Dielectronic Recombination Cross Sections Research Articles

Dielectronic recombination in O4+ near the ionization threshold

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

Enhancement of electron–ion recombination rates at low energy range in the heavy ion storage ring CSRm**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300) and the National Natural Science Foundation of China (Grant Nos. U1932207, 11904371, and U1732133).

Recombination of Ar14+, Ar15+, Ca16+, and Ni19+ ions with electrons has been investigated at low energy range based on the merged-beam method at the main cooler storage ring CSRm in the Institute of Modern Physics, Lanzhou, China. For each ion, the absolute recombination rate coefficients have been measured with electron–ion collision energies from 0 meV to 1000 meV which include the radiative recombination (RR) and also dielectronic recombination (DR) processes. In order to interpret the measured results, RR cross sections were obtained from a modified version of the semi-classical Bethe and Salpeter formula for hydrogenic ions. DR cross sections were calculated by a relativistic configuration interaction method using the flexible atomic code (FAC) and AUTOSTRUCTURE code in this energy range. The calculated RR + DR rate coefficients show a good agreement with the measured value at the collision energy above 100 meV. However, large discrepancies have been found at low energy range especially below 10 meV, and the experimental results show a strong enhancement relative to the theoretical RR rate coefficients. For the electron–ion collision energy below 1 meV, it was found that the experimentally observed recombination rates are higher than the theoretically predicted and fitted rates by a factor of 1.5 to 3.9. The strong dependence of RR rate coefficient enhancement on the charge state of the ions has been found with the scaling rule of q3.0, reproducing the low-energy recombination enhancement effects found in other previous experiments.

KLL dielectronic recombination of hydrogenlike carbon ion in Debye plasmas

The KLL dielectronic recombination (DR) process of C5+ ion embedded in Debye plasmas is investigated using the multiconfiguration Dirac-Fock method with the Debye-Hückel model potential. The resonance energies, radiative and Auger rates as well as DR cross sections are obtained for a large range of Debye screening parameters to explore the influences of the plasma screening on the KLL DR process of C5+ ion. It is found that the total radiative rates and Auger rates of the intermediate states both decrease monotonically with increasing the plasma screening, except the Auger rate for the transition 2p2 1S → 1s that changes nonmonotonically due to such screening imposed on the interaction between the configurations 1s and 2s in C5+ ion. Moreover, for the KLL DR process, blueshift and redshift phenomena are observed for the resonance energies, which originates from the dynamic variations of the energy levels of C4+ and C5+ ions in the Debye plasma. The magnitudes of the DR cross section decrease slightly when the Debye-screening effects are not so strong.

Influence of Debye Plasma on the KLL Dielectronic Recombination of H-Like Helium Ions**Supported by the National Key Research and Development Program of China under Grant No 2017YFA0402300, and the National Natural Science Foundation of China under Grant Nos 11864036, 11564036 and 11774292.

Using the Debye shielding model, the effects of plasma shielding on the dielectronic recombination processes of the H-like helium ions are investigated. It is found that plasma shielding causes a remarkable change in the Auger decay rate of the doubly excited 2p2 3P2 state. As a result, the dielectronic recombination cross sections from the doubly excited 2p2 3P2 state increases with the decreasing Debye shielding length.

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.

State-selective quantum interference studied in the photo-recombination of Ar17+ ion

We investigate the total and partial cross sections of the state-selective photo-recombination (PR) from the ground state 1sS01 of H-like Ar17+ ion to the 1s2S01, 1s2sS01,S13 and 1s2pP0,1,23,P11 states of He-like Ar16+ ion. The analysis is performed based on the close-coupling approximation and the fully relativistic Dirac R-matrix method, in which the unified treatments of the combined electron-ion PR process, including radiative and dielectronic recombination (DR) as coherent, interfering components are considered. The KLL PR resonance group are determined and identified according to the calculated energies and transition rates using the multiconfiguration Dirac–Fock (MCDF) method. The DR cross sections are also presented for comparison purposes. Our results show that the quantum interference between direct recombination and resonant recombination processes will strongly influence the intensity and shape of the PR cross sections, especially for the 2s2pP11 and 2p2D21 resonant regions. Comparison of our computed results with previously published experimental and theoretical values, when available, is made.

Triply excited states in dielectronic recombination with excited He-like uranium

We study process of dielectronic recombination with He-like uranium initially being in one of the metastable states $[{(1s2s)}_{0}$ and ${(1s2{p}_{1/2})}_{0}]$. We consider resonant regions of the incident electron energy corresponding to participation of triply excited states of Li-like uranium. The total and differential cross sections for dielectronic recombination as well as the energies and widths of the autoionizing states are calculated accurately within the QED theory. The cross section of the considered process is comparable in order of magnitude with the cross section of dielectronic recombination with H-like or He-like uranium initially being in the ground states. We investigated the contribution of the Breit interaction to the cross section; in particular, we found that the Breit interaction may both significantly increase and decrease the cross section.

Calculation of differential cross section for dielectronic recombination with two-electron uranium

Calculation of the differential cross section for the dielectronic recombination with two-electron uranium within the framework of QED is presented. The polarization of the emitted photon is investigated. The contributions of the Breit interaction and the interference of the photon multipoles are studied.

Effects of radiation damping on photorecombination ofC4+ions for theKLLresonance

A numerical method based on Zabaydullin and Dubau's work [O. Zabaydullin and J. Dubau, J. Phys. B: At. Mol. Opt. Phys. 45, 115002 (2012)] has been developed to calculate the Cauchy principal value integral in scattering matrices and obtain photorecombination (PR) cross sections of low-lying resonances according to Davies and Seaton's theory [J. Phys. B 2, 757 (1969)], in which radiation damping is included. The Dirac $R$-matrix method is employed to secure the dipole matrix. Using this method, PR cross sections of ${\mathrm{C}}^{4+}$ for the KLL resonance are acquired, and compared with available experimental measurements and other close-coupling theoretical results. It is shown that our damped cross sections reproduce the experimental data and are in agreement with other theoretical results. Meanwhile, radiation damping can reduce the PR cross section for the $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{2}P$ resonance (corresponding to two levels ${[{(1s2{p}_{1/2})}_{1}2{p}_{3/2}]}_{1/2}$ and ${[1s{(2{p}_{3/2}^{2})}_{2}]}_{3/2}$ by three orders of magnitude. The unresolved and underestimated resonances $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{4}P, 1s2s2p\phantom{\rule{4pt}{0ex}}^{4}P$, and $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{2}P$ in the undamped Breit-Pauli $R$-matrix calculations [H. L. Zhang et al., J. Phys. B: At. Mol. Opt. Phys. 32, 1459 (1999)] are corrected. Besides, dielectronic recombination cross sections of ${\mathrm{C}}^{4+}$ for the KLL resonance are also presented for comparison using the relativistic configuration-interaction (RCI) method implemented in flexible atomic code (fac), which show radiation damping has pronounced influences on $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{2}P$ due to much larger radiative rates compared with autoionization rates. Furthermore, radiative and autoionization rates for the intermediate states ${[{(1s2{p}_{1/2})}_{1}2{p}_{3/2}]}_{1/2}$ and ${[1s{(2{p}_{3/2}^{2})}_{2}]}_{3/2}$ of the He-like ions with $6\ensuremath{\le}\phantom{\rule{4pt}{0ex}}Z\ensuremath{\le}83$ are calculated using fac, scaling laws of which are checked. Autoionization rates comply with the ${Z}_{\mathrm{eff}}^{0}$ scaling law for $Z\ensuremath{\ge}32$, which is caused by relativistic effects.

Electron Impact Excitation and Dielectronic Recombination of Highly Charged Tungsten Ions

Electron impact excitation (EIE) and dielectronic recombination (DR) of tungsten ions are basic atomic processes in nuclear fusion plasmas of the International Thermonuclear Experimental Reactor (ITER) tokamak. Detailed investigation of such processes is essential for modeling and diagnosing future fusion experiments performed on the ITER. In the present work, we studied total and partial electron-impact excitation (EIE) and DR cross-sections of highly charged tungsten ions by using the multiconfiguration Dirac–Fock method. The degrees of linear polarization of the subsequent X-ray emissions from unequally-populated magnetic sub-levels of these ions were estimated. It is found that the degrees of linear polarization of the same transition lines, but populated respectively by the EIE and DR processes, are very different, which makes diagnosis of the formation mechanism of X-ray emissions possible. In addition, with the help of the flexible atomic code on the basis of the relativistic configuration interaction method, DR rate coefficients of highly charged W37+ to W46+ ions are also studied, because of the importance in the ionization equilibrium of tungsten plasmas under running conditions of the ITER.

Calculation of differential cross section for dielectronic recombination with one-electron uranium

Calculation of the differential cross section for the dielectronic recombination with one-electron uranium within the framework of QED is presented. The contribution of the QED corrections and the interference of the photon multipoles is investigated.

Calculation of differential cross section for dielectronic recombination with one-electron uranium

Calculation of the differential cross section for the dielectronic recombination with one-electron uranium within the framework of QED is presented. The contribution of the QED corrections and the interfernce of the photon multipoles is investigated.

Importance of the Breit interaction for calculation of the differential cross section for dielectronic recombination with one-electron uranium

Calculation of the differential cross section for dielectronic recombination with one-electron uranium within the framework of quantum electrodynamics is presented. The dielectronic recombination of nonpolarized and polarized incident electrons is considered. The polarization of the emitted photon is investigated. The contributions of the Breit interaction and the interference of the photon multipoles are studied.

Comparison between leaky and pulsed modes of ion extraction from an electron beam ion trap

We present the charge state distributions of highly charged ions extracted from an electron beam ion trap (EBIT). The distributions were obtained in the two different extraction modes, pulsed mode and leaky mode. The number ratio between adjacent charge state ions, which is an important quantity to measure dielectronic recombination cross sections with an EBIT, is compared between the two extraction modes. The results are also compared with recent theoretical predictions by Zhang et al. [17].

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.

KLL dielectronic recombination resonance strengths in He- to O-like gold ions

We present experimental observation of the dielectronic recombination (DR) in He- to O-like gold ions performed with the Tokyo electron beam ion trap (EBIT). In the experiment, the abundance ratios between adjacent ions in the EBIT have been obtained as a function of electron energy by measuring the number of extracted ions from the EBIT. The DR cross sections are deduced from the degree of the abundance ratio change at the resonance energy. The experimental DR resonance strengths are compared with fully relativistic calculations.

Electron-Ion Collision Studies with Highly Charged Sulfur Ions

We have obtained dielectronic recombination (DR) cross sections for H-like and He-like S, using the Stockholm Refrigerated Electron Beam Ion Trap (R-EBIT). The experimental results are compared with a calculation for the resonance positions and strengths and show good agreement within the error bars, but also deviations in some cases.

Dielectronic recombination and resonant transfer excitation processes for helium-like krypton

The relativistic configuration interaction method is employed to calculate the dielectronic recombination (DR) cross sections of helium-like krypton via the 1s2lnl′ (n = 2, 3, …, 15) resonances. Then, the resonant transfer excitation (RTE) processes of Kr34+ colliding with H, He, H2, and CHx (x = 0−4) targets are investigated under the impulse approximation. The needed Compton profiles of targets are obtained from the Hartree—Fock wave functions. The RTE cross sections are strongly dependent on DR resonant energies and strengths, and the electron momentum distributions of the target. For H2 and H targets, the ratio of their RTE cross sections changes from 1.85 for the 1s2l2l′ to 1.88 for other resonances, which demonstrates the weak molecular effects on the Compton profiles of H2. For CHx (x = 0−4) targets, the main contribution to the RTE cross section comes from the carbon atom since carbon carries 6 electrons; as the number of hydrogen increases in CHx, the RTE cross section almost increases by the same value, displaying the strong separate atom character for the hydrogen. However, further comparison of the individual orbital contributions of C(2p, 2s, 1s) and CH4(1t2, 2a1, 1a1) to the RTE cross sections shows that the molecular effects induce differences of about 25.1%, 19.9%, and 0.2% between 2p−1t2, 2s−2a1, and 1s−1a1 orbitals, respectively.

Electron–ion recombination of H- and He-like sulfur

Electron–ion recombination of sulfur ions with electrons in the energy range of 1.6–3 keV was studied at the Stockholm Refrigerated Electron Beam Ion Trap. We obtained the KLn dielectronic recombination (DR) cross sections up to n = 5 for H-like and He-like sulfur ions by observing the x-rays from the trapped ions. A fully relativistic distorted wave approximation method was used for calculating the DR cross sections, while the resonance energies were obtained with a multiconfiguration Dirac–Fock approach using the GRASP II code. The calculations agree with the experimental results within the experimental error bars. Additionally, the obtained total DR resonance strengths were used to check the behaviour of a scaling formula for low-Z, He-like iso-electronic sequence (Watanabe et al 2001 J. Phys. B: At. Mol. Opt. Phys. 34 5095).

Detection of trielectronic recombination of In+ ion

The trielectronic recombination of an In+ (4d105s21S0) ion in collisions with slow electrons, including the two-electron excitation of the 5s2 core of the ion with the simultaneous capture of the triply excited 5p3 intermediate autoionizing state with its subsequent radiative stabilization 5p3 → 5s5p2 + hν has been detected and experimentally examined for the first time. The maximum effective cross section of trielectronic recombination is 1.6 × 10−16 cm2, which is comparable to the effective cross sections for both dielectronic recombination and electron excitation of the In+ ion.