispensable tools for the diagnosis of plasma state and the analysis of complex spectrum formation mechanism. Up to now, however, most of studies have dealt with the linear polarization of X-ray radiation. Fewer publications have reported the circular polarization. Moreover, theoretical studies of the characteristic X-ray emission have just dealt with ions having zero nuclear spin, or have simply omitted all contributions that arise from such a spin. It is known that some kinds of ions each have a nuclear spin I 0. Owing to the hyperfine coupling, new decay channel will be open, namely, hyperfine-induced transition. It is thus important to analyze how the hyperfine interaction affects the polarization properties of X-ray radiation. In this study, we present a systematically theoretical analysis of the polarization and angular distribution of X-ray radiation during the hyperfine-induced transition. The calculations are performed by using a fully relativistic distorted-wave method. Special attention is paid to the studies of angular correlations and polarization properties of the 1s2p 3P2 Fi=3/2 1s2 1S Ff=1/2 decay for highly charged He-like Sc19+ and 205Tl79+ ions with nuclear spin I=1/2 following impact excitation by a completely longitudinally-polarized electron beam. Two effects, i.e.the BI and the mutipole mixing between the leading M2 decay and hyperfine-induced E1 decay, on the polarization of the emitted radiation are discussed. Our results show that both the BI and the E1-M2 interference effects may significantly affect the polarization and angular emission pattern of the transition line. For example, the BI and the E1-M2 mixing lead the circular polarization to increase by about 50% and 40% for 205Tl79+ ions, respectively. With the development of the X-ray detectors, the measurement on the polarization during the hyperfine-induced transition becomes feasible. We hope that the present results would be useful in resolving some disagreement between the theories and experiments relating to the polarization properties of the X-ray radiation.

Circular polarization of X-ray radiation emitted by longitudinally polarized electron impact excitation: Under a screened Coulomb interaction

Longitudinally polarized electron impact excitation from the ground state 1s2 to the excited state 1s2l (l =s,p) levels of highly charged He-like Fe24+ ions in weakly coupled hot-dense plasmas is investigated using a fully relativistic distorted-wave method. The Debye-Hückel potential is used to describe the plasma screening. Benchmark results such as the total cross sections, the magnetic sublevels cross sections, and the circular polarizations of corresponding X-ray radiations are presented. For the excitation process, results show that the plasma screening has an effect in reducing both the total and magnetic sublevels cross sections. For the de-excitation process, it is found that while the plasma screening as a slightly effect on the circular polarizations of radiations for the 1s2s 3S1 → 1s2 1S0,1s2p 3P2 → 1s2 1S0, and 1s2p 1P1 → 1s2 1S0 transition lines, it gives a substantial contribution for the same properties of the 1s2p 3P1 → 1s2 1S0 line.

Collision strength and effective collision strength for Br XXVII

Collision strengths for all 1326 transitions among lowest 52 fine-structure levels of Br XXVII have been computed using Dirac atomic R-matrix code (DARC). Resonances in the threshold region have been completely resolved and the contributions of these resonances to allowed and forbidden transitions have been presented. The partial collision strength for each angular momentum has been studied graphically. Effective collision strengths have also been determined within the temperature range for all 1326 transitions among the lowest 52 levels. Target state energies of the lowest 52 fine-structure levels have been computed from the multi-configuration Dirac–Fock method (MCDF). Additionally, similar calculations with the relativistic distorted wave method and flexible atomic code (FAC) have also been performed to check the accuracy of our results. The present work represents a new and significant work with improvement in the field. We believe that our presented data of collision and effective collision strengths may be useful in the future for benchmark calculations and for plasma diagnostics.

The influence of Breit interaction and E1-M2 quantum interference on polarization following inner-shell electron-impact excitation of Li-like ions

SynopsisThe total and magnetic sublevel cross sections of electron-impact excitation from the ground state 1s22s 2S1/2 to the inner-shell excited states 1s2s2p (J=3/2) are calculated based on a relativistic distorted-wave method for highly charged Li-like ions. The important influence of the Breit interactions and quantum interferences between electronic dipole (E1) and magnetic quadrupole (M2) transition on polarization of emitted X-ray are systematically studied.

Electron impact excitation of tin

We study the electron impact excitation of the fine-structure levels of the ground state configuration 5p 2 to the excited states of the configuration 5p6s in tin atom. These calculations have been carried out in the j j coupling scheme using the relativistic distorted-wave method. Results for differential cross section are reported at incident electron energies 20, 50, 80 and 100 eV while integrated cross sections are presented in the incident electron energy range of 5 to 100 eV.