Close-coupling R-matrix calculations for electron-ion recombination cross sections

Results are presented for the inverse processes of photoionization and electron-ion recombination of (hν + Ne ↔ Ne + e) and (hν + Ne ↔ Ne + e) using the self-consistent unified method. The method employs an identical wave function expansion for both photoionization and recombination, and it includes both radiative and dielectronic recombination. Total, as well as level-specific, photoionization cross sections, σPI(E; nSLJ), and recombination rate coefficients, αR(T; nSLJ), are presented for all fine-structure levels up to n ≤ 10. These correspond to a total of 98 bound fine-structure levels of Ne VIII with 1/2 ≤ J ≤ 17/2, and 178 bound levels of Ne IX with 0 ≤ J ≤ 10. Total recombination cross sections and rates as functions of electron energy are also presented. The coupled channel wave function expansions for the core ions include 17 levels of Ne IX and 16 levels of Ne X. Relativistic fine structure is considered through the Breit-Pauli R-matrix (BPRM) method. The photoionization and recombination cross sections include important atomic effects such as radiation damping, channel coupling, and interference and should be of definitive accuracy. Level-specific σPI(nSLJ) and αR(T; nSLJ) are calculated for the first time. In addition, we describe the applicability of these comprehensive data sets to not only ionization balance and recombination-cascade models for astrophysical and laboratory plasmas, but also to (1) models of UV and X-ray lines in He-like ions from C V to Ne IX involving the 2 3P → 2 3S1 allowed triplet transitions in the UV, and 2(1P, 3P, 3S1) → 1 1S0 allowed, intercombination, and forbidden transitions in the X-ray, and (2) calculation of dielectronic satellite intensities from the highly resolved resonances in the unified recombination cross sections of He-like and Li-like ions through straightforward integration over a Maxwellian or other electron distribution functions.

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.

We present a formalism for cold and ultracold atom-diatom chemical reactions that combines a quantum close-coupling method at short-range with quantum defect theory at long-range. The method yields full state-to-state rovibrationally resolved cross sections as in standard close-coupling (CC) calculations but at a considerably less computational expense. This hybrid approach exploits the simplicity of MQDT while treating the short-range interaction explicitly using quantum CC calculations. The method, demonstrated for D+H$_2\to$ HD+H collisions with rovibrational quantum state resolution of the HD product, is shown to be accurate for a wide range of collision energies and initial conditions. The hybrid CC-MQDT formalism may provide an alternative approach to full CC calculations for cold and ultracold reactions.

We have observed x rays from the electron bombardment of heliumlike argon in the KSU EBIS ion source. The yield of x rays versus electron energy displays strong dielectronic recombination resonances and excitation thresholds. By normalizing to a single resonance strength, cross sections for dielectronic recombination and for 1s excitation are obtained from the data for different radiative decay channels. The results are in good agreement with theory.

Dielectronic recombination of Ni-, Cu-, and Ar-like tungsten and barium through the low inner-shell excited configurations including collision processes

Dielectronic recombination (DR) rate coefficients and cross sections are estimated for the ${\mathrm{O}}^{3+}$ ion where the 2s and 2p electrons of the initial state are excited to higher, n\ensuremath{\ge}3 states (\ensuremath{\Delta}${n}_{t}$\ensuremath{\ne}0 transitions) during the excitation-capture part of the process. This work completes the calculations of DR parameters for the ${\mathrm{O}}^{3+}$ ion, where the \ensuremath{\Delta}${n}_{t}$=0 part of this process had been reported recently. We found that the 2p electron excitation dominates the \ensuremath{\Delta}${n}_{t}$\ensuremath{\ne}0 process, while the 2s excitation is suppressed by the cascade corrections that strongly affect the intermediate states 1${s}^{2}$2s2p3snl and 1${s}^{2}$2s2p3dnl. The 2s contribution is approximately 15% of the \ensuremath{\Delta}${n}_{t}$\ensuremath{\ne}0 mode, while the total \ensuremath{\Delta}${n}_{t}$\ensuremath{\ne}0 contribution is roughly 10% of the \ensuremath{\Delta}${n}_{t}$=0 cross section.

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.

The radiation emitted from ions excited by a directed electron beam can be strongly linearly polarized. According to Itikawa, Srivastava, and Sakimoto [Phys. Rev. A. 44, 7195 (1991)] the degree of polarization should be independent of atomic number in an isoelectronic sequence when expressed as a function of incident-electron energy in threshold units. We used a distorted-wave computer code to calculate cross sections for electron-impact excitation to specific magnetic sublevels of H- and He-like ions with Z=13, 18, 22, 42, 56, 79, and 92. We found that the polarization of the resulting radiation is indeed independent of atomic number in the nonrelativistic limit. But when relativistic effects are properly taken into account, the polarization is markedly Z dependent. We show how the differences between the relativistic and nonrelativistic results vary with the incident-electron energy, as well as with increasing atomic number.

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.

We calculate the recombination spectra of the He-like ions He I, C V, N VI, O VII, Ne IX, Mg XI, Si XIII, S XV, Ar XVII, Ca XIX, and Fe XXV. We include the following physical processes: radiative recombination, dielectronic recombination, three-body recombination, electron impact ionization, and collisional excitation by electrons, protons, and α-particles. The calculations also account for the effects of lowering of the continuum at high densities and high-density corrections to dielectronic recombination. From the populations of all levels in the recombined ions, we construct models for He-like ions for fast computation of their spectra. Every model includes 29 bound levels up to n = 5, a pair of superlevels that account for radiative and collisional cascades from highly excited levels, six doubly excited levels that account for the most important satellite lines, and a level that represents the hydrogenic recombining ion. The models are constructed in a way that allows for the correct approach to LTE under appropriate conditions. These models can simultaneously solve for the H/He-like ionization balance in photoionized or collisionally ionized plasmas and compute emission spectra, including the combined effects of radiative and dielectronic recombination, collisional excitation, photoionization from excited levels, fluorescence, and line trapping. The models can be used for any temperature between 100 and 109 K and electron densities of up to 1018 cm-3. The models can be used easily within spectral modeling codes or as stand-alone tools for spectral analysis. We present comparisons between the results of the present models and previous work. Significant differences are found between the present effective recombination rate coefficients to the n = 2 and those of previous estimates. Later, we study various emission-line ratio diagnostics under collisional ionization and photoionized conditions.

In electron interactions with highly charged Fe ions, the X-ray spectra were theoretically analysed and compared with the experimental results at the Tokyo EBIT. In the present analysis, cross sections for dielectronic recombination, resonance excitation, resonance recombination, and direct excitation were calculated by use of the distorted wave method. Simulated spectra were obtained by convoluting the calculated cross sections with the experimental beam energy resolution and X-ray detector resolution, which are in close agreement with the experimental observations. Based on our calculations including polarization effects, we estimate the charge state balance: He-like Fe24+ (74%), Li-like Fe23+ (18%), and Be-like Fe22+ (8%), and the ion density in the trap to be 6.5−8.5 × 108 cm-3. The present calculations were also compared with the previous high-resolution measurements of the KLL resonances in He-like Fe ions.

Storage rings, a new tool for atomic physics

For the first time, absolute cross sections for electron-impact excitation of a multiply charged ion have been measured using an electron-energy-loss technique. Cross sections for e+${\mathrm{Si}}^{3+}$(3s $^{2}$${\mathit{S}}_{1/2}$)\ensuremath{\rightarrow}e+${\mathrm{Si}}^{3+}$(3p $^{2}$${\mathit{P}}_{1/2,3/2}$)-8.88 eV have been measured with an accuracy of \ifmmode\pm\else\textpm\fi{}20% (at 90% confidence level) over a narrow energy range (\ifmmode\pm\else\textpm\fi{}0.6 eV) about the threshold energy with an energy resolution of 0.2 eV. Results are in good agreement with close-coupling calculations.

An accurate knowledge of atomic collision processes is important for a better understanding of many astrophysical and laboratory plasmas. Collision databases which contain electron-impact excitation, ionization, and recombination cross sections and temperature dependent rate coefficients have been constructed using perturbative distorted-wave methods and non-perturbative R-matrix pseudo-states and time-dependent close-coupling methods. We present recent atomic collision results.

Crossed beams of electrons and ${\mathrm{Al}}^{2+}$ ions combined with fluorescence detection were used to measure the absolute cross section for electron-impact excitation of the ions to yield 186.3 nm and 185.5 nm photons from the $3s\ensuremath{-}3p$ transition. The measured cross section near the 6.7 eV threshold energy is about $16\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}{\mathrm{cm}}^{2},$ and some resonance structure near threshold is indicated. Total relative uncertainties $(1\ensuremath{\sigma})$ are typically about 6%, to be combined with an 11% absolute calibration uncertainty. Total uncertainties at high confidence level (90%) are around 20%, using a coverage factor of 1.7. Comparisons made with various theoretical calculations, specifically distorted wave and nine-state close coupling, show better agreement of experimental values with distorted wave calculations, with the measured values being higher near threshold than the most recent close-coupling calculations.