Multiconfiguration Breit-Pauli Research Articles

Rate Coefficients for Dielectronic Recombination of Carbon-like 40Ca14+

Abstract Dielectronic recombination (DR) rate coefficients for carbon-like 40Ca14+ forming nitrogen-like 40Ca13+ have been measured using the electron–ion merged-beam technique at the heavy-ion storage ring CSRm at the Institute of Modern Physics in Lanzhou, China. The measured DR rate coefficients in the energy range from 0 to 92 eV cover most of the DR resonances associated with 2s 22p 2 → 2s 22p 2 and 2s 22p 2 → 2s2p 3 core transitions (ΔN = 0). Theoretical calculations of the DR cross sections were carried out by using two different state-of-the-art atomic theoretical techniques, multiconfiguration Breit–Pauli (MCBP) code AUTOSTRUCTURE and relativistic configuration interaction code FAC, to compare with the experimental rate coefficients. The theoretical calculations agree with the experimental results at collision energy higher than 10 eV. However, significant discrepancies of resonance energies and strengths can be found at collision energy below 8 eV. Temperature-dependent plasma recombination rate coefficients were derived from the measured DR rate coefficients in the energy range from 0.1 to 1000 eV and compared with the recommended atomic data from the literature. The theoretical data of Gu et al. and Zatsarinny et al. are 30% lower than the experimental results at the temperatures of photoionized plasmas, but have a very good agreement at the temperatures of collisionally ionized plasmas. Other previously published theoretical data of Jacobs et al. and Mazzotta et al. by using Burgess formula and LS-coupling calculations significantly underestimate the plasma rate coefficients in the low temperature range. The present results comprise a set of benchmark data suitable for astrophysical modeling.

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.

ELECTRON-ION RECOMBINATION OF Mg6 +FORMING Mg5 +AND OF Mg7 +FORMING Mg6 +: LABORATORY MEASUREMENTS AND THEORETICAL CALCULATIONS

We have measured electron-ion recombination for C-like Mg6 + forming Mg5 +, and for B-like Mg7 + forming Mg6 +. These studies were performed using a merged electron-ion beam arrangement at the TSR heavy ion storage ring located in Heidelberg, Germany. Both primary ions have metastable levels with significant lifetimes. Using a simple cascade model we estimate the population fractions in these metastable levels. For the Mg6 + results, we find that the majority of the stored ions are in a metastable level, while for Mg7 + the metastable fraction is insignificant. We present the Mg6 + merged beams recombination rate coefficient for DR via N = 2 → N' = 2 core electron excitations (ΔN = 0 DR) and for Mg7 + via 2 → 2 and 2 → 3 core excitations. Taking the estimated metastable populations into account, we compare our results to state-of-the-art multiconfiguration Breit-Pauli theoretical calculations. Significant differences are found at low energies where theory is known to be unreliable. Moreover, for both ions we observe a discrepancy between experiment and theory for ΔN = 0 DR involving capture into high-n Rydberg levels and where the stabilization is primarily due to a radiative transition of the excited core electron. This is consistent with previous DR experiments on M-shell iron ions which were performed at TSR. The large metastable content of the Mg6 + ion beam precludes generating a plasma recombination rate coefficient (PRRC). However, this is not an issue for Mg7 + and we present an experimentally derived Mg7 + PRRC for plasma temperatures from 400 K to 107 K with an estimated uncertainty of less than 27% at a 90% confidence level. We also provide a fit to our experimentally derived PRRC for use in plasma modeling codes.

ELECTRON-ION RECOMBINATION OF Fe XII FORMING Fe XI: LABORATORY MEASUREMENTS AND THEORETICAL CALCULATIONS

We have measured electron–ion recombination for Fe xii forming Fe xi using a merged-beam configuration at the heavy-ion storage ring TSR located at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany. The measured merged-beam recombination rate coefficient (MBRRC) for collision energies from 0 to 1500 eV is presented. This work uses a new method for determining the absolute MBRRC based on a comparison of the ion beam decay rate with and without the electron beam on. For energies below 75 eV, the spectrum is dominated by dielectronic recombination (DR) resonances associated with 3s → 3p and 3p → 3d core excitations. At higher energies, we observe contributions from 3 → N' and 2 → N' core excitation DR. We compare our experimental results to state-of-the-art multi-configuration Breit-Pauli (MCBP) calculations and find significant differences, both in resonance energies and strengths. We have extracted the DR contributions from the measured MBRRC data and transformed them into a plasma recombination rate coefficient (PRRC) for temperatures in the range of 103–107 K. We show that the previously recommended DR data for Fe xii significantly underestimate the PRRC at temperatures relevant for both photoionized plasmas (PPs) and collisionally ionized plasmas (CPs). This is contrasted with our MCBP PRRC results, which agree with the experiment to within 30% at PP temperatures and even better at CP temperatures. We find this agreement despite the disagreement shown by the detailed comparison between our MCBP and experimental MBRRC results. Last, we present a simple parameterized form of the experimentally derived PRRC for easy use in astrophysical modeling codes.

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.

Dielectronic recombination of argon-like ions

We present a theoretical investigation of dielectronic recombination (DR) of Ar-like ions that sheds new light on the behavior of the rate coefficient at low-temperatures where these ions form in photoionized plasmas. We provide results for the total and partial Maxwellian-averaged DR rate coefficients from the initial ground level of K II -- Zn XIII ions. It is expected that these new results will advance the accuracy of the ionization balance for Ar-like M-shell ions and pave the way towards a detailed modeling of astrophysically relevant X-ray absorption features. We utilize the AUTOSTRUCTURE computer code to obtain the accurate core-excitation thresholds in target ions and carry out multiconfiguration Breit-Pauli (MCBP) calculations of the DR cross section in the independent-processes, isolated-resonance, distorted-wave (IPIRDW) approximation. Our results mediate the complete absence of direct DR calculations for certain Ar-like ions and question the reliability of the existing empirical rate formulas, often inferred from renormalized data within this isoelectronic sequence.

Quantifying the strength and asymmetry of giant resonances in the photorecombination ofSc3+and the photoionization ofSc2+

We report on strong interference effects for the dominant, highly correlated, broad, and asymmetric 3p53d2(2F5/2,7/2o) giant resonances in the photorecombination of Sc3+. Using a nonorthogonal perturbative multiconfiguration Breit-Pauli approach, we present theoretical photorecombination cross sections that are in line with the Test Storage Ring measurements of Schippers et al. In order to reproduce the observed asymmetric resonance profiles near threshold, it was necessary to include resonance-continuum interference. Also, we present Sc2+ photoionization cross sections that agree with the Advance Light Source measurements of Schippers et al. This perturbative method is based on analytical expressions for the cross sections in terms of computed energies and transition rates, thereby directly determining resonance strengths and Fano asymmetry parameters. Of particular note, our reported absolute cross sections are in excellent agreement with experimental results, in contrast to all previous theoretical calculations. Furthermore, the apparent violation of the sum rule prediction, determined both from our integrated photoionization cross sections and from experimental results, is found to be due to radiative damping of narrow resonances.

ELECTRON-ION RECOMBINATION OF Fe X FORMING Fe IX AND OF Fe XI FORMING Fe X: LABORATORY MEASUREMENTS AND THEORETICAL CALCULATIONS

We have measured electron-ion recombination for Fe$^{9+}$ forming Fe$^{8+}$ and for Fe$^{10+}$ forming Fe$^{9+}$ using merged beams at the TSR heavy-ion storage-ring in Heidelberg. The measured merged beams recombination rate coefficients (MBRRC) for relative energies from 0 to 75 eV are presented, covering all dielectronic recombination (DR) resonances associated with 3s->3p and 3p->3d core transitions in the spectroscopic species Fe X and Fe XI, respectively. We compare our experimental results to multi-configuration Breit-Pauli (MCBP) calculations and find significant differences. From the measured MBRRC we have extracted the DR contributions and transform them into plasma recombination rate coefficients (PRRC) for astrophysical plasmas with temperatures from 10^2 to 10^7 K. This spans across the regimes where each ion forms in photoionized or in collisionally ionized plasmas. For both temperature regimes the experimental uncertainties are 25% at a 90% confidence level. The formerly recommended DR data severely underestimated the rate coefficient at temperatures relevant for photoionized gas. At the temperatures relevant for photoionized gas, we find agreement between our experimental results and MCBP theory. At the higher temperatures relevant for collisionally ionized gas, the MCBP calculations yield a Fe XI DR rate coefficent which is significantly larger than the experimentally derived one. We present parameterized fits to our experimentally derived DR PRRC.

Resonance asymmetry and external field effects in the photorecombination ofTi4+

We report on multiconfiguration Breit-Pauli calculations for the photorecombination of ${\mathrm{Ti}}^{4+}$ ions. Through a detailed comparison with the Test Storage Ring measurements of Schippers et al., we quantify the interference effects for the broad, asymmetric, near-threshold, highly correlated $3{p}^{5}3{d}^{2}(^{2}F)$ resonances. We also discuss the enhanced field ionization effects on recombined $3{p}^{6}n\mathcal{l}$ Rydberg states. This is due to the perturbation of the below-threshold tails of two of the broad $3{p}^{5}3{d}^{2}(^{2}F)$ resonances, giving rise to a ``forced autoionization'' phenomenon, increasing the field ionization effects. By accounting for interference for the lowest $n=3,4$ resonances, and field effects as $n\ensuremath{\rightarrow}\ensuremath{\infty}$, excellent agreement between our computed results and the experimental photorecombination spectrum is obtained.

Nonmonotonic behavior as a function of nuclear charge of theK-shell Auger and radiative rates and fluorescence yields along the1s2s22p3isoelectronic sequence

Calculations using multiconfiguration Breit-Pauli and multiconfiguration Dirac-Fock methodologies have revealed that the radiative and Auger rates, and the associated fluorescence yields, of the six electron $1s2{s}^{2}2{p}^{3}$ $K$-shell vacancy isoelectronic sequence exhibit nonmonotonic behavior as a function of nuclear charge $Z$. This behavior is explained in terms of an accidental degeneracy, an avoided crossing of two nearly degenerate spin-orbit coupled levels. The results also demonstrate the importance of including both electron-electron correlation and spin-orbit effects even at low $Z$.

Inclusion of Electric Octupole Contributions Explains the Fast Radiative Decays of Two Metastable States inAr+

A laser probing investigation has yielded the lifetimes of the 3s(2)3p(4)(1D)3d (2)G(7/2,9/2) metastable doublet states of Ar+. The results, obtained with the CRYRING ion storage ring of Stockholm, are 3.0+/-0.4 and 2.1+/-0.1 s, respectively. Comparisons with theoretical values calculated with two independent theoretical approaches, i.e., the pseudorelativistic Hartree-Fock method and the multiconfiguration Breit-Pauli approach, have allowed us to establish the unexpected and extraordinary strong contribution of an electric octupole (E3) transition to the ground state, in addition to the M1 decay channels to the 3d ;{2,4}F states and the E2 contributions to the 4s 2P, 2D states.

Dielectronic Recombination of FexvForming Fexiv: Laboratory Measurements and Theoretical Calculations

We have measured resonance strengths and energies for dielectronic recombination (DR) of Mg-like Fe XV forming Al-like Fe XIV via N = 3 → N' = 3 core excitations in the electron-ion collision energy range 0-45 eV. All measurements were carried out using the heavy-ion test storage ring at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany. We have also carried out new multiconfiguration Breit-Pauli (MCBP) calculations using the AUTOSTRUCTURE code. For electron-ion collision energies 25 eV we find poor agreement between our experimental and theoretical resonance energies and strengths. From 25 to 42 eV we find good agreement between the two for resonance energies. But in this energy range the theoretical resonance strengths are ≈31% larger than the experimental results. This is larger than our estimated total experimental uncertainty in this energy range of ±26% (at a 90% confidence level). Above 42 eV the difference in the shape between the calculated and measured 3s3p(1P1)nl DR series limit we attribute partly to the nl dependence of the detection probabilities of high Rydberg states in the experiment. We have used our measurements, supplemented by our AUTOSTRUCTURE calculations, to produce a Maxwellian-averaged 3 → 3 DR rate coefficient for Fe XV forming Fe XIV. The resulting rate coefficient is estimated to be accurate to better than ±29% (at a 90% confidence level) for kBTe ≥ 1 eV. At temperatures of kBTe ≈ 2.5-15 eV, where Fe XV is predicted to form in photoionized plasmas, significant discrepancies are found between our experimentally derived rate coefficient and previously published theoretical results. Our new MCBP plasma rate coefficient is 19%-28% smaller than our experimental results over this temperature range.

Dielectronic Recombination of FexxiiiForming Fexxii: Laboratory Measurements and Theoretical Calculations

We have measured resonance strengths and energies for dielectronic recombination (DR) of beryllium-like Fe XXIII forming boron-like Fe XXII via N = 2 -> N' = 2 and N = 2 -> N' = 3 core excitations. All measurements were carried out using the heavy-ion Test Storage Ring at the Max Planck Institute for Nuclear Physics (MPI-K) in Heidelberg, Germany. We have also calculated these resonance strengths and energies using three independent, perturbative, state-of-the-art theoretical techniques: the multiconfiguration Breit-Pauli (MCBP) method, the multiconfiguration Dirac-Fock (MCDF) method, and the Flexible Atomic Code (FAC). Overall reasonable agreement is found between our experimental results and these theoretical calculations. We have used our measurements to produce a Maxwellian-averaged DR rate coefficient for Fe XXIII. Our experimentally derived rate coefficient is estimated to be accurate to better that approximate to 20%. At temperatures where Fe XXIII is predicted to form in both photo-ionized and electron-ionized gas, we find mixed agreement between our experimental rate coefficient and previously published rate coefficients. We find good agreement at these temperatures between the experimentally derived rate coefficient and our MCBP, MCDF, and FAC results.

Dielectronic Recombination of Fe xxi and Fe xxii via N = 2→ N ′ = 2 Core Excitations

We have measured dielectronic recombination (DR) resonance strengths and energies for carbon-like Fe XXI forming Fe XX and for boron-like Fe XXII forming Fe XXI via N = 2 → N' = 2 core excitations. All measurements were carried out using the heavy-ion Test Storage Ring at the Max-Planck-Institute for Nuclear Physics in Heidelberg, Germany. We have also calculated these resonance strengths and energies using three independent, state-of-the-art perturbative techniques: a multiconfiguration Breit-Pauli (MCBP) method using the code AUTOSTRUCTURE, a multiconfiguration Dirac-Fock (MCDF) method, and a relativistic configuration interaction method using the Flexible Atomic Code (FAC). Overall, reasonable agreement is found between our experimental results and our theoretical calculations. The most notable discrepancies tend to occur for relative collision energies 3 eV. We have used our measured 2 → 2 results to produce Maxwellian-averaged rate coefficients for Fe XXI and Fe XXII. Our experimentally derived rate coefficients are estimated to be accurate to better than ≈20% both for Fe XXI at kBTe > 0.5 eV and for Fe XXII at kBTe > 0.001 eV. For these results, we provide fits that are accurate to better than 0.5% for Fe XXI at 0.001 eV ≤ kBTe ≤ 10,000 eV and for Fe XXII at 0.02 eV kBTe ≤ 10,000 eV. Our fitted rate coefficients are suitable for ionization balance calculations involving Fe XXI and Fe XXII in photoionized plasmas. Previous published Burgess formula and LS-coupling calculations are in poor agreement with our experimentally derived rate coefficients. None of these published calculations reliably reproduce the magnitude or temperature dependence of our experimental results. Our previously published Fe XXI MCDF results are in good agreement with our experimental results for kBTe 0.07 eV. For both ions in this temperature range our new MCBP, MCDF, and FAC results are in excellent agreement with our experimentally derived rate coefficient.

Dielectronic Recombination of FexixForming Fexviii: Laboratory Measurements and Theoretical Calculations

We have measured resonance strengths and energies for dielectronic recombination (DR) of Fe XIX forming Fe XVIII via N = 2 → N' = 2 and N = 2 → N' = 3 core excitations. All measurements were carried out using the heavy-ion Test Storage Ring at the Max Planck Institute for Nuclear Physics in Heidelberg, Germany. We have also calculated these resonance strengths and energies using two independent, state-of-the-art techniques: the perturbative multiconfiguration Breit-Pauli (MCBP) and multiconfiguration Dirac-Fock (MCDF) methods. Overall, reasonable agreement is found between our experimental results and theoretical calculations. The most notable discrepancies are for the 3l3l' resonances. The calculated MCBP and MCDF resonance strengths for the n = 3 complex lie, respectively, ≈47% and ≈31% above the measured values. These discrepancies are larger than the estimated 20% total experimental uncertainty in our measurements. We have used our measured 2 → 2 and 2 → 3 results to produce a Maxwellian-averaged rate coefficient for DR of Fe XIX. Our experimentally derived rate coefficient is estimated to be good to better than ≈20% for kBTe ≥ 1 eV. Fe XIX is predicted to form in photoionized and collisionally ionized cosmic plasmas at kBTe 1 eV. Hence, our rate coefficient is suitable for use in ionization balance calculations of these plasmas. Previously published theoretical DR rate coefficients are in poor agreement with our experimental results. None of these published calculations reliably reproduce the magnitude or temperature dependence of the experimentally derived rate coefficient. Our MCBP and MCDF results agree with our experimental rate coefficient to within ≈20%.

Dielectronic Recombination in Photoionized Gas. II. Laboratory Measurements for Fe xviii and Fe xix

In photoionized gases with cosmic abundances, dielectronic recombination (DR) proceeds primarily via nlj → nl′j′ core excitations (n = 0 DR). We have measured the resonance strengths and energies for Fe XVIII to Fe XVII and Fe XIX to Fe XVIII n = 0 DR. Using our measurements, we have calculated the Fe XVIII and Fe XIX n = 0 DR rate coefficients. Significant discrepancies exist between our inferred rates and those of published calculations. These calculations overestimate the DR rates by factors of ∼ 2 or underestimate it by factors of ∼ 2 to orders of magnitude, but none are in good agreement with our results. Almost all published DR rates for modeling cosmic plasmas are computed using the same theoretical techniques as the above-mentioned calculations. Hence, our measurements call into question all theoretical n = 0 DR rates used for ionization balance calculations of cosmic plasmas. At temperatures where the Fe XVIII and Fe XIX fractional abundances are predicted to peak in photoionized gases of cosmic abundances, the theoretical rates underestimate the Fe - 2 - XVIII DR rate by a factor of ∼ 2 and overestimate the Fe XIX DR rate by a factor of ∼ 1.6. We have carried out new multiconfiguration Dirac-Fock and multiconfiguration Breit-Pauli calculations which agree with our measured resonance strengths and rate coefficients to within typically better than ∼ < 30%. We provide a fit to our inferred rate coefficients for use in plasma modeling. Using our DR measurements, we infer a factor of ∼ 2 error in the Fe XX through Fe XXIV n = 0 DR rates. We investigate the effects of this estimated error for the well-known thermal instability of photoionized gas. We find that errors in these rates cannot remove the instability, but they do dramatically affect the range in parameter space over which it forms.

Low-energy recombination of

Low-energy recombination of has been measured at the storage ring CRYRING with a high-energy precision of 15 meV. Using different electron currents the approach for correcting the variation of the ion energy due to the drag force was checked. A multi-configuration Breit-Pauli perturbation calculation using the program AUTOSTRUCTURE for the dielectronic recombination rates has been implemented. The cut-off of Rydberg states by field ionization in the analysing magnet was modified by taking radiative cascade into account. Comparison of this calculation with the measurement shows a good agreement in resonance strength but a small discrepancy in resonant energy. At very low energy, the non-resonant recombination rate is found to be a factor of 2 higher than the estimated radiative recombination rate. No indication of an electron density dependence is found.

Recombination studies of highly charged ions in the cooler ring CRYRING

Cooler-storage ring facilities offer unique experimental possibilities for studies of electron-ion recombination processes at low relative energies by employing the electron cooler as a target. Through the use of an adiabatically expanded electron beam in the cooler of CRYRING, collisions down to 10−4 eV relative energies were measured with highly charged ions stored in the ring at around 15 MeV/amu energies. Examples of recombination measurements for C4+ and Ar15+ ions at an energy resolution of as low as 10−2 eV FWHM are presented and compared with calculations of the energies and resonance strength for dielectronic recombination using multiconfiguration Breit-Pauli approximations. They agree in spectral shape and absolute cross section but show some deviation for lower n in the Rydberg series.

Dielectronic recombination of boronlike argon.

We present measurements and calculations of \ensuremath{\Delta}n=0 dielectronic recombination resonances of boronlike argon between 0.2 and 6 eV. A storage ring equipped with an electron cooler was used for the measurements. Methods employed to reduce the electron energy distribution and improve the accuracy of resonance energy measurements have yielded an energy resolution of 30 meV full width at half maximum at low energies, and an energy uncertainty better than 30 meV. The high energy resolution results from the use of an adiabatic expansion technique to reduce the transverse electron energy distribution. The improved accuracy in energy determinations is achieved through the inclusion of variations in the ion velocity, which occur during scans of the electron velocity, in the relative velocity transformations. Calculations of the resonance strengths and energies were made using two different methods, multiconfiguration Dirac-Fock and multiconfiguration Breit-Pauli approximations. A comparison of the experimental data to the calculations shows fair agreement in both the spectral features and integrated intensities above 3 eV. However, poor agreement is found below 3 eV. \textcopyright{} 1996 The American Physical Society.