Dielectronic Recombination Rate Research Articles

Benchmarking Dielectronic Recombination Rate Coefficients for Carbon-like Ca14+

Dielectronic recombination (DR) rate coefficients for C-like Ca14+ were measured by Wen et al. at the electron cooler storage ring in Lanzhou, China. The measured DR rate coefficients from 0 to 92 eV cover most of the DR resonances associated with the 2s 22p 2 → 2s 22p 2 and 2s 22p 2 → 2s2p 3 core transitions. In addition, Wen et al. reported theoretical results calculated with the Flexible Atomic Code (FAC) and AUTOSTRUCTURE (AS). However, these theoretical results show widespread and significant differences from the measured DR spectrum in both resonance energies and strengths, as well as between each other. In the present work, we uncover the reasons behind these large differences, both theoretical and experimental. The new FAC and AS results reproduce the observed spectrum in detail, especially at resonance energies below 8 eV, and they are in very close agreement with each other. The present plasma rate coefficients agree with the experimentally determined values to within 20% and 2% in the photoionized plasma (PP) and collisional ionized plasma (CP) temperature ranges, respectively. This is in contrast to the previous theoretical results, which showed differences with the experiment of up to ∼40% over the PP temperature range. The present FAC and AS results agree with each other within 5% in the PP and CP temperature ranges. Thus, the theoretical uncertainty is greatly reduced for the DR of Ca14+ and the present benchmarking with the experiment gives confidence to data users modeling non–local thermodynamic equilibrium plasma.

Modeling Transition Region Hot Loops on the Sun: The Necessity of Rapid, Complex Spatiotemporal Heating and Nonequilibrium Ionization

The study examines the heating profile of hot solar transition region loops, particularly focusing on transient brightenings observed in IRIS 1400 Å slit-jaw images. The findings challenge the adequacy of simplistic, singular heating mechanisms, revealing that the heating is temporally impulsive and requires a spatially complex profile with multiple heating scales. A forward-modeling code is utilized to generate synthetic Interface Region Imaging Spectrograph (IRIS) emission spectra of these loops based on HYDRAD model output, confirming that emitting ions are out of equilibrium. The modeling further indicates that density-dependent dielectronic recombination rates must be included to reproduce the observed line ratios. Collectively, this evidence substantiates that the loops are subject to impulsive heating and that the components of the transiently brightened plasma are driven far from thermal equilibrium. Heating events such as these are ubiquitous in the transition region, and the analysis described above provides a robust observational diagnostic tool for characterizing the plasma.

Dielectronic recombination experiment of Na-like Kr<sup>25+</sup> at heavy ion storage ring CSRe

The experimental study of precision spectroscopy of dielectronic recombination (DR) of highly charged ions is not only important for astronomical plasma and fusion plasma, but also can be used as a new precision spectroscopy to test the strong-field quantum electrodynamic effect, measure isotope shift, and extract the radius of atomic nuclei. An specially designed electron beam energy detuning system for electron-ion recombination precision spectroscopy experiments has been installed on the heavy ion storage ring CSRe in Lanzhou, China, where the electron-ion collision energy in the center-of-mass system can be detuned to 1 keV, and an independently-developed plastic scintillator detector and multiwire proportional chamber detector have been installed downstream of the electron cooler of the CSRe for detecting recombined ions. The multiwire proportional chamber detector has the ability to non-destructively monitor the profile of the ion beam in real-time while acquiring the recombined ion counts, providing guidance for optimizing the ion beam. On this basis, the first test experiment on dielectronic recombination of Kr<sup>25+</sup> ions is carried out at the CSRe, and the dielectronic recombination rate coefficients in a range of 0–70 eV in the frame of center-of-mass are measured. In order to fully understand the experimental results, we calculate the dielectronic recombination rate coefficient of the Kr<sup>25+</sup> ion by using the flexible atomic code (FAC) and make a detailed comparison with the experimental result, showing that they are in good agreement with each other, and only the resonance energy values of the two resonance peaks at 1.695 eV and 2.573 eV are significantly different. In addition, the DR resonance energy values and intensities are obtained by fitting the experimental results in a range of 0–35 eV, and we find that the transition 3s→4l (∆<i>n</i> = 1) contributes significantly to the experimental spectral lines. Furthermore, we compare the plasma rate coefficients derived from the DR rate coefficients with those derived from the AUTOSTRUCTURE and FAC theories, which differ by 20 percent in a temperature range less than 10<sup>6</sup> K. The experimental results show that the DR experimental platform of the CSRe has very good stability and reproducibility, and can provide support for the future DR experiments of highly charged ion, i.e. for testing strong-field quantum electrodynamics effect and measuring the properties of atomic nuclei.

Dielectronic recombination rate coefficients of carbon-like Kr30+

Dielectronic recombination (DR) rate coefficients for carbon-like Kr30+ have been measured over the collision energy of 0–60 eV using the heavy-ion storage ring CSRe at the Institute of Modern Physics in Lanzhou, China. The present DR spectrum covers the resonances associated with the , and core excitations. The corresponding DR resonance energies and strengths have been calculated by using the flexible atomic code (FAC) to understand the measured results. An overall agreement has been obtained between the experiment and theory, except for the data at the collision energies below 7 eV and in 35–38 eV, where the electronic correlation effect is strong. In particular, the resonances from the trielectronic recombination due to have been identified with the help of the FAC calculation. Temperature-dependent plasma recombination rate coefficients were derived from the measured DR rate coefficients for the temperature range 103–107 K and compared with our FAC calculations as well as the previous AUTOSTRUCTURE calculations by Zatsarinny et al (2004 Astron. Astrophys. 417 1173–81). The FAC and AUTOSTRUCTURE calculations are in good agreement with the presently derived plasma rate coefficients. The present work provides the benchmark data for astrophysical and laboratory plasma modeling.

Absolute dielectronic recombination rate coefficients of highly charged ions at the storage ring CSRm and CSRe

Dielectronic recombination (DR) is one of the dominant electron–ion recombination mechanisms for most highly charged ions (HCIs) in cosmic plasmas, and thus, it determines the charge state distribution and ionization balance therein. To reliably interpret spectra from cosmic sources and model the astrophysical plasmas, precise DR rate coefficients are required to build up an accurate understanding of the ionization balance of the sources. The main cooler storage ring (CSRm) and the experimental cooler storage ring (CSRe) at the Heavy-Ion Research Facility in Lanzhou (HIRFL) are both equipped with electron cooling devices, which provide an excellent experimental platform for electron-ion collision studies for HCIs. Here, the status of the DR experiments at the HIRFL-CSR is outlined, and the DR measurements with Na-like Kr25+ ions at the CSRm and CSRe are taken as examples. In addition, the plasma recombination rate coefficients for Ar12+, 14+, Ca14+, 16+, 17+, Ni19+, and Kr25+ ions obtained at the HIRFL-CSR are provided. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00113.00092.

Dielectronic recombination data for dynamic finite-density plasmas

Dielectronic (DR) and radiative (RR) recombination rate coefficients for 19 phosphorous-like ions, between S+ and W59+, forming sulphur-like ions, have been calculated as part of the assembly of a level-resolved database necessary for modelling dynamic finite-density plasmas, within the generalized collisional-radiative framework. Calculations have been performed within the multi-configuration Breit-Pauli approximation using the code AUTOSTRUCTURE, from both ground and metastable initial states, in both LS coupling and intermediate coupling (IC), allowing for ∆n = 0 and ∆n = 1 core-excitations from the ground and metastable levels involved in the DR processes. Partial and total DR coefficients have been calculated for S+ to Zn15+, as well as Kr21+, Mo27+, Xe39+, and W59+. Results for a selection of ions from the sequence are discussed in this paper, and are compared with the existing theoretical and experimental results. Dielectronic recombination results for the Fe11+ resonance spectrum associated with ∆n = 0 core excitations are compared with those from merged-beam measurements. Fits to the total (IC) DR and RR rate coefficients are presented in tabular form. Partial LS and IC DR and RR rate coefficients are archived in the open access database OPEN-ADAS in standard ADAS adf09 and adf48 file formats, respectively.

Development of particle detectors for electron–ion collision spectroscopy with highly charged ions at the storage ring CSRe

The electron cooler at the experimental Cooler Storage Ring (CSRe) has been upgraded with an embedded electron energy fast detuning system for the merged-beams electron–ion collision experiments. A plastic scintillation detector (PSD) and a multi-wire proportional chamber (MWPC) detector have been developed and installed downstream of the electron cooler to detect the recombined and ionized ions in the electron–ion collision experiments at the CSRe. Both detectors have been tested successfully in a recent dielectronic recombination (DR) experiment of Na-like Kr25+ ions at the CSRe. In addition, the measured DR rate coefficients for Kr25+ ions from both detectors were compared with the flexible atomic code (FAC) calculations, and a very good agreement is achieved. The present experimental results demonstrate that the new experimental setups at the CSRe including the electron energy fast detuning system and the particle detectors have high stability and efficiency and meet the needs of the forthcoming electron–ion collision precision spectroscopy at the CSRe.

Experimental dielectronic recombination rate coefficients for lithium-like 40Ca17+

The rate coefficients for dielectronic recombination (DR) of lithium-like 40Ca17+ ions with ∆n = 0 core excitations are derived from electron–ion recombination spectra measured with merged-beams method at the heavy-ion storage ring CSRm. The experimental DR spectrum, in the electron–ion collision energy range of 0 to 42 eV in the center-of-mass frame, comprises of all DR resonance peaks belong to the 2s 2 S 1/2 → 2p 2 P 1/2, 3/2 core excitations. The resonant energies and strengths for the resolved resonances in 2pjnl series are determined by fitting of the measured DR peaks. The further interpretation of the measured DR rate coefficients has been performed by calculating the DR rate coefficients with relativistic configuration-interaction method implemented in flexible atomic code (FAC) and compared with the experimental results. The experimental results and FAC calculations are found to be in a good agreement within the experimental uncertainties. Moreover, temperature dependent plasma rate coefficients were constructed from 4 × 103 to 1 × 107 K energy region by convoluting experimental and theoretical DR rate coefficients with the Maxwellian energy distribution function and then compared with previously available data. The plasma DR rate coefficient is found to be significantly underestimated by the early theoretical data calculated by Jacobs et al, and Mazotta et al in the low temperature. In contrast, a very good agreement has been found between the theoretical DR data of Gu and Colgan et al and the presently measured results at the low temperature region. Therefore, the results in this work composed of a bench-mark data set for plasma modeling at the photoionized temperature range. We have also provided a fit to our measured and theoretical plasma rate coefficients for low temperature plasma modeling.

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.

Charge-state dynamics of heavy-ion beams penetrating a hydrogen plasma

The dynamics of charge-state fractions of Au- and U-ion beams, penetrating hydrogen plasmas, is investigated for 1.4 and 3.6 MeV/u ion energies and plasma electron temperatures Te = (0.6 − 3.0) eV and densities Ne =(1016 − 1020) cm−3. Calculations of the fractions as a function of the plasma thickness are performed by solving the balance rate equations with calculated ionization and recombination rates including those for dielectronic recombination (DR). The DR rates are calculated by the recently created computer code DRIMP using the fully relativistic multi-configuration approach and the so-called shifted Maxwellian velocity distribution function. Calculated by this method DR rates of Au- and U-ion beams passing through a hydrogen plasma are presented for the first time. Using the results obtained, the temperatures Te and densities Ne are found at which the equilibrium mean charges q̄ of Au- and U-ion beams are maximal for hydrogen-plasma length L≤ 100 cm. Dependencies of the plasma equilibrium thicknesses Xeq on the initial charge q0 of incident ions are investigated, and it is found that Xeq values are minimal at q0≈q̄.

Dielectronic recombination in O4+ near the ionization threshold

Relativistic perturbation theory calculations are carried out for dielectronic recombination cross sections involving jj J levels near the ionization threshold. We included levels in the 1s 22p 23l, 1s 22s2p3l, 1s 22s2p4l, 1s 22s2p5l, and 1s 22s2p6l configurations of O3+ that lie within ±5.0 eV of the O4+ ionization threshold. Theoretical dielectronic recombination cross sections are compared with experimental dielectronic recombination rate coefficients from 0.0 eV to 5.0 eV above threshold.

Comprehensive Laboratory Measurements Resolving the LMM Dielectronic Recombination Satellite Lines in Ne-like Fe xvii Ions

Abstract We investigated experimentally and theoretically dielectronic recombination (DR) populating doubly excited configurations (LMM) in Fe xvii, the strongest channel for soft X-ray line formation in this ubiquitous species. We used two different electron beam ion traps and two complementary measurement schemes for preparing the Fe xvii samples and evaluating their purity, observing negligible contamination effects. This allowed us to diagnose the electron density in both EBITs. We compared our experimental resonant energies and strengths with those of previous independent work at a storage ring as well as those of configuration interaction, multiconfiguration Dirac–Fock calculations, and many-body perturbation theory. This last approach showed outstanding predictive power in the comparison with the combined independent experimental results. From these we also inferred DR rate coefficients, unveiling discrepancies from those compiled in the OPEN-ADAS and AtomDB databases.

Dielectronic recombination in non-LTE plasmas

Novel phenomena and methods related to dielectronic capture and dielectronic recombination are studied for non-local thermodynamic equilibrium (LTE) plasmas and for applications to non-LTE ionization balance. It is demonstrated that multichannel autoionization and radiative decay strongly suppress higher-order contributions to the total dielectronic recombination rates, which are overestimated by standard approaches by orders of magnitude. Excited-state coupling of dielectronic capture is shown to be much more important than ground-state contributions, and electron collisional excitation is also identified as a mechanism driving effective dielectronic recombination. A theoretical description of the effect of angular-momentum-changing collisions on dielectronic recombination is developed from an atomic kinetic point of view and is visualized with a simple analytical model. The perturbation of the autoionizing states due to electric fields is discussed with respect to ionization potential depression and perturbation of symmetry properties of autoionization matrix elements. The first steps in the development of statistical methods are presented and are realized in the framework of a local plasma frequency approach. Finally, the impact of collisional–radiative processes and atomic population kinetics on dielectronic recombination is critically discussed, and simple analytical formulas are presented.

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.

Helium Line Emissivities in the Solar Corona

Abstract We present new collisional-radiative models (CRMs) for helium in the quiescent solar corona and predict the emissivities of the He and He+ lines to be observed by DKIST, Solar Orbiter, and Proba-3. We discuss in detail the rates we selected for these models, highlighting several shortcomings we have found in previous work. As no previous complete and self-consistent coronal CRM for helium existed, we have benchmarked our largest model at a density of 106 cm−3 and temperature of 20,000 K against recent CRMs developed for photoionized nebulae. We then present results for the outer solar corona, using new dielectronic recombination rates we have calculated, which increase the abundance of neutral helium by about a factor of 2. We also find that all optical triplet He i lines, and in particular the well-known He i 10830 and 5876 Å lines, are strongly affected by both photoexcitation and photoionization from the disk radiation and that extensive CRMs are required to obtain correct estimates. Close to the Sun, at an electron density of 108 cm−3 and temperature of 1 MK, we predict the emissivity of He i 10830 Å to be comparable to that of the strong Fe xiii coronal line at 10798 Å. However, we expect the He i emissivity to sharply fall in the outer corona, with respect to Fe xiii. We confirm that the He+ Lyα at 304 Å is also significantly affected by photoexcitation and is expected to be detectable as a strong coronal line up to several solar radii.

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.

Calculations of Dielectronic Recombination and Electron-impact Excitation Rate Coefficients of Highly Charged Sulfur Ions

Abstract Connected to the experiment performed at the Stockholm electron beam ion trap, a systematic relativistic configuration-interaction calculation is carried out to compare with the experimental spectra. In particular, separate rate coefficients are calculated for dominant recombination and excitation processes in the range of the impact electron energy determined by the experiment. By means of the relevant experimental parameters, the presently calculated dielectronic recombination rate coefficients for and S14+ ions and electron-impact excitation ones for S15+, S14+, and S13+ ions are employed further to synthesize overall theoretical spectra for comparison with the experimentally measured spectra. Overall, very good agreements with the experimental results are found except for one missing excitation peak around the impact electron energy 2.52 keV, which cannot be explained by the present calculations and thus remains open.

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.

Dielectronic recombination rate coefficients for F-like nickel

SynopsisAt the main cooler storage ring (CSRm) of IMP, Lanzhou, we have measured merged-beams rate coefficients for dielectronic recombination (DR) of F-like Ni in the energy range 0-160 eV which comprises all DR resonances associated with ΔN = 0 core excitations. We compare our results with calculations by the flexible atomic code (FAC). Good agreement is found between calculated and measured resonance parameters except for the low-energy 2s 2p6 (2S1/2)61 resonances. In addition, we have also derived plasma rate-coefficients from our data for applications in astrophysics.

Dielectronic recombination rate coefficients of fluorine-like nickel

Electron-ion recombination rate coefficients for fluorine-like nickel ions have been measured by employing the merged-beam technique at the cooler storage ring CSRm at the Institute of Modern Physics in Lanzhou, China. The measured spectrum covers the energy range of 0–160 eV, including all the dielectronic recombination (DR) resonances associated with ΔN = 0 core excitations. The DR cross sections in this energy range were calculated by a relativistic configuration interaction method using the flexible atomic code (FAC). Radiative recombination (RR) cross sections were obtained from a modified version of the semi-classical Bethe & Salpeter (1957, Quantum Mechanics of One- and Two-Electron 56 Systems (Springer)) formula for hydrogenic ions. The comparison between the measurement and the calculation shows that the present theoretical model still needs to be improved at low collision energies. Temperature dependent plasma recombination rate coefficients were derived from the measured DR rate coefficients in the temperature range of 103–108 K and compared with the presently calculated result as well as previous available data in the literature. The experimentally derived data agree well with the theoretical calculations for temperatures where Ni19+ ions form in collisionally ionized plasmas. At lower temperatures typical for photo-ionized plasmas, discrepancies are found beyond the experimental uncertainty, which can be attributed to the disagreement between the measurement and the calculation of the low-lying DR resonances. The present experimental result benchmarks the plasma DR rate coefficients, in particular for temperatures below 105 K where the ΔN = 0 DR resonances dominate.