Multiconfiguration Dirac Hartree Fock Research Articles

Ionization potentials of the superheavy element livermorium (Z = 116).

Ionization potentials (IPs) of the superheavy element (SHE) livermorium (Lv) and its ions Lvn+ (n = 1, …, 6) are obtained using the multiconfiguration Dirac-Hartree-Fock method. The effects of electron correlation in the subshells {6s, 6p, 6d, 7s, 7p} are taken into account, together with the Breit interaction and quantum electrodynamic (QED) effects. In Lv, the strong relativistic effect causes a large splitting between the energies of the 7p1/2 and 7p3/2 orbitals, which results in a large difference between IP3 and IP2. As a consequence, the behavior of the IPs of Lv differs from that of the lighter oxygen group elements: among the IPn Z (Z = Se, Te, Po, Lv; n = 1, …, 6), IP1,2 Lv are the smallest, whereas IP3,4,5,6 Lv are the second largest among the IP3,4,5,6 Z. This jump in IP can be taken to be a natural characteristic of SHEs because the calculations of the difference between IP3 and IP2 are only weakly affected by electron correlation, the Breit interaction, and QED effects, with only the relativistic effect being significant. We also show that the energies and IPs of neutral Lv and Lv+ are clearly influenced by the electron correlation effect in the subshells {6s, 6p, 6d}. The Breit interaction and QED have an effect on the energies that has an exponential dependence on the atomic number, although they have only a weak influence on the IPs. The analysis of the stabilities of the 2+, 4+, and 6 + states of Lv shows good agreement with predictions from other studies.

Extended Calculations of Energy Levels and Transition Rates for Singly Ionized Lanthanide Elements. I. Pr–Gd

Abstract Lanthanide elements play important roles as an opacity source in the ejected material from neutron star mergers. Accurate and complete atomic data are necessary to evaluate the opacities and to analyze the observed data. In this paper, we perform extended, ab initio atomic calculations from Pr ii (Z = 59) to Gd ii (Z = 64). By using multiconfiguration Dirac–Hartree–Fock and relativistic configuration-interaction methods, implemented in the general-purpose relativistic atomic structure package (GRASP2K), we calculate the energy levels and transition data of electric dipole transitions. These computations are based on strategies (with small variations) of Nd ii published by Gaigalas et al. Accuracy of data is evaluated by comparing computed energy levels with the National Institute of Standards and Technology (NIST) database or other works. For the energy levels, we obtain the average relative accuracy of 8%, 12%, 6%, 8%, and 7% for Pr ii, Pm ii, Sm ii, Eu ii, and Gd ii ions, respectively, as compared with the NIST data. Accuracy of energy transfer to the wavelength is 3%, 14%, and 11% for Pr ii, Eu ii, and Gd ii. Our computed E1 type transition probabilities are in good agreement with experimental values presented by other authors especially for strong transitions.

Energy Level Structure and Transition Data of Er2+

Abstract A majority of Er in the universe is synthesized by the r-process, which can occur in the mergers of neutron stars (NSs). The contribution of this element to the opacity of NS ejecta should be tested, but even the energy levels of first excited configuration have not been fully presented. The main aim of this paper is to present accurate energy levels of the ground [Xe]4f 12 and first excited [Xe]4f 115d configurations of Er2+. The energy level structure of the Er2+ ion was computed using the multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction (RCI) methods, as implemented in the GRASP2018 program package. The Breit interaction, self-energy, and vacuum polarization corrections were included in the RCI computations. The zero-first-order approach was used in the computations. Energy levels with the identification in LS coupling for all (399) states belonging to the [Xe]4f 12 and [Xe]4f 115d configurations are presented. Electric dipole (E1) transition data between the levels of these two configurations are computed. The accuracy of these data is evaluated by studying the behavior of the transition rates as functions of the gauge parameter, as well as by evaluating the cancellation factors. The core electron correlations were studied using different strategies. The rms deviations obtained in this study for states of the ground and excited configurations from the available experimental data are 649 and 754 cm−1, respectively.

The Multi-configuration Dirac-Hartree-Fock Calculations for Cs VII

Theoretical energy levels, wavelengths and transitions probabilities of six-times ionized cesium (Cs VII) are calculated using multi-configuration-Dirac-Hartree-Fock (MCDHF) method. The present calculations have been performed for the 5s\(^2\)5p, 5s\(^2\)6s, 5s\(^2\)5d, 5s5p\(^2\) configurations using the GRASP2018 package. The electron correlation effects, Breit interaction and quantum electro dynamic effects have been considered in the calculations.

Large-scale Multiconfiguration Dirac–Hartree–Fock Calculations for Astrophysics: n = 4 Levels in P-like Ions from Mn xi to Ni xiv

Using the multiconfiguration Dirac-Hartree-Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the lowest 546 (623, 701, 745) states of the $3p^4 3d$, $3s 3p^2 3d^2$, $3s 3p^3 4p$, $3s 3p^4$, $3s^2 3d^3$, $3s^2 3p^2 3d$, $3s^2 3p^2 4d$, $3s^2 3p^2 4s$, $3p^3 3d^2$, $3p^5$, $3s 3p 3d^3$, $3s 3p^3 3d$, $3s 3p^3 4s$, $3s^2 3p 3d^2$, %$3s^2 3p^2 4f$, $3s^2 3p^2 4p$, $3s^2 3p^3$ configurations in Mn~XI (Fe~XII, Co~XIII, Ni~XIV) is provided. The comparison between calculated excitation energies for the $n=4$ states and available experimental values for Fe XII indicate that the calculations are highly accurate, with uncertainties of only a few hundred cm$^{-1}$. Lines from these states are prominent in the soft X-rays. With the present calculations, several recent new identifications are confirmed. Other identifications involving $3p^2 4d$ levels in Fe~XII that were found questionable are discussed and a few new assignments are recommended. As some $n=4$ states of the other ions also show large discrepancies between experimental and calculated energies, we reassess their identification. The present study provides highly accurate atomic data for the $n=4$ states of P-like ions of astrophysical interest, for which experimental data are scarce.

Energy levels, transition rates and electron impact excitation rates for B-like Kr XXXII

Energy levels and transition rates for electric-dipole, electric-quadrupole, electric-octupole, magnetic-dipole, and magnetic-quadrupole transitions among the levels arising from the n≤ 5 configurations in B-like Kr XXXII are calculated by using two state-of-the-art methods, namely, the multi-configuration Dirac–Hartree–Fock (MCDHF) approach and the second-order many-body perturbation theory (RMBPT). Our results are compared with several available experimental and other theoretical values. Electron-impact excitation (EIE) collision strengths are calculated via the independent process and isolated resonance approximation using distorted-wave (denoted by IPIRDW). Radiation damping effects on the resonance excitation contributions are included. Effective collision strengths are calculated as a function of electron temperature by assuming a Maxwellian electron velocity distribution. Spectral line intensities are modelled by using collision radiative model, and several line pairs pointed out might be useful for density diagnostics.

Calculations of transition rates in erbium-like ions Lu IV, Hf V and Ta VI using the Ab initio MCDHF-RCI and semi-empirical HFR methods

In the present paper, the radiative properties of three ions belonging to the erbium isoelectronic sequence, i.e. Lu IV, Hf V and Ta IV, are reported and the effect of configuration interaction on these properties are taken into account for the first time to our knowledge. These heavy elements with Z=71–73 are located near to tungsten (Z=74) in the Periodic Table and are of potential interest in controlled thermonuclear fusion. Indeed, they could be used in plasma-facing materials such as the divertors in tokamaks or/and could be generated by neutron-induced transmutations of divertor’s materials. In this work, two independent theoretical atomic structure computational approaches have been considered, i.e. the semi-empirical Hartree–Fock with relativistic corrections method (HFR) and the ab initio multiconfiguration Dirac–Hartree–Fock with subsequent relativistic configuration interaction method (MCDHF-RCI). The transition probabilities and the oscillator strengths have been calculated for 593, 820 and 1101 E1 transitions in Lu IV, Hf V and Ta VI respectively spanning the spectral range from UV to IR. Finally, this study also underlines the importance of core-valence correlations in these heavy atomic ions.

Benchmarking calculations with spectroscopic accuracy of excitation energies and wavelengths in sulfur-like tungsten

Atomic properties of S-like W are evaluated through a state-of-the-art method, namely, the multi-configuration Dirac-Hartree-Fock (MCDHF) method combined with the relativistic configuration interaction (RCI) approach. The level energies, wavelengths, and transition parameters involving the 88 lowest levels of W$^{+58}$ (W LIX) are calculated. We discuss in detail the relative importance of the valence- and core-valence electron correlation effects, the Breit interaction, the higher order retardation correction beyond the Breit interaction through the transverse photon interaction, and the quantum electrodynamical (QED) corrections. The present level energies are highly accurate, with uncertainties close to what can be achieved from spectroscopy. As such, they provide benchmark tests for other theoretical calculations of S-like W and should assist the spectroscopists in their assignment/identification of observed lines in complex spectra.

Electron–electron interaction energy in He-like isoelectronic sequence with Z = 2–133

Via a differential comparison of the binding energies between H- and He-like ions, the electron–electron interaction energies of the states and () in the He-like isoelectronic sequence are obtained over a wide range of the nuclear charge by using fully relativistic multiconfiguration Dirac–Hartree–Fock and configuration interaction methods. Contributions from the Coulomb and Breit interactions, the nuclear effects, the self-energy and vacuum polarization corrections are evaluated. The results show that, the one-electron corrections to the electron–electron interaction are nearly cancelled out during the deduction of the interelectron interaction energies. Besides the Coulomb interaction, the Breit interaction plays a significant role in the electron–electron interaction for high- ions; it contributes 23% of the electron–electron interaction energy at

Extensive and accurate energy levels, transition rates, lifetimes, hyperfine structures and isotope shifts for the Rb XXXVI spectrum of plasma interest

We present relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) spectrum calculations for Rb XXXVI with correlations within the n = 8 complex. An extensive and accurate set of energy levels, wavelengths, line strengths, weighted oscillator strengths, lifetimes, isotope shifts, hyperfine structure and Landé gJ factors has been calculated for lower 127 odd- and even-parity states arising from the 1s2 and 1snl(n=1−8,0≤l≤n−1) configurations in He-like-Rb. Transition rates for electric-multipole (dipole (E1), quadrupole (E2), and octupole (E3)) and magnetic-multipole (dipole (M1), quadrupole (M2), and octupole (M3)) have been also calculated. For the accuracy of our results, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the Second-Order Many-Body Perturbation Theory (MBPT) method. Additionally, Breit interaction and leading quantum electrodynamic effects (QED) have been included as perturbations in extensive relativistic configuration interaction (RCI) calculations. The results arising in the two sets of calculations MCDHF and MBPT are quite close. Our results are compared with other available theory reported in the literature as well as the experimental data listed in the Atomic Spectra Database (ASD) of the National Institute of Standards and Technology (NIST) online database. Good agreement between them has been found. The present complete and consistent results can be used in line identification, plasma modeling and diagnostics of astrophysical plasma.

Ab initio calculations of atomic parameters of Mo XVIII of fusion interest

The relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) method has been employed to calculate the atomic parameters of Mo XVIII, which are important for fusion determination of plasma properties in different conditions. Atomic data, such as energy levels, lifetimes, wavelengths, spectroscopic labels, and transition rates for the transitions among the lowest 112 states of the 3 s23p63d7, 3 s23p53d8, 3s3 p63d8, and 3s23p63d64s configurations are given. To describe the atomic system accurately, electron correlation effects are taken into account. We also present a calculation within fully relativistic frame based on the Flexible Atomic Code (FAC). This, in turn, allowed us to make an intercomparison on the obtained data. Our two sets of results are also evaluated by comparison with the NIST database recommended values. The new calculated energy levels are, on the average, about 1.5% higher than NIST database recommended values and yield oscillator strengths within 5% of the theoretical values. This study provides a substantial amount of updated atomic data, which are essential for fusion applications.

Combined MCDHF-CI and MBPT calculations for n=4 to n=3 x-ray transitions in Ni-like tungsten

SynopsisThe 4d → 3p, 4p → 3s, and 4f → 3p x-ray transitions in Ni-like tungsten ions have been studied theoretically. The Multiconfiguration Dirac–Hartree–Fock method and the large-scale relativistic Configuration Interaction and Many Body Perturbation Theory methods have been employed in order to take into account electron correlation effects on the lines wavelengths.

Energy Levels and Transition Parameters in Ce6+ from MCDHF Model

Multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations and subsequent Relativistic Configuration Interaction (RCI) calculations have been performed for the 5s\({}^{2}\)5p\({}^{4}\), 5s\({}^{2}\)5p\({}^{3}\)6s and 5s5p\({}^{5}\) configurations of six times ionized cerium using GRASP2018 package. The electron correlation effects, (BI) interaction and Quantum Electrodynamics (QED) effects have been considered in the calculation. Energy levels, oscillator strength and transition probabilities among the transitions of 5s\({}^{2}\)5p\({}^{4}\), 5s5p\({}^{5}\) and 5s\({}^{2}\)5p\({}^{3}\)6s have been calculated. The calculated energy levels are compared with experimental data available and show good agreement with it.

Shannon Entropy in Configuration Space for Ni-Like Isoelectronic Sequence.

Discrete Shannon entropy was introduced in view of the mathematical properties of multiconfiguration methods and then used to interpret the information in atomic states expressed by the multiconfiguration Dirac–Hartree–Fock wavefunction for Ni-like isoelectronic sequence. Moreover, the relationship between the concepts, including sudden change of Shannon entropy, information exchange, eigenlevel anticrossing, and strong configuration interaction, was clarified by induction on the basis of the present calculation of the energy structure for Ni-like isoelectronic sequence. It was found that there is an interesting connection between the change of Shannon entropies and eigenlevel anticrossings, along with the nuclear charge Z, which is helpful to conveniently locate the position of eigenlevel anticrossings and information exchanging and understand them from the point of view of information, besides the traditional physical concepts. Especially, it is concluded that in a given configuration space eigenlevel anticrossing is a sufficient and necessary condition for the sudden change of Shannon entropy, which is also a sufficient condition for information exchange.

Near L-edge Single and Multiple Photoionization of Triply Charged Iron Ions

Abstract Relative cross sections for m-fold photoionization (m = 1,…, 5) of Fe3+ by single-photon absorption were measured employing the photon-ion merged-beams setup PIPE at the PETRA III synchrotron light source operated at DESY in Hamburg, Germany. The photon energies used spanned the range of 680–950 eV, covering both the photoexcitation resonances from the 2p and 2s shells, as well as the direct ionization from both shells. Multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations were performed to simulate the total photoexcitation spectra. Good agreement was found with the experimental results. These computations helped to assign several strong resonance features to specific transitions. We also carried out Hartree–Fock calculations with relativistic extensions taking into account both photoexcitation and photoionization. Furthermore, we performed extensive MCDHF calculations of the Auger cascades that result when an electron is removed from the 2p and 2s shells of Fe3+. Our theoretically predicted charge-state fractions are in good agreement with the experimental results, representing a substantial improvement over previous theoretical calculations. The main reason for the disagreement with the previous calculations is their lack of inclusion of slow Auger decays of several configurations that can only proceed when accompanied by de-excitation of two electrons. In such cases, this additional shake-down transition of a (sub)valence electron is required to gain the necessary energy for the release of the Auger electron.

Large-scale Multiconfiguration Dirac–Hartree–Fock Calculations for Astrophysics: Cl-like Ions from Cr viii to Zn xiv

Abstract We use the multiconfiguration Dirac–Hartree–Fock (MCDHF) method combined with the relativistic configuration interaction approach (GRASP2K) to provide a consistent set of transition energies and radiative transition data for the lower n = 3 states in all Cl-like ions of astrophysical importance, from Cr viii to Zn xiv. We also provide excitation energies calculated for Fe x using the many-body perturbation theory (MBPT, implemented within FAC). The comparison of the present MCDHF results with MBPT and with the available experimental energies indicates that the theoretical excitation energies are highly accurate, with uncertainties of only a few hundred cm−1. Detailed comparisons for Fe x and Ni xii highlight discrepancies in the experimental energies found in the literature. Several new identifications are proposed.

Coulomb (Velocity) Gauge Recommended in Multiconfiguration Calculations of Transition Data Involving Rydberg Series

Astronomical spectroscopy has recently expanded into the near-infrared (nIR) wavelength region, raising the demands on atomic transition data. The interpretation of the observed spectra largely relies on theoretical results, and progress towards the production of accurate theoretical data must continuously be made. Spectrum calculations that target multiple atomic states at the same time are by no means trivial. Further, numerous atomic systems involve Rydberg series, which are associated with additional difficulties. In this work, we demonstrate how the challenges in the computations of Rydberg series can be handled in large-scale multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) calculations. By paying special attention to the construction of the radial orbital basis that builds the atomic state functions, transition data that are weakly sensitive to the choice of gauge can be obtained. Additionally, we show that the Babushkin gauge should not always be considered as the preferred gauge, and that, in the computations of transition data involving Rydberg series, the Coulomb gauge could be more appropriate for the analysis of astrophysical spectra. To illustrate the above, results from computations of transitions involving Rydberg series in the astrophysically important C IV and C III ions are presented and analyzed.

Parameters of Isotope Shifts for 2s2p 3,1P1 → 2s2 1S0 Transitions in Heavy Be-Like Ions**Supported by the National Natural Science Foundation of China under Grant Nos 11874090, 11604385, 91536106 and 11204374, and the Research Project of National University of Defense Technology under Grant No ZK17-03-11.

The field shift and mass shift parameters of the 2s2p 3,1P1 → 2s2 1S0 transitions in Be-like ions (70 ≤ Z ≤ 92) are calculated using the multi-configuration Dirac–Hartree–Fock and the relativistic configuration interaction methods with the inclusion of the Breit interaction and the leading QED corrections. We find that the mass shift parameters of these two transitions do not change monotonously along the isoelectronic sequence in the high-Z range due to the relativistic nuclear recoil effects. A minimum value exists for the specific mass shift parameters around Z = 80, especially for the 2s2p 3P1 → 2s2 1S0 transition. In addition, the field shifts and mass shifts of these two transitions are estimated using an empirical formula, and their contributions are compared along the isoelectronic sequence.

Energy levels, oscillator strengths, radiative transition probabilities, level lifetimes and electron-impact excitation rate coefficients for Ne-like Mo XXXIII

The energy levels, oscillator strengths, radiative decay rates, lifetimes, collision strengths, direct and resonance electron-impact excitation rate coefficients have been computed for the 257 fine-structure levels arising from 1s22s22p5nl and 1s22s2p6n′l′ configurations belonging to the Mo32+ ion with n≤7, l≤4 and n′≤5, l′≤4. The model-potential approach is used for the target ion structure calculations. Additionally, we employ the multiconfiguration Dirac–Hartree–Fock method to further assess the energy levels and transition probabilities. The collision strengths for the electron-impact direct excitation are computed within the relativistic distorted-wave approximation at 34, 135, 680, 1700, 5436, and 12,740 eV scattered electron energy values. We also perform collision calculations at 85, 175, and 450 keV electron energies using the plane-wave approximation and interpolate the reduced cross section within Fano plots, thus accounting for relativistic effects at asymptotic energies. This assures the convergence of Maxwellian integration for effective collision strengths calculation at electron temperatures up to 80 keV. The resonance contribution to the excitation rates is accounted for within the independent process isolated resonance approximation by including Na-like Mo31+ doubly excited autoionization states arising from the 1s227nln′l′ configurations with n≤7,l≤4,n′≤20,l′≤8. Contributions from high n′≥21 Rydberg states to the excitation rate coefficients are included by employing the n′−3 extrapolation law for radiative and autoionization decay rates. Radiative decay of resonances to lower autoionization states followed by autoionization cascade as well as radiative damping via core transitions are included in our model. The highest rate coefficients corresponding to ground state excitations are the 2p–3d allowed and 2p–3p electric monopole transitions, respectively. Intercombination and generally higher-order electric multipole transitions amount to lower excitation rate coefficients but are not to be neglected. Magnetic transitions are only relevant for low electron temperatures since both their direct and resonance contributions to excitation significantly decrease with increasing electron energy. Present results compare well with existing data from literature. The resonance contributions play an important role in the accuracy of rate coefficients, especially for weak forbidden transitions at low electron temperatures. These results may be useful in fusion related plasmas, astrophysics and fundamental physics.

Ab initio MCDHF/RCI and semi-empirical HFR calculations of transition probabilities and oscillator strengths in Xe XI

The atomic structure of ten-times ionized xenon (Xe XI) has been computed by two independent methods, i.e. the ab initio relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) approach within the relativistic configuration interaction (RCI) approximation and the semi-empirical pseudo-relativistic Hartree–Fock (HFR) method. The transition probabilities and oscillator strengths of the 4d8 − (4p54d9 + 4d75p + 4d74f) transition array have been determined in both models and allowed us to estimate their accuracy taking into account both the gauge agreements and the cancellation effects on the line strengths. It has been found that core – core and core – valence correlations through the explicit inclusion of single- to triple-hole 4p-subshell configurations in our RCI model systematically decrease the transition rates by about 20% for the strong lines (with log gf > 0) with respect to our HFR values that did not consider those effects. Further opening of the core shells has also been investigated and did not give rise to significant systematic change on the transition probabilities.