Relativistic Configuration Interaction Method Research Articles

Allowed and forbidden transition rates and corresponding wavelengths for Si-like Au ion (Au65+) by relativistic configuration interaction method

Large-scale atomic calculations are carried out to produce data of atomic structure and transitions rates for Si-like Au ion (Au65+). Generated atomic data are essential for modeling of M-shell spectra of gold ions in Au plasma, and fusion research. Energy levels are calculated by applying two methods: the relativistic configuration interaction method (RCI) of the flexible atomic code (FAC) and the multi-reference many body perturbation theory method (MR-MBPT). Energy levels, oscillator strengths, and transition rates are calculated for transitions between excited and ground states from n = 3l to n′l′, where n′ = 4, 5, 6, and 7; and l and l′ are the proper angular momenta of shells n and n′, respectively. The electric dipole (E1), electric quadrupole (E2), electric octupole (E3), magnetic dipole (M1), magnetic quadrupole (M2), and magnetic octupole (M3) transitions are all considered in the calculations. Correlation effects, relativistic effects, and QED effects are also included in the calculations. The two methods yield comparable values of energy levels. Data of energy levels of low-lying states and data for inner shell transitions reported in this study demonstrate good agreement with published experimental and theoretical data.

Relativistic large scale CI calculations of energies, transition rates and lifetimes in Ca-like ions between Co VIII and Zn XI

Energies, E1, E2 and M1 transition rates and lifetimes are reported for the lowest 134 fine-structure levels of the 3p63d2, 3p63d4s, 3p53d3 and 3p63d4p configurations in all Ca-like ions between Co VIII and Zn XI. The calculations have been performed using the multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods. Important core–valance and core–core electron correlation effects are systematically accounted with large scale configuration interaction expansion. The Breit interaction and leading quantum-electrodynamical (QED) contributions such as the vacuum polarization and self-energy corrections are also included in the RCI calculations. The results are compared with the compiled data from the NIST ASD and other calculations to evaluate the accuracy of the present calculations. Our results have good agreement with previous relativistic many-body perturbation theory (RMBPT) calculations and the data from the NIST ASD, except for Zn XI. Present calculations provide some missing data, especially for Cu X and Zn XI, in the NIST ASD.

Theoretical investigation of electron-ion recombination processes of Li-like tungsten ions

Dielectronic recombination (DR) and radiative recombination (RR) spectra of highly charged Tungsten ions are important for modeling and diagnosing magnetic fusion plasmas. We studied the DR process of Li-like W71+(2s) ions using the flexible atomic code (FAC) based on the relativistic configuration interaction (RCI) method with Breit and QED corrections. The detailed resonance energies, widths and strengths were calculated systematically for the dominated doubly excited states (2p1/2nlj)J(n=19∼29) and (2p3/2n′lj)J(n′=7∼29) of Be-like W70+ ions. The contributions from the higher Rydberg states with n=30∼ncut(ncut=116) are obtained by extrapolation based on the quantum defect theory (QDT). The electron-ion recombination spectra (DR+RR), covering the center-of-mass energy range 0–1700 eV, are presented by taking into account the electron beam temperature at the experimental cooler storage ring (CSRe). It is found that the DR resonances associated with 2s1/2 → 2p1/2 and 2s1/2 → 2p3/2 transitions are not blending for the whole Δn=0 collision energy range, which will provide a good chance for testing fundamental theory clearly by experimental investigation. Finally the plasma rate coefficients are deduced from the calculated recombination spectra in the temperature range from 5.0 × 103 to 1.0 × 108 K. Compared with the AUTOSTUCTURE results, a good agreement is obtained except for the DR rates at the low electron temperature (Te < 5.0 × 105K), which were mainly attributed to the difference of the first resonance group 2p1/219l. The present results will guide the DR experiment of Tungsten ions at the CSRe and also be useful for ITER fusion plasmas modeling.

Ground and low-lying excited states of DyCl studied by the four-component relativistic configuration interaction methods

The ground and low-lying excited states of the DyCl molecule are investigated by the four-component relativistic CI methods. Electronic states are classified into so-called families by applying the f-shell Omega decomposition method to the CI wavefunctions, and the characters of the states are clarified. The X7.5 ground state may be described as Dy+[(4f)9(6s)2]Cl−, but at large nuclear distance (R > 4.80 au), beyond the equilibrium nuclear distance (4.724 au), the dominant configuration changes to Dy+[(4f)10(6s)1]Cl−. The dominant configuration of Dy+[(4f)9(6s)2]F− is retained in DyF, but the dominant configuration in DyCl changes drastically as R increases. The calculated value (231 cm−1) of the vibrational frequency (ωe) agrees well with the value of 233 cm−1 observed by Linton et al. (J Mol Spectrosc 232:30–39, 2005). This low frequency reflects the weakness of the Cl− ligand compared to F−. The Y[0.15]8.5, Z[0.85]7.5, and [0.97] states observed by Linton et al. are found to have a dominant configuration of [(4f)10(6s)1], and the A[16.4]8.5 and B[15.4]Ω states observed both have (4f)10([6p1/2,1/2])1, belonging to different families. (The number in square brackets denotes the excitation energy in unit of k cm−1, and the number after a right square bracket denotes an Ω value.) The Ω value of the B[15.4]Ω state, which has not been determined experimentally, is calculated to be 6.5.

Energy Levels of Core-Excited 1s2l2l′ States in Lithium-Like Ions: Argon to Uranium

Energy levels and fine-structure intervals of the 1s2l2l′ core-excited states are calculated for ions along the Li isoelectronic sequence from argon to uranium. The calculation is performed by the relativistic configuration-interaction method adapted for treatment of autoionizing core-excited states. The calculational approach includes the relativistic treatment of the nuclear recoil effect, the leading quantum electrodynamics (QED) shifts as delivered by the model QED operator, and the frequency dependence of the Breit interaction. The 1s2l2l′–1s22l transition energies are obtained by combining the present results for the 1s2l2l′ states with energies of the 1s22l states compiled from previous calculations. All theoretical energies are supplied with uncertainty estimates. Our theoretical predictions for the 1s2l2l′–1s22l transitions are significantly more accurate than the best experimental results available today and can be used for calibrating experimental X-ray spectra.

Collisional radiative model for the M1 transition spectrum of the highly-charged W54+ ions

A detailed-level collisional-radiative model for the M1 transition spectrum of the Ca-like W54+ ion as observed in an electron beam ion trap (EBIT) was constructed based on atomic data calculated by the relativistic configuration interaction method and distorted wave theory. The present calculated transition energy, rate and intensity of W54+ M1 transitions are compared with previous theoretical and experimental values. The results are in reasonable agreement with the available experimental and theoretical data. The synthetic spectrum explained the EBIT spectrum in the 12–20 nm region, while a new possibly strong transition has been predicted to be observable with an appropriate electron beam energy. The present work provides accurate atomic data that may be used in plasma diagnostics applications.

Photorecombination studies of highly charged tungsten ions at Shanghai EBIT

In this paper, we report studies on photorecombination (PR) processes for highly charged W ions. The experiment was performed at Shanghai electron beam ion trap by employing a fast electron beam-energy scanning technique. The KLL dielectronic recombination (DR) resonance strengths for He- up to O-like W ions were determined. The strong interference effect between DR and radiative recombination (RR) was observed and the Fano factor, which measures the interference degree, was determined for the main resonances of ground state He-, Be-, B-, C-, N-, and O-like W ions. In addition, we show experimentally that an autoionizing state can have both Fano and Lorentzian behavior naturally, depending on the processes involved. A fully relativistic configuration interaction method implemented in the flexible atomic code was employed to calculate DR, RR processes and also the inference effect.

Theoretical determination of two-electron one-photon transition characteristics for low- Z K -shell hollow atoms

Studying $K$-shell hollow atom spectra broadens our knowledge on femtosecond phenomena in atomic physics, chemistry, and biology. Recent synchrotron measurements of the two-electron one-photon (TEOP) transitions of low-$Z$ atoms have shown discrepancies between experiment and theoretical predictions of the TEOP relative intensities and their linewidths. The discrepancies seem to be a result of an incomplete description of an atomic response to the strong perturbation due to the $K$-shell double photoionization (DPI). A theoretical attempt, based on the multiconfiguration Dirac-Fock relativistic configuration interaction method, is presented for Mg, Al, and Si atoms. It is demonstrated that both the branching ratios and the TEOP linewidths can be closely reproduced by taking into account the influences of the core and valence electron correlations, open-shell valence configuration, and the outer-shell ionization and excitation processes following the $K$-shell DPI.

Observation of an extremely-long-lived metastable level in a Ti-like system via an L -shell dielectronic recombination measurement in highly charged 3dn ions of tungsten

In this paper we report the L-shell dielectronic recombination measurement in highly charged $3{d}^{n}$ ions of tungsten by employing a fast electron beam-energy scanning technique at Shanghai EBIT. The studies of the LMM DR resonance strengths of Ar-like up to Mn-like tungsten were implemented through the experiment as well as a fully relativistic configuration interaction method in the flexible atomic code. In the analysis of DR spectrum, an isolated resonant peak was discovered coming from the DR processes via an extremely-long-lived metastable level in a Ti-like system. This work indicated the population of this Ti-like metastable level in the present EBIT plasma condition was as large as 45%.

Theoretical investigation on the soft X-ray spectrum of the highly-charged W54+ ions

A detailed level collisional-radiative model of the E1 transition spectrum of Ca-like W54+ ion has been constructed. All the necessary atomic data has been calculated by relativistic configuration interaction (RCI) method with the implementation of Flexible Atomic Code (FAC). The results are in reasonable agreement with the available experimental and previous theoretical data. The synthetic spectrum has explained the EBIT spectrum in 29.5–32.5 Å , while several new strong transitions has been predicted to be observed in 18.5–19.6 Å for the future EBIT experiment with electron density ne = 1012 cm−3 and electron beam energy Ee = 18.2 keV.

Theoretical study of the dielectronic recombination process of Li-like Xe51+ ions

The dielectronic recombination of Li-like Xe51+ (2s) ions was studied using the flexible atomic code based on the relativistic configuration interaction method. The resonance energies, radiative and autoionization rates, and resonance strengths were calculated systematically for the doubly excited states (2p 1/2 n l j ) J (n = 18−32) and (2p 3/2 n′l j ) J (n′ = 9−27) of Be-like Xe50+ ions. For the higher Rydberg resonance states with n ≥ 33 and n′ ≥ 28, the resonance energies and strengths were obtained by extrapolation based on quantum defect theory. The theoretical rate coefficients, covering the center-of-mass energy range 0–505 eV, are in a better agreement with the experimental results measured at the heavy-ion storage ring ESR than the Multi-Configuration Dirac-Fock calculations, especially at the resonance energy range close to the series limits.

Uncertainty evaluation of the isotope shift factors for transitions in B II**Project supported by the National Natural Science Foundation of China (Grant Nos. 91436103, 11404025, and 91536106), the Research Program of National University of Defense Technology, China (Grant No. JC15-0203), and the China Postdoctoral Science Foundation (Grant No. 2014M560061).

Accurate isotope shift factors of the transitions in B II, obtained with the multi-configuration Dirac–Hartree–Fock and the relativistic configuration interaction methods, are reported. We found a linear correlation relation between the mass shift factors and the energies for the transitions concerned, considering all-order electron correlations. This relation is important for estimating the uncertainty in the calculation of isotope shift factors. These atomic data can be used to extract the nuclear mean-square charge radii of the boron isotopes with halo structures or to resolve the high precise spectroscopy of B II in astronomical observation.

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.

Ab initio study: the potential energy curves and ro-vibrational spectrum of low-lying excited states of HCl+ cation

ABSTRACTThe potential energy curves (PECs) of 11 electronic states of HCl+ cation are obtained by using the high-level relativistic multi-reference configuration interaction plus Davidson correction (MRCI + Q) method. The spin-orbit coupling effect is also taken into account in electronic structure calculations. The PECs of X2Π and A2Σ+ states accord well with corresponding Rydberg--Klein–Rees PECs. The spectroscopic constants for the bound states of HCl+ agree well with available theoretical and experimental data. The dipole moments (DMs) and transition dipole moment of the X2Π→A2Σ+ are also in agreement with previous results. According to the PEC and DM, we calculated Einstein A-coefficients and ro-vibrational line intensities of 1–0, 2–0, 2–1, 3–0, 3–1, 4–0 and 4–1 bands for X2Π1/2 state.

KLL dielectronic recombination resonant strengths of He-like up to O-like tungsten ions

Dielectronic recombination (DR) is an important process in hot plasma physics as well as in atomic structure and collision theory. This work reports the studies of the KLL DR resonance strengths of He-, Li-, Be-, B-, C-, N-, and O-like tungsten ions, through both experiment and calculation. The experimental resonance strengths were determined within uncertainty below 11% at the Shanghai electron beam ion trap by employing a fast electron beam-energy scanning technique. A fully relativistic configuration interaction method implemented in the flexible atomic code was employed to calculate DR process and also radiative recombination (RR). The consideration of the interference effect between DR and RR was revealed to be necessary to determine the resonance strength.

Quantum interference between resonant and nonresonant photorecombination

In this paper, we present experimental and theoretical studies on the interference between resonant and nonresonant photorecombinations for the main resonances of ground-state He-, Be-, B-, C-, N-, and O-like W ions. Experiments were done using a fast electron energy scanning technique at the upgraded Shanghai electron-beam ion trap. Asymmetric resonances were observed, and their Fano factors, which measure the interference degree, were determined. The calculations were done under the framework of Fano's theory by using the flexible atomic code, in which the relativistic configuration interaction method was employed. Among the nine resonances studied in this work, eight experimental results agree with the calculation within experimental uncertainties. But the experimental result for the resonance of Be-like W ions, through the intermediate state of ${[{(1s2{s}^{2}2{p}_{1/2})}_{1}2{p}_{3/2}]}_{5/2}$, deviates from its corresponding theoretical result by 1.3 times experimental uncertainty.

Ab initio MRCI + Q calculations on the low-lying excited states of the MgBr radical including spin–orbit coupling

Accurate theoretical calculations on the MgBr radical have been carried out by using the high-level relativistic multireference configuration interaction method with Davidson correction (MRCI+Q) using correlation-consistent Quintuple-ζ quality basis set. The potential energy curves (PECs) of the 14 Λ-S states of MgBr have been computed. In order to improve the PECs, the core–valence correlation, scalar relativistic effect, and spin–orbit coupling effect are taken into account in the computations. The spectroscopic constants of the bound states have been determined from the computed PECs. The results of the ground state X2Σ+ and the first excited state A2Π are in good agreement with those from the available experiments, while spectroscopic constants of the other electronic states are firstly reported. The low-lying ion-pair state B2Σ+ correlated to ion-pair dissociation limit Mg+ (2Sg)+Br− (1Sg) is characterized. The permanent dipole moments (PDMs) of Λ-S states and the R-dependent spin–orbit (SO) matrix elements are computed. The results indicate that the abrupt changes of PDMs and the SO matrix elements are attributed to the changes of the electronic configurations near the avoided crossing point. After taking the SOC effect into account, the 14 Λ-S states split into 30Ω states, and the SOC splitting for the A2Π is calculated to be 102.58cm−1. The SOC effect, leading to the double-well potential of the Ω=(3)1/2 state, is found to be substantial for MgBr. In order to further illustrate the SOC effect and the avoided crossing phenomenon of the PECs, the Λ-S compositions in the Ω state wavefunctions are analyzed in detail. Finally, the transition dipole moments (TDMs) of several transitions from upper Ω states to the ground X2Σ+1/2 state and the corresponding radiative lifetimes have been studied. It is shown that the (1)3/2–X2Σ+1/2 and (2)3/2–X2Σ+1/2 are particularly important to the observed transitions A2Π–X2Σ+ and C2Π–X2Σ+. The present study should shed more light on the electronic structures and transition properties of electronic states of the MgBr radical.

Collisional-radiative model for the visible spectrum of W26+ ions

Plasma diagnostics in magnetic confinement fusion plasmas by using visible spectrum strongly depends on the knowledge of fundamental atomic properties. A detailed collisional-radiative model of W26+ ions has been constructed by considering radiative and electron excitation processes, in which the necessary atomic data had been calculated by relativistic configuration interaction method with the implementation of Flexible Atomic Code. The visible spectrum observed at an electron beam ion trap (EBIT) in Shanghai in the range of 332 nm to 392 nm was reproduced by present calculations. Some transition pairs of which the intensity ratio is sensitive to the electron density were selected as potential candidates of plasma diagnostics. Their electron density dependence is theoretically evaluated for the cases of EBIT plasmas and magnetic confinement fusion plasmas.

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.

Radiative rates and electron-impact excitation for then≤ 6 fine-structure levels in H-like ions with 13 ≤Z≤ 42

Context. Many observed emission lines from space missions are due to highly charged H-like ions. An analysis of the lines provides information on the temperature, density, and chemical composition of plasmas. A wide range of atomic parameters, such as energy levels, radiative rates, and excitation rate coefficients are needed to achieve this goal.Aims. In this paper we report on calculations for energy levels, radiative rates, collision strengths, and effective collision strengths for transitions among the 36 lowest levels of the n ≤ 6 configurations of highly charged H-like ions with 13 ≤ Z ≤ 42.Methods. The widely used Flexible Atomic Code (FAC) is adopted for the calculation. Energy levels and radiative rates are calculated within the relativistic configuration-interaction method. Employing relativistic distorted-wave approximation, direct excitation collision strengths are calculated at eleven scattered electron energies E ′ f = 0.001, 0.002, 0.005, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0, and 2.5, where E ′ f is in units of Z 2 rydbergs. Collision strengths at higher energies are estimated by interpolation/extrapolation using relativistic Bethe form. Resonance contributions through the relevant He-like doubly excited n ′l ′n ′′l ′′ configurations with n ′ ≤ 7 and n ′′ ≤ 75 are explicitly taken into account using the independent-process isolated-resonance approximation. Radiation damping effects are taken into account.Results. We present the radiative rates, oscillator strengths, and line strengths for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), magnetic quadrupole (M2), electric octupole (E3), and magnetic octupole (M3) transitions. Assuming a Maxwellian electron velocity distribution, we report effective collision strengths over a wide temperature range between 2 × 103 × Z 2 and 2 × 106 × Z 2 K. We believe that the present results are the most extensive and definitive atomic dataset to date for highly charged H-like ions.