Total Recombination Rate Coefficients Research Articles

Total and state-specific electron-ion recombination rates and photoionization of Ca XV for high temperature plasma

The inverse processes of photoionization and electron-ion recombination of (Ca XV + hν↔ Ca XVI + e), are studied using the unified method of Nahar and Pradhan for a large number of bound states, 582 in total with n≤10 and l≤9, for their characteristic features particularly in the high energy region that can impact plasmas at high temperature. The unified method which implements close-coupling (CC) approximation and the R-matrix method includes both the radiative recombination (RR) and dielectronic recombination (DR) for the total recombination and yields self-consistent sets of results for both the inverse processes. The present study, carried out in large scale computations, employs a large CC wavefunction expansion of 29 LS states belonging to n=2,3 complexes of the core ion Ca XVI, and appeared to be the first detailed study for the electron-ion recombination of the ion. The present results include (i) state-specific photoionization cross sections (σPI(nLS)) leaving the core ion in the ground state, (ii) state-specific recombination rate coefficients (αRC(nLS,T)) that include both the RR and DR, (iii) total recombination rate coefficients (αRC) with temperature that include contributions of infinite number of recombined states, and (iv) a spectrum of total electron-ion recombination cross sections and rates with respect to photoelectron energy. The study finds that the core ion excitations from the ground to high n=3 states have introduced Rydberg resonances which are stronger and Seaton resonances which are more enhanced in the high energy region of σPI compared to those introduced by excitations to the n=2 states. Such features have contributed to the shape of the temperature dependent state-specific αRC(nLS,T), and have resulted in three DR bumps/ shoulders in the high temperature region of the total αRC(T) where the third DR bump at temperature of ∼ 4 MK has raised αRC(T) at high T above all previous rates. The results are expected to be accurate within 10%–15% and provide more complete and precise spectral modelings for the high temperature plasmas where the highly charged Ca XV is more abundant.

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.

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 recombination of the open 4d-shell of tungsten: W37+–W28+

Tungsten is an important element for magnetically confined fusion plasmas but has the potential to cool, or even quench the plasma due to it being an efficient radiator. Total and level-resolved dielectronic recombination (DR) rate coefficients, for all ionisation stages, are essential to model tungsten. We describe a set calculations performed using the distorted wave code autostructure for the tungsten ions –. We demonstrate the importance of relativistic configuration mixing in such calculations. In particular, we show that the partial DR rate coefficients calculated in level and configuration resolution can differ by as little as 5%, and up to as much as 75%. Using the new data, we calculate a revised steady-state ionisation fraction for tungsten. We find that, relative to the ionisation fraction calculated using the recombination rate coefficients of Putterich et al (2008 Plasma Phys. Control. Fusion 50 085016), the peak temperatures of – ionisation states are shifted to lower temperatures spanning 0.9–1.6 keV. This temperature range is important for understanding the performance of large tokamaks, such as ITER, because the temperatures in the pedestal, edge, scrape-off-layer and divertor region fall in this range.

Inelastic processes in collisions of lithium positive ions with hydrogen anions and atoms

Inelastic processes in the low-energy collisions Li3+ + H−, Li2+ + H, Li2+ + H- and Li+ + H are investigated for all collisional channels with the excited ionic lithium states Li2+ (nl) and Li+ (1s nl) up to and including the corresponding ion-pair states for the temperature range 1000–20 000 K. For all possible processes in the Li3+ + H- and Li2+ + H collisions inelastic cross sections and rate coefficients are calculated for the transitions between the ion-pair channel Li3+ + H- and the 35 below lying contributing Li2+ (nl) + H channels. It is found that the highest values of cross sections and rate coefficients are obtained for the recombination processes and their inverse, the ion-pair formation processes, involving the Li2+ (3l), Li2+ (4l), and Li2+ (5l) states. For the processes in the Li2+ + H- and Li+ + H collisions, cross sections and rate coefficients are calculated for all transitions between 34 Li+ (1s nl) + H channels lying below Li2+ + H- plus this ion-pair channel. In this case the highest rate coefficients correspond to the recombination processes with the Li+(1s3l1,3L) and Li+(1s4l1,3L) final states, as well as their inverse processes of ion-pair production. Rate coefficient values for these most efficient processes are rather high, of the order of 10−8 cm3/s. This leads to total recombination rate coefficients in Li3+ + H- and Li2+ + H- collisions with values larger than 10−7 cm3/s.Graphical abstract

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.

Calculation of Photo-Ionisation Cross Sections and Radiative Recombination Rate Coefficients for CO and CO+ Molecules

A method based upon the weighted total cross section (WTCS) theory is proposed to calculate the photo-ionisation cross sections and the radiative recombination rate coefficients between the fundamental level of CO and the main electronic states of its corresponding ion. Total photo-ionisation cross sections and radiative recombination rate coefficients are determined from the calculation of elementary vibrational photo-ionisation cross sections. Transitions between CO+(X, A and B) and CO(X) are considered. Total photo-ionisation cross sections and recombination coefficients are computed in the temperature interval 500–15000 K.

Dielectronic recombination experiment of P-like Tin on HIRFL-CSRm at Lanzhou

Total recombination rate coefficients of 112Sn35+ ions have been firstly measured by employing the electron-ion merged-beams technique on the main cooler storage ring at Lanzhou. Using an electron beam energy detuning system, we precisely tuned the relative energies from 0 to 6.0 eV between the electron beam and the ion beam (momentum spread Δp/p ~ 5 × 10−4). A multi-configuration Breit-Pauli calculation utilizing kappa-averaged relativistic orbitals has been carried-out for the recombination rate coefficients. We find that there are obvious differences between the experimental total rate coefficients and the theoretical calculations.

Photoionization and electron–ion recombination of He I

Results from the unified method for photoionization and electron–ion recombination of ( He I + h ν ↔ He II + e ) are presented. He I wave function is represented by an expansion that includes 10 core states for excitations to n = 2, 3, and 4 states. A total of 99 bound LS states with n ⩽ 10 are obtained. They all, except two, agree with the observed energies in less than 1%. Photoionization cross sections σ PI for the total ionization, leaving the residual ion in all excited states, and the partial ionization, leaving the ion in the ground state, are presented for all 99 bound states. Calculated σ PI agree very well with the measured ground state cross section. Detailed resonant features of σ PI and coupling effects on the background cross sections are illustrated. For the recombination process, state-specific and total recombination rate coefficients are presented. These include both the radiative and dielectronic recombination processes. In addition, the total recombination spectrum with electron energy is presented and exhibits the resonant features that were observed experimentally. Recombination rates for hydrogenic He II is also presented. The present results obtained in LS coupling approximation provide a unified and self-consistent sets of results for astrophysical modelings of the two inverse radiative processes until highly accurate and precise results will be available through comprehensive relativistic calculations.

Radiative recombination rate coefficients for highly-charged tungsten ions

Partial and total radiative recombination rate coefficients are presented for highly-charged ions of tungsten with closed shells, W 28 + , W 38 + , W 46 + , W 56 + , W 64 + , W 70 + , and W 72 + , as well as for the H-like ion W 73 + and the bare nucleus W 74 + . The temperature range 10 3 – 10 10 K is considered. Calculations have been performed in the framework of the fully relativistic Dirac–Fock treatment of photoionization and radiative recombination processes taking into account all significant multipoles of the radiation field. We assess the influence of multipole effects on recombination rate coefficients as compared with the commonly used dipole approximation. For the first time, we show that the relativistic Maxwell–Boltzmann distribution of continuum electrons should be used at high temperature. This decreases the rate coefficient significantly compared to the nonrelativistic distribution.

Electron–ion recombination and photoionization of Fe XXI

Results for electron–ion recombination and photoionization of ( Fe XXI + h ν ↔ Fe XXII + e ) , with emphasis in high-temperature region, are presented from ab initio unified method. The unified method, based on close coupling (CC) approximation and R-matrix method, (i) subsumes both the radiative recombination (RR) and dielectronic recombination (DR), (ii) enables self-consistent sets of photoionization and recombination cross sections from using an identical wavefunction for both the processes, and (iii) provides state-specific recombination rates of a large number of bound states. A large CC wavefunction expansion, which includes the ground and 28 core excitations of n = 2 and 3 complexes and span a wide energy range, has been used. Compared to Δ n = 2 – 2 , Δ n = 2 – 3 core excitations are found to introduce strong resonant structures and enhance the background photoionization cross sections ( σ PI ) in the high-energy region. These features along with prominent photoexcitation-of-core (PEC) resonances at n = 3 core thresholds have increased the unified total recombination rate coefficients ( α R ( T ) ) at temperatures T > 10 6 K , region of maximum abundance of the ion in collisional equilibrium, by a factor of 1.6 over previous calculations. State-specific recombination rate coefficients α R ( nLS ) , which include both the RR and DR, are presented for the first time for 685 bound states with n ⩽ 10 and l ⩽ 9 . The unified total recombination rate with photoelectron energy α R ( E ) is presented and the role of low-energy near-threshold fine structure resonances is illustrated. The present results should provide a reasonably complete self-consistent set of recombination rates and photoionization cross sections for astrophysical modelings of high-temperature plasmas from optical to far-ultraviolet wavelength regions.

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.

Electron-Iron Recombination Rate Coefficients and Photoionization Cross Section for S XIV and SXV for X-ray and UV modeling

The inverse processes of photoionization and electron-ion recombination of (hv + S XIV 1:::; S XV + e) and (hv + S XV =r SXVI+ e) are studied in detail using ab initio unified method that provides self-consistent sets ofresults for these processes. Results are presented for large number of fine structure levels where n S 10 and 0 ~ l ~ 9; 98 levels for Li-Iike S XIV with 1/2 S J ~. 17/2 and 188 levels for He-like S XV with 0 ::;J ~ 10. Photoionization cross section, O'PI, of the levels of both S XIV and S XV decay smoothly in the lower region. However, narrow and high peak autoionizing Rydberg series of resonances belonging to various excited core levels appear in the high energy region and enhance the background cross section of the excited levels. The resonance series of n=2 core levels dominate while they become weaker with higher n. The prominent feature is the enhancement of the background cross section at n=2 core thresholds due toK-shell ionization leaving the ion in excited 2p states. 0' PI also show wide PEe (photo-excitation-of-core) resonances at the photon energies that equal to the core excitation energies. Level-specific photoionization cross sections, O'PJ(nSLJ), and recombination rate coefficients, QRc(nSLJ), are obtained for the first time for theseions. Currently available results correspond to photoionization for L8 terms with missing features and to only total recombination rate coefficients. Present QRc(nSLJ) incorporates both the radiative recombination. (RR) and dielectronic recombination (DR), and show a 'bump' or 'shoulder' in the high temperature region due to DR dominance. The total unified recombination rate coefficients show good agreement with the availableRR and DR rates. Recombination rates over photoelectron energy are presented for astrophysical and laboratory plasma applications. Total recombination rates for H-like S XVI are given for completeness. The results should be accurate within 10-15% based on the unified method that includes important atomic effects such as radiation damping, channel couplings, interference of DR and RR, and relativistic fine structure effects. The comprehensive datasets are applicable for various models such as for ionization balance and recombination-cascade for UV'and X-ray lines.

Dielectronic recombination data for dynamic finite-density plasmas

We have calculated total and partial final-state level-resolved dielectronic recombination (DR) rate coefficients for the ground and metastable initial levels of 21 Mg-like ions between Al + and Xe 42+ . This is the final part of the assembly of a levelresolved DR database necessary for modelling dynamic finite-density plasmas within the generalized collisional-radiative framework. Calculations have been performed in both LS - and intermediate coupling, allowing for ∆n = 0a nd∆n = 1 core-excitations from ground and metastable levels. Complementary partial and total radiative recombination RR coefficients have been calculated for the same ions viz. Al + through Zn 18+ ,a s well as Kr 24+ ,M o 30+ ,a nd Xe 42+ . Fitting coefficients which describe the total RR and DR rate coefficients (separately) are also presented here. Results for a selection of ions from this sequence are discussed, and compared with existing theoretical and experimental results. A full set of results can be accessed from the Atomic Data and Analysis Structure (ADAS) database or from the Oak Ridge Controlled Fusion Atomic Data Center (http://www-cfadc.phy.ornl.gov/data_and_codes). The complexity of further M-shell sequences, both from the atomic and modelling perspectives, renders this juncture a natural conclusion for the assemblage of the partial database. Further M-shell work, has and will, focus more on total rate coefficients, rather than partials, at least in the medium term.

Dielectronic recombination of Fe13+: benchmarking the M-shell

We have carried-out a series of multi-configuration Breit–Pauli AUTOSTRUCTURE calculations for the dielectronic recombination of Fe13+. We present a detailed comparison of the results with the high-energy-resolution measurements reported recently from the Heidelberg heavy-ion Test Storage Ring by Schmidt et al. Many Rydberg series contribute significantly from this initial 3s23p M-shell ion, resulting in a complex recombination ‘spectrum’. While there is much close agreement between theory and experiment, differences of typically 50% in the summed resonance strengths over 0.1–10 eV result in the experimentally based total Maxwellian recombination rate coefficient being a factor of 1.52–1.38 larger than theory over 104–105 K, which is a typical temperature range of peak abundance for Fe13+ in a photoionized plasma. Nevertheless, the present theoretical recombination rate coefficient is an order of magnitude larger than that used by modellers to date. This may help explain the discrepancy between the iron M-shell ionization balance predicted by photoionization modelling codes, such as ION and CLOUDY, and that deduced from the iron M-shell unresolved-transition-array absorption feature observed in the x-ray spectrum of many active galactic nuclei. Similar data are required for Fe8+ through Fe12+ in order to remove the question mark hanging over the atomic data though.

Determination of the recombination rate coefficients for Na-like Si IV forming Mg-like Si III

Aims. Absolute, total recombination rate coefficients for Si iv were determined using the CRYRING heavy-ion storage ring.Calculated rate coefficients were used to estimate recombination into states ...

Dielectronic recombination data for dynamic finite-density plasmas

We have calculated total and final-state resolved partial dielectronic recombination (DR) rate coefficients for 32 H-like ions: He+ through Zn29+ plus Kr35+, Mo41+ and Xe53+. Breit–Pauli intermediate coupling calculations have been carried-out which allow for l-mixing within the He-like autoionizing complex. We discuss the comparison of these results with those of other workers, and with experiment. Fitting coefficients which describe the total DR rate coefficients are presented in this paper. A full set of partial results can be accessed from the Atomic Data and Analysis Structure (ADAS) database or from the Oak Ridge Controlled Fusion Atomic Data Center under http://www-cfadc.phy.ornl.gov/data_and_codes.

Electron‐Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. IX. Ni xxvi and Ni xxvii for Ultraviolet and X‐Ray Modeling

The inverse processes of photoionization and electron-ion recombination of (hnu + Ni XXVI --> Ni XXVII + e and (hnu + Ni XXVII --> Ni XXVIII + e) are studied using the unified method for the total recombination. The method subsumes both the radiative and di-electronic recombination processes and enables self-consistent sets of results for photoionization and electron-ion recombination by using the same wavefunction expansion. Photoionization cross sections (sigma_PI), recombination cross sections (sigma_{RC}), recombination collision strengths (Omega_{RC}), and recombination rate coefficients (alpha_{RC}) are obtained for ionization balance and spectral analysis of UV and X-ray lines. Level-specific photoionization cross sections and recombination rates are presented to enable accurate computation of recombination-cascade matrices for all fine structure levels n(SLJ) up to n <= 10: 98 bound fine structure levels of Ni XXVI with 0 <= l <= 9, 0 <= L <= 11, 1/2 <= J <= 17/2, and 198 levels of Ni XXVII with 0 <= l <= 9, 0 <= L <= 14, 0 <= J <= 10. Total alpha_{RC} for Ni XXVI and Ni XXVII are compared with the existing values with very good agreement. Total recombination rate coefficients for the hydrogen-like recombined ion, Ni XXVIII, are also presented. The calculations are carried out in relativistic Breit-Pauli R-matrix (BPRM) approximation with inclusion of radiation damping of resonances. With consideration of all details of the processes, the results, which include the level specific sigma_{PI} and alpha_{R} calculated for the first time, should be the most accurate for these ions.

Electron‐Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. VIII. Ar xiii with New Features

Ar xiii is found to be unique with new features in electron-ion recombination not seen in any other ion. The ion has been studied with the unified method, which provides a theoretically self-consistent set of atomic parameters for the inverse processes of photoionization and total electron-ion recombination. Unified method subsumes both the radiative recombination (RR) and dielectronic recombination (DR) within the framework of close-coupling formulations using the R-matrix method. A set of four DR ‘‘bumps,’’ two in the low-temperature and two in the high-temperature regions, is found to exist in the recombination rates of Ar xiv þ e ! Ar xiii. This is in contrast to two typical DR ‘‘bumps,’’ one at high temperature common for most ions and one at low temperature depending on the presence of near threshold autoionizing resonances in the bound-free process. Large-scale ab initio calculations have been carried out for photoionization and electron-ion recombination cross sections of Ar xiii. The ion is represented by a large close-coupling eigenfunction expansion of 37 core Ar xiv states from n ¼ 2 and 3 complexes. This enables core excitations of type n ¼ 0 and 1. The n ¼ 1 transitions have much higher radiative decay rates than those of n ¼ 0 and cause the fourth DR bump around 2 ;10 6 K. For a large number of bound states, Ar xiii exhibits more extensive resonant structures and wider PEC (photoexitation-of-core) resonances for n ¼ 3 core states than those of n ¼ 2 states. Hence, the high-energy regions of photoionization and recombination are dominated by these structures. A total of 684 bound states with valence electron n � 10 and l � 9 are found for Ar xiii. Total and partial photoionization cross sections of all bound states, state-specific recombination rates of 561 bound states, and total recombination rate coefficients at a large temperature range are presented for Ar xiii. Subject headingg atomic data — atomic processes

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.