Multiconfiguration Dirac Hartree Fock Research Articles

Extended Calculations of Energy Levels and Transition Rates for Singly Ionized Lanthanide Elements. II. Tb−Yb

Abstract In this work, we continue large-scale ab initio computations for single ionized lanthanides. Extended atomic calculations for the set of ions from Pr ii (Z = 59) to Gd ii (Z = 64) have been performed in our previous work. In this study, ions from Tb ii (Z = 65) to Yb ii (Z = 70) are analyzed. By employing the same multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods that are implemented in the general-purpose relativistic atomic structure package GRASP2018, the energy levels and transition data of electric dipole (E1) transitions are computed. These computations are based on the strategies (with small variations) of Paper I. Accuracy of data is evaluated by comparing the computed energy levels with the data provided by the National Institute of Standards and Technology (NIST) database and with data from various methods. We obtain the average accuracy in the energy level compared with the NIST database: 6%, 5%, 4%, 5%, 3%, and 3% for Tb ii, Dy ii, Ho ii, Er ii, Tm ii, and Yb ii, respectively. We also provide extensive comparison of transition probabilities and wavelengths. Our results reach the average accuracy of transition wavelengths: 9%, 9%, 9%, 3%, 4%, and 11% for Tb ii, Dy ii, Ho ii, Er ii, Tm ii, and Yb ii, respectively.

Accurate line strengths, transition rates and lifetimes of 2s2p2(4P)3s in N II

Abstract The accurate line strengths, transition rates, oscillator strengths, and lifetimes from the inner-shell 2s2p2(4P)3s states 5P and 3P of N II are reported within the framework of the multiconfiguration Dirac-Hartree-Fock (MCDHF) method. The effects of core-core, core-valence, and valence correlations; the Breit interaction; and QED effect are taken into account. Through investigating the influences of electron correlation effects on the quintet states, it is found that the core correlation effect has certain compensation effect in accurately optimizing the line strengths, transition rates and lifetimes of quintet states; the branching fractions of 2s2p3 5S$^\circ _{2}$–2s2p2(4P)3s 5P1, 2, 3 tend to 1, which is inferred as a peculiar intrinsic property that can be useful for plasma diagnostics; unlike 3P0, 1, 2 and 5P1, 3, the calculations of lifetime of 5P2 show some J-dependence, and the velocity form calculations for this J=2-dependence are much more sensitive to electron correlations of 1s22s2p2(4P)3l (l = p, d) than those in the length gauge, which will be helpful to deal with the calculations of lifetime with J=2-dependence in the carbon like isoelectronic series.

Effect of Electron Correlation and Breit Interaction on Energies, Oscillator Strengths, and Transition Rates for Low-Lying States of HeliumSupported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300), and the National Natural Science Foundation of China (Grant Nos. 11774344 and 11474033).

The transition energies, E1 transitional oscillator strengths of the spin-allowed as well as the spin-forbidden and the corresponding transition rates, and complete M1, E2, M2 forbidden transition rates for 1s 2, 1s2s, and 1s2p states of He I, are investigated using the multi-configuration Dirac–Hartree–Fock method. In the subsequent relativistic configuration interaction computations, the Breit interaction and the QED effect are considered as perturbation, separately. Our transition energies, oscillator strengths, and transition rates are in good agreement with the experimental and other theoretical results. As a result, the QED effect is not important for helium atoms, however, the effect of the Breit interaction plays a significant role in the transition energies, the oscillator strengths and transition rates.

Transition spectral parameters of In-like Ba, La, and Ce ions

The spectral parameters (energy levels, wavelengths, transition probabilities, line strengths, and oscillator strengths) of resonance lines for Ba VIII, La IX, and Ce X have been obtained using the multiconfiguration Dirac–Hartree–Fock method, with contributions of quantum electrodynamics and Breit interaction corrections taken into consideration. The calculated results of energy levels and wavelengths are in good agreement with experimental values and other calculations. The number of energy levels and wavelengths considered is larger than that of any other experiment or other calculations. The transition probabilities, line strengths, and oscillator strengths are also calculated where no other theoretical results and experimental values are available.

Theoretical calculation of the quadratic Zeeman shift coefficient of the clock state for strontium optical lattice clock

In the weak-magnetic-field approximation, we derived an expression of quadratic Zeeman shift coefficient of clock state for 88Sr and 87Sr atoms. By using this formula and the multi-configuration Dirac–Hartree–Fock theory, the quadratic Zeeman shift coefficients were calculated. The calculated values C 2 = –23.38(5) MHz/T2 for 88Sr and the , F = 9/2, MF = ±9/2 clock states for 87Sr agree well with the other available theoretical and experimental values, especially the most accurate measurement recently. In addition, the calculated values of the , F = 9/2, MF = ±9/2 clock states were also determined in our 87Sr optical lattice clock. The consistency with measurements verifies the validation of our calculation model. Our theory is also useful to evaluate the second-order Zeeman shift of the clock transition, for example, the new proposed 1 S 0, F = 9/2, MF = ±5/2–, F = 9/2, MF = ±3/2 transitions.

Relativistic excitation energies and transition data for Ag XLIV and Cd XLV

Excitation energies, LS-compositions, and lifetimes for the 184 fine-structure levels related to the 2s2, 2p2, 2snl (n = 3 − 6; l = 0 − 4), and 2pnl (n = 3 − 5; l = 0 − 4) configurations as well as transition data for the electric/magnetic-dipole (E1/M1) and electric/magnetic-quadrupole (E2/M2) transitions between these levels are calculated for Be-like Ag XLIV and Cd XLV. The GRASP2018 atomic structure computer package, which is based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, is used to perform the present computations. The Breit interaction and quantum electrodynamics (QED) effects are included in the relativistic configuration interaction (RCI) computations. The convergence of excitation energies for various active sets is discussed and the discrepancy between the present energies and oscillator strengths with other theoretical results is graphically illustrated. The uncertainty estimation of the present results for lifetimes and line strengths is performed by comparing the two active sets of the present MCDHF calculations.

Emission Lines in 290–360 nm of Highly Charged Tungsten Ions W20+–W29+

Forbidden transitions in the near-UV and visible wavelength of highly charged tungsten (W) ions are potentially useful as novel tungsten diagnostics means of fusion plasmas. Emission lines in 290–360 nm from Wq+ ions interacting with an electron beam of 540–1370 eV are measured, using a compact electron-beam-ion-trap. The charge states of 64 lines are identified as W20+–W29+. A magnetic-dipole (M1) line of W29+ between the excited states (4d84f)[(4d5/2−2)44f7/2]13/2→[(4d5/2−2)44f5/2]13/2 is newly identified; the wavelength is determined as 351.03(10) nm in air. The theoretical wavelength calculated using the multiconfiguration Dirac–Hartree–Fock method is in a good agreement with the measurement.

Energy and transition data computations for P-like ions: As, Kr, Sr, Zr, Mo, and W

The multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods were used to compute excitation energies and transition data for the 147 lowest states of the even 3s3p4, 3s23p23d, 3p43d, 3s3p23d2 configurations and for the 124 lowest states of the odd 3s23p3, 3p5, 3s3p33d, 3s23p3d2, 3p33d2 configurations for the P-like ions: As XIX, Kr XXII, Sr XXIV, Zr XXVI, Mo XXVIII, and W LX. E1 transition rates and weighted oscillator strengths among these states are given. Valence–valence, core–valence and core–core electron correlation effects are included. Computed excitation energies and transition data are compared with the NIST recommended values and experimental or theoretical results of other authors. All calculations were performed using the general relativistic atomic structure package GRASP2018.

A Theoretical Investigation of the Magnetic-field-induced Transition in Fe X, of Importance for Measuring Magnetic Field Strengths in the Solar Corona

Abstract The use of the magnetic-field-induced transition (MIT) in Fe X for the measurement of the magnetic field strength in the solar corona has been discussed and demonstrated in a number of recent studies. This diagnostic technique depends on, among other conditions, the accuracy of the atomic data for Fe X. In the present work, we carry out a large-scale calculation for the atomic properties needed for the determination of the MIT rate using the multiconfiguration Dirac–Hartree–Fock method. Four computational schemes are employed to study the convergence of the atomic properties of interest. Comparison with other experimental and theoretical sources are performed and recommended values are suggested for important properties, e.g., the magnetic induced transition probabilities as a function of magnetic field strengths. The present calculations affect magnetic field measurements by decreasing the magnetic field strengths by 10%–15%, leading to differences in magnetic energy up to 30%. We recommend that the current data should be employed in magnetic field measurements in the future.

Partition function and thermodynamic quantities with atomic data of Ag XLIV

In this work, the atomic parameters of Ag XLIV (Be-like Ag) are examined and evaluated by implementing the GRASP2K package with the multi-configuration Dirac–Hartree–Fock (MCDHF) method for the calculation of wave-functions. We have listed fine structure energy levels of the lowest 170 levels with radiative data for multipole moments, such as electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions, that lie in the region of extreme ultraviolet (EUV) and soft X-ray (SXR) for Ag XLIV from the ground state within the lowest 170 levels. We have compared our GRASP2K and FAC results with theoretical results available in the literature for some levels. Additionally, we have also calculated partition function and thermodynamic quantities for temperature ranges from 104to 107K. We believe that our presented details and data may be beneficial not only in plasma modeling but also in imaging of nanostructure as well as in medicine, semiconductors, and EUV and SXR laser applications.

Theoretical calculations of hyperfine splitting, Zeeman shifts, and isotope shifts of 27Al+ and logical ions in Al+ clocks* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11604385 and 91536106), the Natural Science Foundation of Hunan Province, China (Grant No. 2019JJ50743), and the Research Project of the National University of Defense Technology (Grant No. ZK17-03-11).

Based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, similar models are employed to simultaneously calculate the first-order and second-order Zeeman coefficients as well as the hyperfine interaction constants of the related energy levels of 27Al+ and its logical ions 9Be+ and 25Mg+ in the 27AI+ optical clock. With less than 0.34% deviations from experimental values in Zeeman coefficients of 27Al+, these calculated parameters will be of great help for better evaluation of the systematic uncertainty. We also calculate the isotope shift parameters of the related energy levels, which could extend our knowledge and understanding of nuclear properties of these ions.

Relativistic multiconfiguration Dirac-Hartree-Fock calculations for energies, lifetimes, and E1, E2, M1, and M2 line strengths of Y XXXII

Energies, wavelengths, line strengths, transition probabilities, and weighted oscillator strengths for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among the levels arising from the n ≤ 3 configurations of oxygen-like yttrium, Y XXXII, are calculated using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method. In the calculations, the valence-valence (VV) and core-valence (CV) correlations, as well as the Breit interaction (BI) and the leading quantum electrodynamics (QED) contributions are considered. Comparisons with the available results are used to determine the uncertainty for energies, wavelengths, and oscillator strengths. For lifetimes, E1, E2, M1, and M2 line strengths, the comparisons are also made between the two sets of the present MCDHF calculations to determine the accuracy of the results.

Benchmarking calculations with spectroscopic accuracy of level energies and wavelengths in W LVII–W LXII tungsten ions

Atomic properties of n=3 states of the W56+ - W61+ ions are systematically investigated through two state-of-the-art methods, namely, the second-order many-body perturbation theory, and the multi-configuration Dirac–Hartree–Fock method combined with the relativistic configuration interaction approach. The contributions of valence-valence and core-valence electron correlations, the Breit interaction, the higher-order retardation correction beyond the Breit interaction through the transverse photon interaction, and the quantum electrodynamical corrections to the excitation energies are studied in detail. The excitation energies and wavelengths obtained with the two methods agree with each other within ≈0.01%. The present results achieve spectroscopic accuracy and provide a benchmark test for various applications and other theoretical calculations of W56+ - W61+ ions. They will assist spectroscopists in their assignment and direct identification of observed lines in complex spectra.

Multiconfiguration Dirac–Hartree–Fock energy levels, weighted oscillator strengths, transitions probabilities, lifetimes, hyperfine interaction constants, Landé g-factors and isotope shifts of O VII

Energy levels, weighted oscillator strengths and transition probabilities, lifetimes, hyperfine interaction constants, Landé gJ factors and isotope shifts have been calculated for all levels of 1s2 and 1snl (n=2-8,l⩽7) configurations of He-like oxygen ion (O VII). The calculations were performed using the Multiconfigurational Dirac-Hartree–Fock (MCDHF) and the Relativistic Configuration Interaction (RCI) methods. A second set of calculations was obtained with the Many Body Perturbation Theory (MBPT) method. Transition probabilities are reported for all E1,E2,M1 and M2 transitions. Breit interactions and quantum electrodynamics effects were included in the RCI calculations. Comparisons have been made with the compiled data from the NIST ASD and other calculations and a good agreement was found which confirms the reliability of our results. The accuracy of the present calculations is high enough to facilitate identification of many observed spectral lines. For the first time, we present some missing data for the He-like oxygen ion.

Energy levels, transition rates, lifetimes of He-like-ions with [formula omitted] deduced from relativistic multiconfiguration Dirac–Hartree–Fock and many body perturbation theory calculations

We disclose relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) spectrum calculations for He-like-ions with Z=72–76. The excitation energy and the oscillator strength values have been computed for the 127 odd- and even-parity states as well as lifetimes and transition rates between different states. To study the accuracy of our results, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the many body perturbation theory (MBPT). Additionally, the Breit interaction and leading quantum electrodynamics effects (QED) are included as perturbations in the present calculations.

Role of hyperfine interaction in Landé [formula omitted]-factors of [formula omitted] clock states

In the weak-magnetic-field approximation, we calculated the hyperfine-induced Landé g-factors of the 3P0o clock states in 27Al+ and 87Sr by using the multi-configuration Dirac–Hartree–Fock method. The present results, δghfs(1)(3P0o)=−1.183(6)×10−3 for 27Al+ and δghfs(1)(3P0o)=7.78(30)×10−5 for 87Sr, agree with experimental values very well. The influence of relativistic effects and electron correlations on the involving hyperfine interaction and Zeeman matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the g-factors concerned so as to truncate the summation over the perturbing states without loss of accuracy. Based on these, the computational uncertainties were systematically analyzed for the hyperfine-induced Landé g-factors of the 3P0o clock states in these two atomic systems.

Determination of atomic properties in the oxygen isoelectronic sequence

Atomic data including energy levels, excitation energies, line strengths, transition probabilities, and weighed oscillator strengths for 2s22p4, 2s2p5 and 2p6 levels are evaluated for O-like ions (Kr, Rb, Sr, Y, Nb, Zr, Mo, La, Ce) by using Multiconfiguration Dirac-Hartree-Fock (MCDHF) approach. Valence and core-valence correlation effects were accounted for through single-double multireference (SD − MR) expansions to increasing sets of active orbitals. To confirm the accuracy of present results, independent calculations have been performed by using fully relativistic Flexible Atomic Code (FAC). Comparisons are made between our two different set of results, as well as with the other available experiments measurements and theoretical calculations. The present data are accurate enough for identification and are also useful for modeling and diagnosis fusion plasmas. We have reported many new atomic data which is not available in the literature and we believe our presented data can be considered as a benchmark of other calculations.

Extended theoretical transition data in C i–iv

ABSTRACT Accurate atomic data are essential for opacity calculations and for abundance analyses of the Sun and other stars. The aim of this work is to provide accurate and extensive results of energy levels and transition data for C i–iv. The Multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods were used in this work. To improve the quality of the wavefunctions and reduce the relative differences between length and velocity forms for transition data involving high Rydberg states, alternative computational strategies were employed by imposing restrictions on the electron substitutions when constructing the orbital basis for each atom and ion. Transition data, for example, weighted oscillator strengths and transition probabilities, are given for radiative electric dipole (E1) transitions involving levels up to 1s22s22p6s for C i, up to 1s22s27f for C ii, up to 1s22s7f for C iii, and up to 1s28g for C iv. Using the difference between the transition rates in length and velocity gauges as an internal validation, the average uncertainties of all presented E1 transitions are estimated to be 8.05 per cent, 7.20 per cent, 1.77 per cent, and 0.28 per cent, respectively, for C i–iv. Extensive comparisons with available experimental and theoretical results are performed and good agreement is observed for most of the transitions. In addition, the C i data were employed in a re-analysis of the solar carbon abundance. The new transition data give a line-by-line dispersion similar to the one obtained when using transition data that are typically used in stellar spectroscopic applications today.

Energy levels, line strengths, and lifetimes for Mo XXXVI

The fully relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) method implemented in the GRASP2018 atomic structure package has been used for the calculation of the excitation energies, lifetimes, wavelengths, weighted oscillator strengths, transition probabilities, and line strengths for electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions of N-like molybdenum, Mo XXXVI. The contributions from the Breit interaction (BI), and quantum electrodynamic (QED) corrections have been included in the calculations. The present excitation energies, wavelengths, line strengths, transition probabilities, and oscillator strengths are compared with the other available theoretical results. The uncertainties of the E1, M1, E2, and M2 line strengths are estimated using the comparison between the results from the present MCDHF largest layers.

A strong-field approach with realistic wave functions to the above-threshold ionization of Ba+

We study the above-threshold ionization of atoms in intense circularly polarized laser pulses. In order to compute photoelectron energy spectra, we apply the strong-field approximation with different models for the initial state wave function. Specifically, we compare the spectra for singly ionized Barium (Ba+) using hydrogenic wave functions and realistic one-particle wave functions obtained by multiconfiguration Dirac–Hartree–Fock computations, respectively. As a particular example, we discuss the dependence of the photoelectron spectra on the magnetic quantum number m of the initial state and we reproduce the well known m-selectivity in strong-field ionization. Here, we show that the photoelectron spectra exhibit noticeable differences for the two models of the initial state and that the m-selectivity is enhanced when realistic wave functions are used. We conclude that the description of strong-field processes within the strong-field approximation will benefit from a realistic description of the initial atomic state.