Dielectronic Recombination Rate Coefficients Research Articles

Dielectronic recombination rate coefficients of initially rubidium-like tungsten

Ab initio calculations of dielectronic recombination (DR) rate coefficients of initially rubidium-like W37+ ions have been performed for the electron temperatures from 1 eV to 5 × 104 eV, by using the Flexible Atomic Code based on the relativistic configuration-interaction method. Special attention has been paid to the partial contributions to total DR rate coefficients as associated with the excitation of individual subshells. A detailed comparison of the calculations shows that the excitation from 4p subshell dominates total DR rate coefficients followed by the excitations from 4s and 4d subshells, while the contribution of excitations from 3l(l = s, p, d) subshells becomes important only at high temperatures. Besides, it is found that the electron excitations associated with △n = 0,1 dominate at low-temperature plasmas, however, the excitations associated with △n ≥ 2 become non-negligible at high-temperature ones.

Dielectronic recombination of berylliumlike Xe50+ ions: Measurement and theoretical calculations

Absolute rate coefficients for dielectronic recombination (DR) of Be-like 136Xe50+ have been measured at the heavy-ion storage ring ESR. The experimental results are compared with relativistic distorted-wave calculations employing the multiconfiguration Dirac-Fock method. Based on the DR measurements, multiple intra-L-shell excitation energies were determined.

Dielectronic recombination of lithiumlike Xe51+ ions: Storage ring experiment and theoretical calculations

Absolute rate coefficients for dielectronic recombination (DR) of Li-like 136Xe51+ have been measured at the heavy-ion storage ring ESR. The experimental results are compared with relativistic distorted-wave calculations employing the multiconfiguration Dirac-Fock method. Based on the DR measurements the 2s-2p1/2 and 2s-2p3/2 excitation energies in Li-like Xe51+ were determined with a relative accuracy of ~400 ppm.

Dielectronic recombination of the 4p and 4d open sub-shell tungsten ions

Dielectronic recombination rate coefficients are given theoretically for several highly charged tungsten ions. As 4p open sub-shell ions, Ga-, Ge-, As-, Br-, Kr-like ions are considered. Rb-like ion is further considered as a 4d open sub-shell ion. Theoretical calculations are carried out using a relativistic atomic code FAC. The effect of configuration interaction is taking into account. Inner-shell electron excitations play a significant role for the dielectronic recombination process. Simple analytical formulae are given for the total rate coefficients by fitting to the presently obtained numerical results.

Suppression of Dielectronic Recombination at Finite Densities

Density-dependent effective dielectronic recombination rate coefficients are determined in order to explore finite-density effects on the ionization balance of plasmas.

Dielectronic Recombination of Br-Like Tungsten Ions

Accurate data for dielectronic recombination of tungsten ions are essential in the modeling of tungsten impurity transport and radiative power loss in International Thermonuclear Experimental Reactor (ITER). Theoretical calculations have been made for dielectronic recombination (DR) rate coefficients of Br-like tungsten ions using a flexible relativistic atomic code (FAC) from 1 eV to 50 keV. Level-by-level calculations are carried out for evaluating the contributions to DR through all the relevant Kr-like tungsten ions autoionizing inner-shell excited configuration complexes: (3s23p63d10)−14s24p5nln′l′ (n = 4–5, n′ = 4–100, l′ = 0–8), (4s24p5)−1 nln′l′ (n = 4–6, n′ = 4–100, l′ = 0–12). Comparison of the rate coefficients for 3s, 3p, 3d, 4s and 4p subshell excitations shows that the 4p subshell excitation dominates over the whole temperature region, 4s subshell excitation at low temperature and 3p, 3d subshell excitations at high temperature can not be neglected. In order to facilitate simple applications, the total DR rate coefficient, Δn = 0, 1 and 2 core excitations DR rate coefficients are fitted to an empirical formula.

SUPPRESSION OF DIELECTRONIC RECOMBINATION DUE TO FINITE DENSITY EFFECTS

We have developed a general model for determining density-dependent effective dielectronic recombination (DR) rate coefficients in order to explore finite-density effects on the ionization balance of plasmas. Our model consists of multiplying by a suppression factor those highly-accurate total zero-density DR rate coefficients which have been produced from state-of-the-art theoretical calculations and which have been benchmarked by experiment. The suppression factor is based-upon earlier detailed collision-radiative calculations which were made for a wide range of ions at various densities and temperatures, but used a simplified treatment of DR. A general suppression formula is then developed as a function of isoelectronic sequence, charge, density, and temperature. These density-dependent effective DR rate coefficients are then used in the plasma simulation code Cloudy to compute ionization balance curves for both collisionally ionized and photoionized plasmas at very low (ne = 1 cm^-3) and finite (ne=10^10 cm^-3) densities. We find that the denser case is significantly more ionized due to suppression of DR, warranting further studies of density effects on DR by detailed collisional-radiative calculations which utilize state-of-the-art partial DR rate coefficients. This is expected to impact the predictions of the ionization balance in denser cosmic gases such as those found in nova and supernova shells, accretion disks, and the broad emission line regions in active galactic nuclei.

Investigation of dominant states in the collisions of Ar VII and Kr XXIV with H_2 and He targets

In thermal plasma, the ion--atom collisions proceed most probably through resonance processes. One of the important processes is the resonant transfer excitation followed by emission of X-rays (RTEX), which causes self-cooling for plasma. In addition, it is identical to the dielectronic recombination (DR) in electron-ion collisions. The present work deals with the calculation of DR cross-sections (\sigma^{DR}s) and DR rate coefficients (\alpha^{DR}s) as well as RTEX cross-sections (\sigma^{RTEX}s) for Mg-like ions [Ar^{6+} and Kr^{24+}] with L-shell and K-shell excitation for \Deltan = 0 and \Delta n \neq 0. Comparison between the present results and other calculations for the rates are presented. RTEX cross-sections are calculated for the collision of Ar^{6+} and Kr^{24+} ions with He and H_2 targets. The calculations are carried out using the adapted angular momentum average scheme in the isolated resonance approximation.

Storage ring meets astrophysics: Dielectronic recombination of L-shell and M-shell iron ions

A status report is given on an ongoing experimental effort to provide reliable rate coefficients for dielectronic recombination of highly charged iron ions for the modeling of astrophysical and other plasmas. The experimental work has been carried out at the Heidelberg heavy-ion storage-ring TSR.

Dielectronic recombination of metastable berylliumlike xenon ions

Absolute rate coefficients for dielectronic recombination of Be-like Xe50+ have been measured by employing the electron-ion merged beam technique at GSI's heavy-ion storage ring ESR in the center-of-mass energy range 0 – 600 eV. In addition to ground state ions, resonances from metastable Xe50+ (2s2p3P0) parent ions have been observed. These may be exploited in future measurements of the E1M1 two photon 2s2p3P0 → 2s2 1S0 transition rate.

Breit interaction in dielectronic recombination of H-like uranium

Absolute rate coefficients for dielectronic recombination (DR) of hydrogenlike U91+ have been measured at GSI's heavy-ion storage ring ESR in the center-of-mass energy range 63–90 keV. We find an excellent agreement between the measured DR rate coefficients and theoretical results from multi-configuration Dirac-Fock theory which includes the Breit interaction. The latter contributes nearly one half to the total resonance strengths of the KL1/2L1/2 and KL1/2M1/2 resonance groups.

Effects of configuration interaction for dielectronic recombination of Na-like ions forming Mg-like ions

Dielectronic recombination (DR) of Na-like ions forming Mg-like ions via excitation of a 2l core electron has been investigated for selected ions from Ca9+ to Zn19+. We find that configuration interaction (CI) between DR resonances with different captured electron principal quantum numbers n can lead to a significant reduction in resonance strengths for n ≳ 5. We also explored the effect of this multi-n CI for the total DR rate coefficient. DR rate coefficients can be reduced by up to ∼ 10% at temperatures where an ion is predicted to form in collisional ionization equilibrium and up to ∼ 15% at higher temperatures.

ELECTRON–ION RECOMBINATION RATE COEFFICIENTS FOR C II FORMING C I

We have determined absolute dielectronic recombination rate coefficients for C II, using the CRYRING heavy-ions storage ring. The resonances due to 2s-2p (▵n = 0) core excitations are detected in the center-of-mass energy range of 0-15 eV. The experimental results are compared with intermediate coupling AUTOSTRUCTURE calculations. Plasma rate coefficients are obtained from the DR spectrum by convoluting it with a Maxwell-Boltzmann energy distribution for temperatures in the range of 103-106 K. The derived temperature-dependent plasma recombination rate coefficients are presented graphically and parameterized by using a fit formula for convenient use in plasma modeling codes. The experimental rate coefficients are also compared with the theoretical data available in literature. In the temperature range of 103-2 × 104 K, our experimental results show that previous calculations severely underestimate the plasma rate coefficients and also our AUTOSTRUCTURE calculation does not reproduce the experimental plasma rate coefficients well. Above 2 × 104 K, the agreement between the experimental and theoretical rate coefficients is much better, and the deviations are smaller than the estimated uncertainties.

Dielectronic recombination of Rh-like Gd and W

Ab initio calculations of dielectronic recombination rate coefficients of Rh-like gadolinium and tungsten have been performed. Energy levels, radiative transition probabilities, and autoionization rates of Pd-like gadolinium and tungsten for [Zn]4${p}^{6}$4${d}^{8}$4fnl, [Zn]4${p}^{6}$4${d}^{8}$5${l}^{\ensuremath{'}}$$nl$, [Zn]4${p}^{6}$4${d}^{8}$6${l}^{\ensuremath{'}}$$nl$ and [Zn]4${p}^{5}$4${d}^{10}nl,$ [Zn]4${p}^{5}$4${d}^{9}$4fnl, [Zn]4${p}^{5}$4${d}^{9}$5${l}^{\ensuremath{'}}$$nl$, [Zn]4${p}^{5}$4${d}^{9}$6${l}^{\ensuremath{'}}$$nl$ ($n$ \ensuremath{\leqslant} 18) complexes were calculated using the flexible atomic code. The contributions from resonant and nonresonant radiative stabilizing transitions to the total rate coefficients are discussed. Results show that the contributions from nonresonant radiative stabilizing transitions are significantly enchanced for W when compared with Gd as a result of lowering of energy levels relative to the ionization limit. In addition, the widely used Burgess-Merts semiempirical formula may underestimate the dielectronic recombination rate coefficients in the temperature regions of interest. The present calculated rate coefficients are fitted to a semiemperical formula. The data obtained are expected to be useful for modelling plasmas both for extreme ultraviolet lithography source development and for fusion applications.

Excitation energies, radiative and autoionization rates, dielectronic satellite lines, and dielectronic recombination rates for excited states of Yb-like W

Energy levels, radiative transition probabilities and autoionization rates for [Cd]4f145p65l′nl, [Cd]4f145p66l″nl, [Cd]4f145p55d2nl, [Cd]4f145p55d6l″nl, [Cd]4f135p65d2nl and [Cd]4f135p65d6l″nl (l′ = d, f, g, l″ = s, p, d, l = s, p, d, f, g and n = 5–7) states of Yb-like tungsten (W4 +) are calculated using the relativistic many-body perturbation theory method (RMBPT code), the multiconfiguration relativistic Hebrew University–Lawrence Livermore Atomic Code (HULLAC code) and the Hartree–Fock relativistic method (COWAN code). Branching ratios relative to the [Cd]4f145p65d, [Cd]4f145p66s and [Cd]4f145p66p thresholds in Tm-like tungsten and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the singly excited, as well as non-autoionizing core-excited states in Yb-like tungsten. Contributions from the autoionizing doubly excited states [Cd]4f145p65fnl, [Cd]4f145p66l″nl and core-excited [Cd]4f145p55d2nl, [Cd]4f145p55d6l″nl, [Cd]4f135p65d2nl, [Cd]4f135p65d6l″nl states (with n up to 100), which are particulary important for calculating the total DR rates, are estimated. Synthetic dielectronic satellite spectra from Yb-like W are simulated in a broad spectral range from 200 to 1400 Å. These calculations provide recommended values critically evaluated for their accuracy for a number of W4 + properties useful for a variety of applications including for fusion applications.

Dielectronic recombination of Au20 +: a theoretical description of the resonances at low electron energies

In recent years, there has been significant interest in the dielectronic recombination (DR) of complex ions involving open d and open f subshells. Experimental measurement of DR in Au25 + (Hoffknecht et al 1998 J. Phys. B: At. Mol. Opt. Phys. 31 2415) and W20 + (Schippers et al 2011 Phys. Rev. A 83 012711), both with ground configurations of 4p64d104f8, revealed extremely large and broad resonances at low electron energies. DR in such ions is very difficult to describe in detail theoretically because of the complexity of the recombining resonant states and the source of these resonant structures has not been fully explained for the aforementioned ions. However, a very recent measurement of DR in Au20 + (Schippers et al 2011 Phys. Scr. T 144 014039) with a ground configuration of 4p64d104f13 displayed very large but narrower resonances in the low-energy region. With the somewhat reduced complexity of the recombining resonances in this ion, we have been able to complete the first full intermediate-coupling level-resolved DR calculation for Au20 +. In the low-energy region, we find excellent agreement with the experimental measurements, and have been able to show that the DR rate coefficient in this ion is completely dominated by Δn = 1 transitions and that the low-energy resonances are primarily due to recombining levels of the 4d104f125lnl′ configurations as suggested by Schippers et al (2011 Phys. Scr. T 144 014039) based on atomic structure calculations.

Dielectronic recombination of Pd-like gadolinium

As research and development of extreme ultraviolet lithography (EUVL) sources at 6.7 nm (which will be based on emission from ionized gadolinium) has already begun, reliable atomic data are required in order to determine the optimum plasma conditions. However, the complexity of the atomic structure means that ab initio level-resolved dielectronic recombination (DR) calculations are currently unavailable for the ions of interest. Here we report the first detailed calculation of the DR rate coefficients for the ground state and first excited states of Pd-like gadolinium. Energy levels, radiative transition probabilities, and autoionization rates of Ag-like gadolinium for [Kr]4${d}^{9}$4$fnl$, [Kr]4${p}^{5}$4${d}^{10}$4$fnl$, [Kr]4${d}^{9}$5$l$\ensuremath{'}$nl$, and [Kr]4${d}^{9}$6$l$\ensuremath{'}$nl$ ($n$ \ensuremath{\leqslant} 18) complexes were calculated using the flexible atomic code (FAC). It was found that inclusion of 4${p}^{5}$4${d}^{10}$4$fnl$ configurations has significant influence on the total DR rate coefficient. The DR rate coefficients obtained here are compared with radiative recombination and three-body recombination coeffcients. The results show that the DR rate coefficient is almost an order of magnitude higher than the coefficients for the other two recombination processes combined at plasma electron temperatures around 110 eV, which suggests that the DR process should be included in theoretical modeling for Pd-like gadolinium in EUVL source plasmas.

The study of dielectronic recombination (DR) rate coefficient for ground state of Ne-like isoelectronic sequence ions

The dielectronic recombination (DR) rate coefficients for Ne-like isoelectronic sequence ions in the ground state 2s22p6 are calculated by using relativistic configuration interaction (RCI) method over a wide temperature ranging from 0.1EI to 10EI where EI is the ionization energy of corresponding Na-like ion. The (2s2p)73ln'l', (2s2p)74l4l' and (2s2p)74l5l' complexes are considered as autoionizing doubly excited states of Ne-like ions in the calculation. The contribution of (2s2p)73ln'l' complex with l' >8 is found to be negligible. The contribution of high Rydberg states of (2s2p)73ln'l' complex obeys the complex-complex n'-3 extrapolation, and the larger the nuclear charge, the smaller the value of n' is. On the basis of the detailed level-by-level results, a general analytic formula for the total DR rate coefficient for all the ions along the Ne-like isoelectronic sequence is constructed. This formula can generally reproduce the calculated DR rate coefficients within 2% for electron temperature between 0.1EI and 10EI. Burgess-Merts semiempirical formula is found to be inadequate for predicting the DR rates of Ne-like ions at low electron temperatures (kTeEI) and may be used for high electron temperatures (kTe > 2EI).

Dielectronic recombination data for dynamic finite-density plasmas

Context. A comprehensive study of dielectronic recombination (DR) for the aluminum-like isoelectronic sequence has been completed. Aims. Total and final-state resolved DR rate coefficients for the ground and metastable initial levels of 17 ions between Si ii and Zn xviii are presented. Methods. Within an isolated-resonance, distorted-wave (IPIRDW) approximation, multiconfiguration Breit-Pauli (MCBP) calculations are carried out for the total and partial DR rate coefficients of Al-like ions. Both Δnc = 0 and Δnc = 1 core-excitations are included, using LS-coupled and intermediate-coupling (IC) schemes. Results. The inaccuracies of earlier empirical data and/or LS-coupling calculations, particularly at lower temperatures characteristic of photoionized plasmas, is demonstrated by comparison with present, state-of-the-art IC DR rate coefficients. Fine-structure effects are found to increase the DR rate coefficient at low temperatures and decrease it at high temperatures, rendering earlier LS calculations incomplete. Good agreement is found between present IC results and experimental measurements.

Relativistic calculations of dielectronic recombination and satellite lines of an Ar-like Ni ion

Dielectronic recombination (DR) plays an important role in understanding atomic processes and identifying spectra, including astrophysical and tokamak plasmas in particular. Because this process involves numerous singly- and doubly-excited autoionizing states, which merge with continuum states, it is challenging to calculate, and relativistic data for a lot of ions do not exist. This paper focuses on relativistic calculations of dielectronic recombination in Ar-like Ni and dielectronic satellite lines in K-like Ni. Specifically, energy levels, radiative transition probabilities and autoionization rates for the [Ne]3s23p53dnl (n = 4–7), [Ne]3s23p54l′nl (n = 4–7), [Ne]3s3p63dnl (n = 4–7), [Ne]3s3p64l′nl (n = 4–7), [Ne]3s23p55l′5l and [Ne]3s3p65l′5l states in K-like nickel (Ni9 +) are calculated by the Hartree–Fock relativistic method (Cowan code) and the relativistic many-body perturbation theory method (RMBPT code). In addition, these results are compared with atomic data from two more codes, HULLAC and FAC, as well as with the NIST data. DR rate coefficients are determined for the singly-excited [Ne]3s23p6nl,(n = 4–7), as well as non-autoionizing doubly-excited [Ne]3s23p53d2, [Ne]3s23p53d4l, [Ne]3s3p63d4s and [Ne]3s3p63d4p states. Contributions from the autoionizing doubly-excited states [Ne]3s23p53dnl and [Ne]3s3p63dnl (with n up to 500), which are very important for calculating total DR rates, are estimated. Synthetic dielectronic satellite spectra from K-shell Ni are simulated in a broad spectral range from 45 to 600 Å.