Electron-ion Recombination Rate Coefficients Research Articles

Photoionization and Electron-Ion Recombination of n = 1 to Very High n-Values of Hydrogenic Ions

Single electron hydrogen or hydrogenic ions have analytical forms to evaluate the atomic parameters for the inverse processes of photoionization and electron-ion recombination (H I + hν↔ H II + e) where H is hydrogen. Studies of these processes have continued until the present day (i) as the computations are restricted to lower principle quantum number n and (ii) to improve the accuracy. The analytical expressions have many terms and there are numerical instabilities arising from cancellations of terms. Strategies for fast convergence of contributions were developed but precise computations are still limited to lower n. This report gives a brief review of the earlier precise methodologies for hydrogen, and presents numerical tables of photoionization cross sections (σPI), and electron-ion recombination rate coefficients (αRC) obtained from recombination cross sections (σRC) for all n values going to a very high value of 800. σPI was obtained using the precise formalism of Burgess and Seaton, and Burgess. αRC was obtained through a finite integration that converge recombination exactly as implemented in the unified method of recombination of Nahar and Pradhan. Since the total electron-ion recombination includes all levels for n = 1–∞, the total asymptotic contribution of n = 801–∞, called the top-up, is obtained through a n−3 formula. A FORTRAN program “hpxrrc.f” is provided to compute photoionization cross sections, recombination cross sections and rate coefficients for any nl. The results on hydrogen atom can be used to obtain those for any hydrogenic ion of charge z through z-scaling relations provided in the theory section. The present results are of high precision and complete for astrophysical modelings.

Database NORAD-Atomic-Data for Atomic Processes in Plasma

The online atomic database of NORAD-Atomic-Data, where NORAD stands for Nahar OSU Radiative, is part of the data sources of the two international collaborations of the Opacity Project (OP) and the Iron Project (IP). It contains large sets of parameters for the dominant atomic processes in astrophysical plasmas, such as, (i) photo-excitation, (ii) photoionization, (iii) electron–ion recombination, (iv) electron–impact excitations. The atomic parameters correspond to tables of energy levels, level-specific total photoionization cross-sections, partial photoionization cross-sections of all bound states for leaving the residual ion in the ground state, partial cross-sections of the ground state for leaving the ion in various excited states, total level-specific electron–ion recombination rate coefficients that include both the radiative and dielectronic recombination, total recombination rate coefficients summed from contributions of an infinite number of recombined states, total photo-recombination cross-sections and rates with respect to photoelectron energy, transition probabilities, lifetimes, collision strengths. The database was created after the first two atomic databases, TOPbase under the OP and TIPbase under the IP. Hence the contents of NORAD-Atomic-Data are either new or from repeated calculations using a much larger wave function expansion making the data more complete. The results have been obtained from the R-matrix method using the close-coupling approximation developed under the OP and IP, and from atomic structure calculations using the program SUPERSTRUCTURE. They have been compared with available published results which have been obtained theoretically and experimentally, and are expected to be of high accuracy in general. All computations were carried out using the computational facilities at the Ohio Supercomputer Center (OSC) starting in 1990. At present it contains atomic data for 154 atomic species, 98 of which are lighter atomic species with nuclear charge Z ≤ 28 and 56 are heavier ones with Z > 28. New data are added with publications.

Electron-ion recombination rate coefficients of carbon-like Ar12+

Electron-ion recombination of carbon-like Ar12+ forming Ar11+ has been investigated for the first time by using the cooler storage ring CSRm at the Institute of Modern Physics in Lanzhou, China. The absolute recombination rate coefficients are derived from the measurement in the electron-ion collision energy range of 0–50 eV, covering dielectronic recombination (DR) resonances associated with 2s22p2 and 2s2p3 (Δn = 0) core excitations. Theoretical results are obtained by employing FAC code and compared with the experimental recombination spectrum. An overall agreement is found in resonance energy positions between merged-beam and calculated spectra. Temperature dependent rate coefficients are derived from the measured DR spectrum by convoluting it with a Maxwell–Boltzmann energy distribution and compared with the calculations from the literature. In the presented temperature range 103–107 K, the experimentally derived rate coefficients agree with the theoretical results of Gu (2003 Astrophys. J. 590 1131) within the experimental uncertainties. The calculation by Zatsarinny et al (2004 Astron. Astrophys. 417 1173) underestimates the rate coefficients in the temperature range 103–5 × 104 K. The combination of the experimental results and theoretical calculation provides a benckmark for Ar12+ recombination data used in astrophysical modeling.

Complex scaling in relativistic calculations of cross sections for electron-ion recombination processes

SynopsisWe present an approach to calculate cross sections for electron-ion recombination processes. It is based on the combination of relativistic many-body perturbation theory and complex scaling method. A preliminary comparison between measured and calculated spectra for the electron-ion recombination rate coefficients for Be-like Ca will be given.

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.

Electron–ion Recombination Rate Coefficients of Be-like 40Ca16+

Abstract Electron–ion recombination rate coefficients for beryllium-like calcium ions in the center of mass energy from 0 to 51.88 eV have been measured by means of the electron–ion merged-beam technique at the main cooler storage ring at the Institute of Modern Physics in Lanzhou, China. The measurement energy range covers the dielectronic recombination (DR) resonances associated with the core excitations and the trielectronic recombination (TR) resonances associated with the core excitations. In addition, the AUTOSTRUCTURE code was used to calculate the recombination rate coefficients for comparison with the experimental results. Resonant recombination originating from parent ions in the long-lived metastable state ions has been identified in the recombination spectrum below 1.25 eV. A good agreement is achieved between the experimental recombination spectrum and the result of the AUTOSTRUCTURE calculations when fractions of 95% ground-state ions and 5% metastable ions are assumed in the calculation. It is found that the calculated TR resonance positions agree with the experimental peaks, while the resonance strengths are underestimated by the theoretical calculation. Temperature dependent plasma rate coefficients for DR and TR in the temperature range of 103–108 K were derived from the measured electron–ion recombination rate coefficients and compared with the available theoretical results from the literature. In the temperature range of photoionized plasmas, the presently calculated rate coefficients and the recent results of Gu & Colgan et al. are up to 30% lower than the experimentally derived ones, and the older atomic data are even up to 50% lower than the present experimental result. This is because strong resonances situated below electron–ion collision energies of 50 meV were underestimated by the theoretical calculation, which also has a severe influence on the rate coefficients in low-temperature plasmas. In the temperature range of collisionally ionized plasmas, agreement within 25% was found between the experimental result and the present calculation as well as the calculation by Colgan et al. The present result constitutes a set of benchmark data for use in astrophysical modeling.

Investigations of the dielectronic recombination of phosphorus-like tin at CSRm**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300) and the Chinese Academy of Sciences and the National Natural Science Foundation of China (Grant Nos. U1732133, 11320101003, 11611530684, and 11604003).

The electron–ion recombination for phosphorus-like 112Sn35+ has been measured at the main cooler storage ring of the Heavy Ion Research Facility in Lanzhou, China, employing an electron–ion merged-beams technique. The absolute total recombination rate coefficients for electron–ion collision energies from 0 eV–14 eV are presented. Theoretical calculations of recombination rate coefficients were performed using the Flexible Atomic Code to compare with the experimental results. The contributions of dielectronic recombination and trielectronic recombination on the experimental rate coefficients have been identified with the help of the theoretical calculation. The present results show that the trielectronic recombination has a substantial contribution to the measured electron–ion recombination spectrum of 112Sn35+. Although a reasonable agreement is found between the experimental and theoretical results the precise calculation of the electron–ion recombination rate coefficients for M-shell ions is still challengeable for the current theory.

Dielectronic and Trielectronic Recombination Rate Coefficients of Be-like Ar 14+

Electron–ion recombination of Be-like 40Ar14+ has been measured by employing the electron–ion merged-beams method at the cooler storage ring CSRm. The measured absolute recombination rate coefficients for collision energies from 0 to 60 eV are presented, covering all dielectronic recombination (DR) resonances associated with 2s 2 → 2s2p core transitions. In addition, strong trielectronic recombination (TR) resonances associated with 2s 2 → 2p 2 core transitions were observed. Both DR and TR processes lead to series of peaks in the measured recombination spectrum, which have been identified by the Rydberg formula. Theoretical calculations of recombination rate coefficients were performed using the state-of-the-art multi-configuration Breit–Pauli atomic structure code AUTOSTRUCTURE to compare with the experimental results. The plasma rate coefficients for DR+TR of Ar14+ were deduced from the measured electron–ion recombination rate coefficients in the temperature range from 103 to 107 K, and compared with calculated data from the literature. The experimentally derived plasma rate coefficients are 60% larger and 30% lower than the previously recommended atomic data for the temperature ranges of photoionized plasmas and collisionally ionized plasmas, respectively. However, good agreement was found between experimental results and the calculations by Gu and Colgan et al. The plasma rate coefficients deduced from experiment and calculated by the current AUTOSTRUCTURE code show agreement that is better than 30% from 104 to 107 K. The present results constitute a set of benchmark data for use in astrophysical modeling.

Stationary afterglow measurements of the temperature dependence of the electron–ion recombination rate coefficients of and in He/Ar/H2/D2 gas mixtures at T = 80–145 K

We report measurements of the binary and ternary recombination rate coefficients of deuterated isotopologues of . A cavity ring-down absorption spectrometer was used to monitor the fractional abundances of , , and during the decay of a plasma in He/Ar// mixtures. A dependence of the measured effective recombination rate coefficients on the helium buffer gas density was observed and hence both the binary and the ternary recombination rate coefficients for and were obtained in the temperature range 80–145 K.

Photoionization and electron-ion recombination of Ti I

Study of the inverse processes of photoionization and electron-ion recombination of (Ti I + hν⇋ Ti II + e) using the unified method is reported. The method, based on close coupling (CC) approximation and R-matrix method, subsumes both the radiative recombination (RR) and dielectronic recombination (DR) in a unified manner and provides state-specific and total electron-ion recombination rate coefficients which are self-consistent with the state-specific photoionization cross sections. The present results include state-specific electron-ion recombination rates (αRC(i))and partial photoionization cross sections (σPI(i)) leaving the ion in the ground state of 813 bound states with n ≤ 10 and l ≤ 9 of Ti I. Various features of state-specific and total electron-ion recombination with temperature, and the corresponding photoionization cross sections with energies are discussed with illustrations. Due to closely lying excited states near the ground state of the core, photoionization cross sections show presence of narrow Rydberg resonances in low energy region near the ionization threshold. Many excited states also show broad and enhanced Seaton resonances due to PEC (photo-excitation-of-core) which contribute to the high temperature recombination. The total recombination rate coefficient is found to show a low hump around temperature 280 K and a high dielectronic recombination peak at temperature 25,000 K. Total spectrum of recombination cross sections and rates with photoelectron energy are also presented for experimental observation. Calculations were carried out using a CC wave function expansion of 36 states of the core ion Ti II. The large set of data for recombination rates and partial photoionization cross sections with resonances should provide a complete and accurate modelings of plasmas.

Dielectronic recombination of boronlike Si9+ ions at the heavy-ion storage ring TSR

Absolute electron-ion recombination rate coefficients of B-like Si9+ have been measured employing the merged-beams method at the storage ring TSR. Center-of-mass energies were studied over the range 0-50 eV, covering all dielectronic recombination (DR) resonances associated with electron excitations within the L-shell.

Ternary Recombination of H3+ and D3+ with Electrons in He–H2 (D2) Plasmas at Temperatures from 50 to 300 K

We present results of plasma afterglow experiments on ternary electron-ion recombination rate coefficients of H3(+) and D3(+) ions at temperatures from 50 to 300 K and compare them to possible three-body reaction mechanisms. Resonant electron capture into H3* Rydberg states is likely to be the first step in the ternary recombination, rather than third-body-assisted capture. Subsequent interactions of the Rydberg molecules with ambient neutral and charged particles provide the rate-limiting step that completes the recombination. A semiquantitative model is proposed that reconciles several previously discrepant experimental observations. A rigorous treatment of the problem will require additional theoretical work and experimental investigations.

Electron-ion recombination rate coefficients and photoionization cross-sections for Al XI, Al XII, Si XII, Si XIII for UV and X-ray modeling

Results are presented from detailed study of inverse processes of photoionization and electron-ion recombination of ( hν + Al XI ⇋ Al XII + e), ( hν + Al XII ⇋ Al XIII + e), ( hν + Si XII ⇋ Si XIII + e), and ( hν + Si XIII ⇋ Si XIV + e) using ab initio unified method. These are the first results on photoionization cross-sections ( σ PI( nSLJ)) with autoionizing resonances and level-specific recombination rate coefficients, incorporating both the radiative and dielectronic recombination, for these ions. All fine structure levels with n ⩽ 10 and 0 ⩽ l ⩽ 9 are considered. A total of 98 fine structure levels with 1/2 ⩽ J ⩽ 17/2 for Al XI and Si XII, and 190 for Al XII and 189 for Si XIII with 0 ⩽ J ⩽ 10 are found. σ PI( nSLJ) show background enhancements due to core excitations and narrow high-peak resonances. Level-specific recombination rates show smooth decay with a small bump at high temperature. Present total recombination rate coefficients with temperature ( α R( T)) show good agreement with available rates. Recombination rates over photoelectron energy ( α R( E)) are presented for astrophysical and laboratory plasma applications. Total recombination rates for H-like Al XIII and Si XIV are given for completeness. Calculations are carried out in the relativistic Breit-Pauli R-matrix method using coupled channel wavefunctions. Inclusion of important atomic effects such as radiation damping, channel couplings, interference of DR and RR, and relativistic fine structure effects should provide accuracy within 10–15%. The comprehensive datasets are applicable for various models such as for ionization balance and recombination-cascade for UV and X-ray lines.

Spectroscopic study of doubly excited states in Mg-like Si using dielectronic recombination

We present calculated and experimentally derived electron–ion recombination rate coefficients for Na-like Si IV, recombining into Mg-like Si III, and provide accurate spectroscopic data for doubly excited states located above the ionization threshold of Si III. The experimental recombination rate coefficients were measured in a merged-beam-type experiment at the heavy-ion storage ring CRYRING at the Manne Siegbahn Laboratory in Stockholm. Changing the electron–ion relative energy from 0 to 20 eV we covered the energy region from the first to the third ionization threshold. We find that even for the low-charged Si2+ ion, a relativistic many-body perturbation theory calculation is necessary, to describe the recombination rate coefficients in the low-energy region, up to 1.5 eV, satisfactorily. Doubly excited states, forbidden to form in LS coupling, are responsible for the most prominent dielectronic recombination resonances at low energies and contribute with 40% to the strength. Several wide resonances give rise to a plateau-like formation in the recombination spectrum. A broader energy range, up to 6.7 eV, was covered with a non-relativistic many-body calculation. This range contains, in addition to 3pnℓ resonances, several resonances of the type 3dnℓ, with the LS-forbidden 3d23F states giving rise to a strong, isolated peak at 2.976 eV. The NIST database lists eleven doubly excited states of Si III with energy positions deviating considerably from our determination. Since the listed lines are also not fully matching those with the largest fluorescence yields it must be concluded that they are misidentified.

Electron-Ion Recombination Measurements Motivated by AGN X-Ray Absorption Features: Fe xiv Forming Fe xiii

Recent spectroscopic models of active galactic nuclei (AGN) have indicated that the recommended electron-ion recombination rate coefficients for iron ions with partially filled M-shells are incorrect in the temperature range where these ions form in photoionized plasmas. We have investigated this experimentally for Fe XIV forming Fe XIII. The recombination rate coefficient was measured employing the electron-ion merged beams method at the Heidelberg heavy-ion storage-ring TSR. The measured energy range of 0-260 eV encompassed all dielectronic recombination (DR) 1s2 2s2 2p6 3l 3l' 3l'' nl''' resonances associated with the 3p1/2 -> 3p3/2, 3s -> 3p, 3p -> 3d and 3s -> 3d core excitations within the M-shell of the Fe XIV 1s2 2s2 2p6 3s2 3p parent ion. This range also includes the 1s2 2s2 2p6 3l 3l' 4l'' nl''' resonances associated with 3s -> 4l'' and 3p -> 4l'' core excitations. We find that in the temperature range 2--14 eV, where Fe XIV is expected to form in a photoionized plasma, the Fe XIV recombination rate coefficient is orders of magnitude larger than previously calculated values.

Time-resolved measurements of ionization and vibration-to-electronic energy transfer in optically pumped plasmas

A method for direct measurements of electron number density, ionization rate, and the electron–ion recombination rate coefficient in optically pumped non-equilibrium plasmas has been developed. In this method, a pulsed, non-self-sustained discharge created by applying square-shaped, below breakdown voltage pulses to two electrodes placed outside the plasma (a Thomson probe) is used to remove electrons from the plasma. The electron number density is inferred for CO/Ar and CO/N2 optical mixtures with small amounts of O2 additive present. The results are compared with microwave attenuation measurements. The electron–ion recombination rate coefficients in CO/Ar/O2 and in CO/N2/O2 plasmas are β = (3–4) × 10−8 cm3 s−1 and β = (2–3) × 10−7 cm3 s−1, respectively. Time-dependent measurements of the electron concentration and vacuum ultraviolet radiation (CO fourth positive system) are used to study the mechanism of CO(A1Π) population in the optically pumped plasma. The experimental results are compared with kinetic modelling calculations. The results systematically show that the intensity of the CO fourth positive radiation closely follows the electron number density in the laser-excited plasma region after the Thomson probe voltage is turned on or off. This demonstrates that electrons play a major role in the excitation of the A1Π electronic state of CO and provides additional evidence that vibrational-to-electronic (V–E) energy transfer in plasmas sustained without external electric fields is mediated by collisions with electrons.

New Radiative Atomic Data

AbstractLarge amount of new radiative atomic data for I) energy levels, II) oscillator strengths (f), line strengths (S), radiative transition probabilities (A), III) photoioniztion cross sections (σPI) – total and level-specific, and IV) unified total and level-specific electron-ion recombination rate coefficients, αR, including radiative and dielectronic recombination (RR and DR) are reported for various astrophysical applications. Most of the data are with fine structure. These data are not yet available from any databases. Photoionization and recombination data are self-consistent, using the same wave-function for both processes.

Interference effects in the photorecombination of argonlikeSc3+ions: Storage-ring experiment and theory

Absolute total electron-ion recombination rate coefficients of argonlike Sc3+(3s2 3p6) ions have been measured for relative energies between electrons and ions ranging from 0 to 45 eV. This energy range comprises all dielectronic recombination resonances attached to 3p -> 3d and 3p -> 4s excitations. A broad resonance with an experimental width of 0.89 +- 0.07 eV due to the 3p5 3d2 2F intermediate state is found at 12.31 +- 0.03 eV with a small experimental evidence for an asymmetric line shape. From R-Matrix and perturbative calculations we infer that the asymmetric line shape may not only be due to quantum mechanical interference between direct and resonant recombination channels as predicted by Gorczyca et al. [Phys. Rev. A 56, 4742 (1997)], but may partly also be due to the interaction with an adjacent overlapping DR resonance of the same symmetry. The overall agreement between theory and experiment is poor. Differences between our experimental and our theoretical resonance positions are as large as 1.4 eV. This illustrates the difficulty to accurately describe the structure of an atomic system with an open 3d-shell with state-of-the-art theoretical methods. Furthermore, we find that a relativistic theoretical treatment of the system under study is mandatory since the existence of experimentally observed strong 3p5 3d2 2D and 3p5 3d 4s 2D resonances can only be explained when calculations beyond LS-coupling are carried out.

Electron‐Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. III. Si‐Sequence Ions: Si i , S iii , Ar v , Ca vii , and Fe xiii

Photoionization cross sections, σPI, and electron-ion recombination rate coefficients, αR, for silicon-like ions are calculated. Calculations are carried out in the close coupling approximation using the R-matrix method. Each ion has a large number of bound states with n ≤ 10 and l ≤ 9: 433 for Ar V, 631 for Ca VII, and 1223 for Fe XIII. Both the partial photoionization cross sections leaving the core ion in the ground state and the total cross sections for ionization in the ground state as well as the excited core states are obtained for all bound states. The electron-ion recombination rates are obtained using a unified method, based on the close coupling R-matrix method, that incorporates both the radiative and dielectronic recombination processes in a self-consistent and unified manner. Total recombination rate coefficients are presented for a wide range of temperatures for practical applications. State-specific recombination rate coefficients for individual bound states are also presented. Results of Si I and S III, derived from earlier works, are also presented for completeness.

Electron‐Ion Recombination Rate Coefficients, Photoionization Cross Sections, and Ionization Fractions for Astrophysically Abundant Elements. I. Carbon and Nitrogen

We present a comprehensive and self-consistent set of new atomic data for ionization balance in radi- atively and collisionally ionized astrophysical plasmas. Complex resonant phenomena resulting in rapid energy variation in the cross sections for photoionization and recombination require accurate and large- scale calculations, as reported. Another new development is the consideration of the uni-ed nature of the recombination process in an ab initio manner, via resonances embedded in the electron-ion continua, which have been heretofore considered as separate processes of radiative recombination and dielectronic recombination. A single set of total electron-ion recombination rate coefficients is thereby obtained as a function of electron temperature. The present calculations also meet the hitherto neglected, but theoreti- cally essential, criterion of self-consistency between the rates for the inverse processes of photoionization and recombination, ensured by describing all atomic processes with an identical set of eigenfunction expansion within the close-coupling approximation using the R-matrix method. Photoionization cross sections and total electron-ion recombination rate coefficients for the carbon and nitrogen isonuclear sequences, C IEC VI and N IEN VII, are presented. Ionization fractions in coronal equilibrium are also computed. The present photoionization cross sections have been calculated using more extensive eigen- function expansions than those in the Opacity Project. In addition to the total photoionization and recombination data, state-speci-c cross sections are also obtained for a large number of excited states for non-LTE models. Complete data sets are available electronically. Subject headings: atomic data E atomic processes E plasmas