Dielectronic Recombination Processes Research Articles

Collisional-radiative modeling for the EUV spectrum of W40+-W42+ions

The wavelengths and transition rates of W40+-W42+ ions within the range of 40–140 Å, have been calculated using the Flexible Atomic Code of the Dirac-Fock-Slater method with a central potential. We investigated the charge state distribution of W38+-W45+ ions at different temperatures by constructing an appropriate rate equation and demonstrate the importance of the dielectronic recombination process. Additionally, we simulated the emission spectra of W40+-W42+ ions in a Tokamak plasma environment using collisional-radiative modeling. Our findings demonstrate strong agreement with experimental results and other related theoretical investigations. Finally, we propose certain pairs of transition lines as diagnostic tools for plasma temperature and density, leveraging the correlation between line intensity ratio and electron temperature and density.

Theoretical study on dielectronic recombination process and X-ray line polarization of B-like Ar13+ ion

Theoretical study on dielectronic recombination process and X-ray line polarization of B-like Ar13+ ion

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.

Dielectronic recombination strengths and plasma rate coefficients of multiply charged ions

Context. Dielectronic recombination (DR) has been known as the dominant electron-ion recombination process in different astrophysical and laboratory plasmas, and that it determines the level population and ionization balance over a range of temperatures. Apart from a fundamental interest into the details of this process, DR plasma rate coefficients are frequently applied to estimate plasma densities and temperatures, but have been found to be notoriously difficult to calculate as they require good knowledge of the ionic resonances, which are embedded into the continuum of the next higher charges states. Aims. In this paper we explain and demonstrate how DR resonance strengths and plasma rate coefficients can be readily computed within the framework of the Jena Atomic Calculator (JAC). In contrast to other available codes, the JAC toolbox supports a much simpler handling and control of different approximations, shell structures and temperature regions, for which doubly excited resonances need to be taken into account. Methods. A multi-configuration Dirac–Hartree–Fock expansion of all atomic states is generated and applied in order to compute the transition rates (radiative and nonradiative) that contribute to the DR process. For the plasma rate coefficients, moreover, a cascade model has been developed that automatically determines and incorporates all doubly excited configurations of interest for the given plasma temperatures. Results. To demonstrate the quite flexible use of JAC, we discuss and compare the DR of initially fluorine-like Ni19+ ions with previous measurements and computations. Since it is based on Dirac’s equation, the JAC toolbox is suitable for most ions across the periodic table.

Dielectronic recombination along high Rydberg states of Mg+ and Si11+ ions

In solving the multi-channel equation, I got the analytical expression of the multi-channel wave functions in terms of the solutions of the corresponding homogeneous equations. The homogeneous solutions are described in WKB Wenzel (1926 Z. Phys. 38 518) representation for both open and closed channels, and are calculated numerically using analogous means. By treating the open and closed channels equivalently in the calculation of the multi-channel wave functions, the generalized interaction matrix and generalized scattering matrix can be obtained for all the channels. With the obtained wave functions and generalized scattering matrix, the dielectronic recombination (DR) process can be calculated within the close-coupling framework by employing Bell and Seaton’s analytical deductions. In the method, high Rydberg states can easily be involved in numerical calculations. The method was applied to the calculations of DR of Mg+ and Si11+ ions along their high Rydberg states. The results are compared with those of the published experiments. Excellent agreements have been achieved, except at the extreme high Rydberg states for Si11+ ions, which is discussed in this paper.

Line analysis of EUV spectra of molybdenum laser-produced plasmas using a comparison method

A comparison method for estimating the electron temperature in the plasmas of heavy elements was further developed. The method is based on the diagnostics of laser-produced plasmas from the spectra of light [H]- and [He]-like ions, for which the methods of measuring the electron temperature are well developed and widely used. The spectra of heavy elements are obtained at the same laser intensities on the target as for light elements, which makes it possible to assign a certain electron temperature to each spectrum. The temperature-calibrated spectra of the laser-produced plasmas can be used to estimate the electron temperature of the investigated radiation source (Z-pinch plasmas, tokamak plasmas). The best coincidence of the shape and the structure of the investigated spectrum with the calibrated one determines the electron temperature of the radiation source under study. In this work, the method was applied to diagnose laser-produced Mo plasmas. The electron temperature of the Mo plasmas was determined using the spectra of [He]-like Mg ions. A detailed analysis of the experimental EUV spectra of the Mo plasmas was carried out, which included the identification of the lines of multiply charged Mo11+ - Mo19+ ions, the determination of the spectral features and the contributions of different processes to the spectral structure, and the study of the dependence of the structure on the electron temperature. Theoretical modeling of the EUV spectra of Mo11+ - Mo19+ confirmed the experimental estimates of the electron temperatures. Calculations were carried out for electron temperatures in the range 150–250 eV in order to determine the temperature at which the relative intensities of the spectral peaks in the spectral region λ = 20–180 Å coincide with the experimental ones. The theoretical analysis revealed the important role of dielectronic recombination processes in the formation of the spectral structure at various electron temperatures.

Absolute rate coefficients for dielectronic recombination of Na-like Kr25+

The absolute rate coefficients for dielectronic recombination (DR) of sodiumlike krypton ions were measured by employing the electron-ion merged-beam technique at the heavy-ion storage ring CSRm at the Institute of Modern Physics in Lanzhou, China. The measured DR spectrum covers the electron-ion collision energy range of 0--70 eV, encompassing all of the DR resonances due to $3s\ensuremath{\rightarrow}3p$ and part of the DR resonances from $3s\ensuremath{\rightarrow}3d(\mathrm{\ensuremath{\Delta}}n=0)$ and $3s\ensuremath{\rightarrow}4l(\mathrm{\ensuremath{\Delta}}n=1)$ core excitations. A series of peaks associated with DR processes have been identified by the Rydberg formula. The experimental DR results are compared with the theoretical calculations using a relativistic configuration interaction flexible atomic code and the distorted-wave collision package autostructure. A very good agreement has been achieved between the experimental results and the theoretical calculations by considering the strong mixing among the low-energy resonances in both calculations. The experimentally derived DR spectrum is then convolved with a Maxwellian-Boltzmann distribution to obtain the temperature dependent plasma recombination rate coefficients and compared with previously available results from the literature. The present experimental result yields a precise plasma rate coefficients at the low temperature range up to $\ensuremath{\sim}1\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and the calculated data by Altun et al. [Z. Altun, A. Yumak, N. R. Badnell, S. D. Loch, and M. S. Pindzola, Astron. Astrophys. 447, 1165 (2006)] provide reliable plasma rate coefficients at high temperature range above $2\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$.

Effect of dielectronic recombination on charge-state distribution in laser-produced plasma based on steady-state collisional-radiative models

Armed with four different steady-state collisional-radiative (CR) models, we investigated the effect of dielectronic recombination (DR) on the charge-state distribution in laser-produced silicon plasma. To assess this effect, we performed a series of temporally resolved spectra of highly charged Si ions in the extreme ultraviolet region. Ab initio calculations of the DR rate coefficients were done for Si6+–Si4+ ions. We also analyzed the evolution of the collisional ionization, radiative recombination, three-body recombination, photo-ionization, and DR rate coefficients as a function of electron temperature. The electron temperature and electron density for different delay times were obtained by comparing the normalized experimental and simulated spectra. The ion fraction and average charge state from the four different CR models were also obtained. The results indicate that the DR process has a greater influence in the stage of plasma evolution that cannot be neglected in plasma diagnoses.

Role of dielectronic recombination in the interaction of fast heavy-ion beams with cold plasmas

The influence of dielectronic recombination (DR) of projectile ions on characteristics of fast heavy-ion beams passing through cold plasmas is studied on the basis of fully relativistic multi-configuration calculations of DR rate coefficients. Present results are compared with the first (and, to our knowledge, the only ones) results for DR rates of 1.5-MeV/u iodine ions penetrating fully ionized hydrogen plasma with the electron temperature Te = 10 eV and density Ne = 1020 cm−3 calculated in the hydrogenic approximation (Th. Peter and J. Meyer-ter-Vehn, Phys. Rev. A 43, 2015 (1991)). Confirming the importance of DR processes of ions moving through plasma, our calculations give much higher DR-rate values than those calculated by Th. Peter and J. Meyer-ter-Vehn, which significantly changes the non-equilibrium and equilibrium ion charge-state fractions, the mean and equilibrium charges of projectile ions, as well as the equilibrium thickness of hydrogen plasmas. In order to perform DR-rate calculations for arbitrary ions passing through plasma, a new computer code DRIMP (Dielectronic Recombination of Ions Moving in Plasmas) is developed and described in the paper.

Prominent enhancement on the radiative branching ratio of the doubly excited resonant states due to the Breit interaction induced ion-core energy inversion

The Breit interaction is the relativistic correction to the electron-electron interaction which mainly affects the level energies, and it is minor in general. We present a new manifestation of the Breit interaction effects in the highly charged Li- and B-like ions based on the multi-configuration Dirac-Fock calculations, where the strongly correlated many-body wavefunctions of the doubly excited resonant states [1s2p1/22p3/2]3/2 (or [1s(2s2)2p1/22p3/2]3/2) 4P3/2 and 2D3/2 are drastically influenced by the Breit interaction. The strong variation of wavefunctions results in a prominent enhancement of the radiative branching ratio between the two dominant transitions 2p3/2-1s and 2p1/2-1s of the doubly excited states. We elucidate the intrinsic mechanism of this effect is due to the ion-core energy inversion induced by the Breit interaction, and suggest that the possible experimental measurements can be achieved via the dielectronic recombination processes in an electron beam ion trap facility. Based on this effect, we also propose an alternative experimental determination of the fine structure splitting of [1s2p1/2]0,1 (or [1s(2s2)2p1/2]0,1) in heavy He-like (or Be-like) ions from the branching ratio of the doubly excited Li-like (or B-like) ions, which is sensitive to the fine structure level inversions and can be served as a complementary tool to the available hyperfine quenching experimental method aiming for the absolute value of the splitting.

Enhancement of electron–ion recombination rates at low energy range in the heavy ion storage ring CSRm**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300) and the National Natural Science Foundation of China (Grant Nos. U1932207, 11904371, and U1732133).

Recombination of Ar14+, Ar15+, Ca16+, and Ni19+ ions with electrons has been investigated at low energy range based on the merged-beam method at the main cooler storage ring CSRm in the Institute of Modern Physics, Lanzhou, China. For each ion, the absolute recombination rate coefficients have been measured with electron–ion collision energies from 0 meV to 1000 meV which include the radiative recombination (RR) and also dielectronic recombination (DR) processes. In order to interpret the measured results, RR cross sections were obtained from a modified version of the semi-classical Bethe and Salpeter formula for hydrogenic ions. DR cross sections were calculated by a relativistic configuration interaction method using the flexible atomic code (FAC) and AUTOSTRUCTURE code in this energy range. The calculated RR + DR rate coefficients show a good agreement with the measured value at the collision energy above 100 meV. However, large discrepancies have been found at low energy range especially below 10 meV, and the experimental results show a strong enhancement relative to the theoretical RR rate coefficients. For the electron–ion collision energy below 1 meV, it was found that the experimentally observed recombination rates are higher than the theoretically predicted and fitted rates by a factor of 1.5 to 3.9. The strong dependence of RR rate coefficient enhancement on the charge state of the ions has been found with the scaling rule of q3.0, reproducing the low-energy recombination enhancement effects found in other previous experiments.

Investigation of TEOP transitions in dielectronic recombination with H-like ions

SynopsisWe consider theoretically the process of dielectronic recombination (DR) with H-like ions where two-electron one-photon (TEOP) transitions take place. We focus our attention on the channel with transitions to the ground state of the He-like ions and emission of Kαα photon. Total and differential cross sections of DR with TEOP are calculated for wide range of H-like ions: from B4+ to Xe53+. The resonant Fano-like structure of the cross section is observed. The resonant energies, widths and TEOP transition probabilities are calculated.

Theoretical study of the dielectronic recombination process of Mg-like W62+ ions

SynopsisThe dielectronic recombination of Mg-like W62+ (3s2) ions was studied using the flexible atomic code based on the relativistic configuration interaction method with considering Breit and QED corrections. Theoretical results are compared with the experimental results from electron beam ion trap, good consistency is obtained.

K-shell electron-impact excitation and polarization of x-ray emission of Fe20+ ion

SynopsisThe total and magnetic cross sections for K-shell electron impact excitation (EIE) of Fe20+ have been calculated using the fully relativistic distorted-wave approach. Degrees of linear polarization of x-ray emission following EIE are presented for several stronger 2p→1s transitions, and compared with the values for the same transition lines but from dielectronic recombination process of Fe21+ in the ground state, obvious differences are found that can be employed in diagnosing the formation mechanism of corresponding x-ray lines.

KLL dielectronic recombination of hydrogenlike carbon ion in Debye plasmas

The KLL dielectronic recombination (DR) process of C5+ ion embedded in Debye plasmas is investigated using the multiconfiguration Dirac-Fock method with the Debye-Hückel model potential. The resonance energies, radiative and Auger rates as well as DR cross sections are obtained for a large range of Debye screening parameters to explore the influences of the plasma screening on the KLL DR process of C5+ ion. It is found that the total radiative rates and Auger rates of the intermediate states both decrease monotonically with increasing the plasma screening, except the Auger rate for the transition 2p2 1S → 1s that changes nonmonotonically due to such screening imposed on the interaction between the configurations 1s and 2s in C5+ ion. Moreover, for the KLL DR process, blueshift and redshift phenomena are observed for the resonance energies, which originates from the dynamic variations of the energy levels of C4+ and C5+ ions in the Debye plasma. The magnitudes of the DR cross section decrease slightly when the Debye-screening effects are not so strong.

Influence of Debye Plasma on the KLL Dielectronic Recombination of H-Like Helium Ions**Supported by the National Key Research and Development Program of China under Grant No 2017YFA0402300, and the National Natural Science Foundation of China under Grant Nos 11864036, 11564036 and 11774292.

Using the Debye shielding model, the effects of plasma shielding on the dielectronic recombination processes of the H-like helium ions are investigated. It is found that plasma shielding causes a remarkable change in the Auger decay rate of the doubly excited 2p2 3P2 state. As a result, the dielectronic recombination cross sections from the doubly excited 2p2 3P2 state increases with the decreasing Debye shielding length.

CHIANTI—An Atomic Database for Emission Lines. XV. Version 9, Improvements for the X-Ray Satellite Lines

Abstract CHIANTI contains a large quantity of atomic data for the analysis of astrophysical spectra. Programs are available in IDL and Python to perform calculation of the expected emergent spectrum from these sources. The database includes atomic energy levels, wavelengths, radiative transition probabilities, rate coefficients for collisional excitation, ionization, and recombination, as well as data to calculate free–free, free–bound, and two-photon continuum emission. In Version 9, we improve the modeling of the satellite lines at X-ray wavelengths by explicitly including autoionization and dielectronic recombination processes in the calculation of level populations for select members of the lithium isoelectronic sequence and Fe xviii–xxiii. In addition, existing data sets are updated, new ions are added, and new total recombination rates for several Fe ions are included. All data and IDL programs are freely available at http://www.chiantidatabase.org or through SolarSoft, and the Python code ChiantiPy is also freely available at https://github.com/chianti-atomic/ChiantiPy.

EBIT Observation of Ar Dielectronic Recombination Lines near the Unknown Faint X-Ray Feature Found in the Stacked Spectrum of Galaxy Clusters.

Motivated by possible atomic origins of the unidentified emission line detected at 3.55-3.57 keV in a stacked spectrum of galaxy clusters, an electron beam ion trap (EBIT) was used to investigate the resonant dielectronic recombination (DR) process in highly charged argon ions as a possible contributor to the emission feature. The He-like Ar DR-induced transition 1s22l-1s2l3l' was suggested to produce a 3.62 keV photon near the unidentified line at 3.57 keV and was the starting point of our investigation. The collisional-radiative model NOMAD was used to create synthetic spectra for comparison with both our EBIT measurements and with spectra produced with the AtomDB database/Astrophysical Plasma Emission Code (APEC) used in the Bulbul et al. work. Excellent agreement was found between the NOMAD and EBIT spectra, providing a high level of confidence in the atomic data used. Comparison of the NOMAD and APEC spectra revealed a number of missing features in the AtomDB database near the unidentified line. At an electron temperature of T e = 1.72 keV, the inclusion of the missing lines in AtomDB increases the total flux in the 3.5-3.66 keV energy band by a factor of 2. While important, this extra emission is not enough to explain the unidentified line found in the galaxy cluster spectra.

Theoretical investigation of electron-ion recombination processes of Li-like tungsten ions

Dielectronic recombination (DR) and radiative recombination (RR) spectra of highly charged Tungsten ions are important for modeling and diagnosing magnetic fusion plasmas. We studied the DR process of Li-like W71+(2s) ions using the flexible atomic code (FAC) based on the relativistic configuration interaction (RCI) method with Breit and QED corrections. The detailed resonance energies, widths and strengths were calculated systematically for the dominated doubly excited states (2p1/2nlj)J(n=19∼29) and (2p3/2n′lj)J(n′=7∼29) of Be-like W70+ ions. The contributions from the higher Rydberg states with n=30∼ncut(ncut=116) are obtained by extrapolation based on the quantum defect theory (QDT). The electron-ion recombination spectra (DR+RR), covering the center-of-mass energy range 0–1700 eV, are presented by taking into account the electron beam temperature at the experimental cooler storage ring (CSRe). It is found that the DR resonances associated with 2s1/2 → 2p1/2 and 2s1/2 → 2p3/2 transitions are not blending for the whole Δn=0 collision energy range, which will provide a good chance for testing fundamental theory clearly by experimental investigation. Finally the plasma rate coefficients are deduced from the calculated recombination spectra in the temperature range from 5.0 × 103 to 1.0 × 108 K. Compared with the AUTOSTUCTURE results, a good agreement is obtained except for the DR rates at the low electron temperature (Te < 5.0 × 105K), which were mainly attributed to the difference of the first resonance group 2p1/219l. The present results will guide the DR experiment of Tungsten ions at the CSRe and also be useful for ITER fusion plasmas modeling.

Influence of the Breit interaction on linear polarization of radiation lines following electron-impact excitation of the boron isoelectronic sequence

Electron-impact excitation cross sections from the ground state $1{s}^{2}2{s}^{2}2{p}_{1/2}$ to the excited states ${[{(1{s}^{2}2s2{p}_{1/2})}_{0}2{p}_{3/2}]}_{3/2}$, ${[{(1{s}^{2}2s2{p}_{3/2})}_{1}2{p}_{3/2}]}_{5/2}$, ${[{(1s2{s}^{2}2{p}_{1/2})}_{0}2{p}_{3/2}]}_{3/2}$, and ${[{(1s2{s}^{2}2{p}_{3/2})}_{1}2{p}_{3/2}]}_{5/2}$ of highly charged boronlike ${\mathrm{Ca}}^{15+}$, ${\mathrm{Xe}}^{49+}$, and ${\mathrm{W}}^{69+}$ ions have been calculated with the fully relativistic distorted-wave method. The degrees of linear polarization of the corresponding radiation lines are further obtained. It is found that the Breit interaction makes the lines corresponding to the $2p\ensuremath{\rightarrow}2s$ transition depolarized, and it makes the ones corresponding to the $2p\ensuremath{\rightarrow}1s$ transition more polarized. These characteristics are very different from the results obtained for the linear polarization of the same radiation lines but formed via the dielectronic recombination process [Phys. Rev. A 91, 042705 (2015)], in which the Breit interaction has no effect on the linear polarization.