Multiconfiguration Dirac Hartree Fock Research Articles

Theoretical exploration of atomic structure calculation of sodium atom confined in the fullerene cage: a primer investigation for EIT applications

Alterations in the electronic structural properties of a sodium atom confined inside a fullerene cage are investigated in this manuscript; the engineered atom is explored to suit for the quantum technique applications. A Gaussian annular square well (GASW) model has been used to mimic the fullerene environment. Electronic properties such as energy levels, probabilities, the lifetime of the levels, etc, have been studied for various confinement depths of GASW using the multi-configuration Dirac Hartree–Fock technique. The wavelengths of the D lines of the sodium atom have been shifted from the typical yellow to the blue and then to the ultraviolet region upon confinement. Using the range-shifted blue D lines of the engineered atom, a typical Λ-type electromagnetically induced transparency configuration is proposed. Furthermore, we have shown the explicit dependency of relevant atomic parameters on the confinement depth, which showcases the tunability to suit the engineered atoms for various applications; for instance, increasing the confinement depth increases the lifetime of 3D5/2 and 3D3/2 states significantly from the typical lifetime value, which has potential applications in quantum technologies.

Investigation of the M1 transitions from the ground configuration of W23+

To extend the research on the atomic structure of tungsten ions with an open 4f-shell, we conducted an investigation into the M1 transitions originating from the ground configuration of W23+ using the SHHtscEBIT in the 420–600 nm range. Three different calculational methods, including the relativistic configuration interactions (RCI) and the relativistic many-body perturbation theory (RMBPT) implemented in FAC, as well as the multiconfiguration Dirac-Hartree-Fock (MCDHF) in GRASP2018, are performed to investigate the energy level structure of W23+. The excitation energies obtained through RCI and RMBPT are in good agreement, with an average difference of 0.62 %. When comparing RCI and MCDHF, this difference increases to 1.20 %. The observed 12 lines of W23+are identified using the detailed collisional-radiative model with the atomic data calculated by RCI. The average wavelength deviations from experimental results are 0.77 %, 1.38 %, and 2.02 % for RCI, RMBPT, and MCDHF, respectively.

The excitation energies and hyperfine structures for 2l, 3l states in lithiumlike ions

Combining the multi-configuration Dirac–Hartree–Fock method and the model-quantum electrodynamics (QED) approach, the wave functions, transition energies and hyperfine structure constants for 2l, 3l states in Li-like Ne7+, Mg9+, Al10+, P12+, Ar15+ and Ca17+ ions are calculated. The effects of electron correlation, Breit interactions, nuclear recoil and QED effects are analyzed in detail. We find that the contribution of the non-diagonal elements of the self-energy is significant for the 2p1/2→2s1/2 and 2p3/2→2s1/2 transitions. However, for the 3l→2s1/2 transitions, the contribution of non-diagonal elements is small. The accuracy of the currently calculated hyperfine structure constants is expected to be within 1%.

Theoretical investigation of energy levels and transitions for Ce iii with applications to kilonova spectra

ABSTRACT Doubly ionized cerium (Ce2+) is one of the most important ions to understand the kilonova spectra. In particular, near-infrared (NIR) transitions of Ce iii between the ground (5p6 4f2) and first excited (5p6 4f 5d) configurations are responsible for the absorption features around 14 500 Å. However, there is no dedicated theoretical studies to provide accurate transition probabilities for these transitions. We present energy levels of the ground and first excited configurations and transition data between them for Ce iii. Calculations are performed using the grasp2018 package, which is based on the multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods. Compared with the energy levels in the NIST data base (Kramida et al. 2024), our calculations reach the accuracy with the root-mean-square (rms) of 2732 or 1404 cm−1 (excluding one highest level) for ground configuration, and rms of 618 cm−1 for the first excited configuration. We extensively study the line strengths and find that the Babushkin gauge provides the more accurate values. By using the calculated gf values, we show that the NIR spectral features of kilonova can be explained by the Ce iii lines.

Relativistic configuration-interaction calculations on K α X-ray satellites of medium-charge Be-like ions

This study puts forward a calculation of the transitions of 1s2s22p 1P1−1s22s2 1S0 and 1s2s22p 3P1−1s22s2 1S0 for Be-like ions (Z = 6–30) using the multiconfiguration Dirac-Hartree–Fock (MCDHF) and relativistic configuration interaction methods. The computational results include transition wavelengths, transition probabilities, line strengths, and weighted oscillator strengths. The calculations also consider the contributions of the Breit interaction and quantum electrodynamics corrections (QED) to these levels. The results show that the contribution of the Breit interaction, self-energy, and vacuum polarization increase rapidly with increasing nuclear charge for certain configurations. The present calculated values are in good agreement with previous theoretical and experimental results, with errors better than 0.3%. A V/A L comparisons demonstrate the reliability of the data.

The study of atomic structure parameters of n = 2-n = 3 for Cl XII ion

This study utilized the multiconfiguration Dirac-Hartree-Fock (MCDHF) method to compute transition wavelengths among the 2s22p2, 2s22p3s, 2s22p3d, 2s2p23p configurations of the carbon-like Cl ion, as the same time, the transition rates, weighted oscillator strengths, and line strengths for these transitions are investigated. Comparison with experimental and theoretical results demonstrated favorable agreement, validating the accuracy of the calculated results. The study's results for transition rates deviated by no more than 20 % from reference values and showed good agreement for weighted oscillator strengths compared to Hartree-Fock Relativistic (HFR) method calculations. The line strength results served to assess the reliability of the calculated atomic structure parameters. We hope these results are anticipated to contribute to the expansion of the Cl ions database and furnish valuable help for studies within the plasma domain.

Relativistic calculations of energy levels, lifetimes, transition parameters, and electron impact excitation cross sections for Kr XIX

In this study, we present a detailed analysis of atomic properties for Kr XIX, specifically focusing on the lowest 128 fine-structure levels originating from the 3s23p6, 3s23p53d, 3s3p63d and 3s23p43d2 configurations. We report energy levels, lifetimes, wavelengths, weighted oscillator strengths, and transition probabilities for multipole transition types (E1, E2, M1, and M2). To achieve this, we employed the GRASP2018 code, which implements the fully relativistic multiconfigurational Dirac–Hartree–Fock method and accounts for Breit interaction and quantum electrodynamic effects. We performed another set of calculations using the many-body perturbation theory implemented in the flexible atomic code (FAC). By comparing the results obtained from GRASP2018 and FAC, we established the accuracy and consistency of our calculations. Furthermore, using the relativistic distorted wave theory, we studied electron impact excitation of all transitions to upper levels from the ground and metastable levels and reported excitation cross sections for incident electron energies up to 5 keV. To enhance the practical utility of our findings, we also provided analytical fittings of these cross sections and excitation rate coefficients for their applications in plasma modeling. This work contributes to the atomic properties and excitation cross sections of Kr XIX, addressing a marked gap in the available atomic data.

The Landé g factors of highly charged Sn47+ and Bi80+ ions

The wavefunctions and eigenvalues of the ground states of Sn47+, and Bi80+ ions are calculated using the fully relativistic multiconfiguration Dirac-Hartree–Fock (MCDHF) method. Detailed investigation are carried out to study the effects of electron correlation, Breit interaction, quantum electrodynamics (QED), and nuclear recoil. Based on these calculations, the theoretical predictions for the g factors of the ground states of Sn47+ and Bi80+ ions are 1.980429 and 1.934759, respectively. The accuracy of these calculations is expected to be on the order of 10−5.

The 3d 2 D 5/2−2 D 3/2 magnetic dipole transition in potassium-like ions

Spectral lines of the magnetic-dipole transition between the 3d2D3/2,5/2 levels of K-like Kr17+, Zr21+, Nb22+, Mo23+, and Ru25+ ions were measured in a compact electron beam ion trap. By means of dedicated calibration methods, the transition wavelengths of Kr17+, Zr21+, and Mo23+ ions reduce uncertainties by at least one order of magnitude and the wavelengths of Nb22+ and Ru25+ ions are measured for the first time at a few ppm level. In addition, the fine-structure energy splittings were systematically calculated using the multiconfiguration Dirac–Hartree–Fock method combined with the relativistic configuration interaction approach. The contributions of the core-valence and core-core electron correlations, the Breit interaction and QED effect were discussed in detail. The results show that it is essential to include deep core-valence correlation of L-shell and core-core valence correlation of 3p subshell to obtain an agreement better than 0.15% with existing experimental values. The calculation model can be performed to predict the wavelength within a high accuracy for a wide range of potassium-like ions.

Theoretical study on Mα transition parameters of He-like to C-like cobalt ions

The multi-configuration Dirac–Hartree–Fock method is employed to investigate the Mα transitions of He-like to C-like Co ions. This study encompasses various parameters, such as energy levels, wavelengths, transition rates, oscillator strengths, and line strengths. The Breit interaction, vacuum polarization, and self-energy corrections were included in the computation of energy levels. The computed results we obtained align well with both experimental and theoretical findings. The differences for most energy levels, transition wavelengths, and oscillator strengths are all below 0.6%, 0.8%, and 20%, respectively. The uncertainty estimation method of the transitions of line strength is evaluated using quantitative and qualitative evaluation methods. The resulting accurate and consistent MCDHF data are expected to be useful for theoretical research on cobalt ions.

Investigation of optical spectroscopy in W13+ ions

This study presents the investigation of magnetic dipole transition lines of W13+ ions in the wavelength range of 200–700 nm at a low-energy electron beam ion trap. Seventeen lines emitted from W13+ ions have been observed with three being reported experimentally for the first time. The atomic structure calculation and spectra simulation of W13+ ions have been carried out using the multiconfiguration Dirac–Hartree–Fock method combined with the relativistic configuration interaction approach and the collisional–radiative model, respectively. The theoretical calculations are in reasonable agreement with the experimental observations, and most of the observed lines have been identified.

The study of atomic structure parameters for [formula omitted] = 4 - [formula omitted] = 3 transitions in Mg-like ions with [formula omitted

Multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods are utilized for theoretical calculations of energy levels, wavelengths, line strengths, absorption oscillator strengths, and transition probabilities in 3s2-3s4p, 3s3p-3s4s, 3s3p-3s4d, 3s3p-3p4p, 3s3d-3s4f, 3p2-3p4s, 3p2-3p4d, and 3p3d-3p4f transitions in Mg-like ions with 15≤Z≤30. The calculations of energies account for Breit interaction and quantum electrodynamics (QED) contributions. The active space approximation is employed for the calculations, and energy converges when the active orbital set is increased to n = 7. The calculated lowest 78 levels including valence and core–valence correlations in Mg-like ions with Z=15–30 show good agreement with experiment results and other calculations. The relative difference between calculated wavelengths and experiment values exhibits a decreasing trend as the atomic numbers increase, and the difference is better than 1% for a majority of transitions. To evaluate the accuracy of the wave functions and transition parameters, the quantity dT is analyzed within 0.1 for most strong transitions. The transition probabilities are compared with other theoretical values to analyze with line strength S. Such calculations may provide valuable data for the experimental study of plasma diagnostics and modeling as there are others.

Overview of the contributions from all lanthanide elements to kilonova opacity in the temperature range from 25000 to 40000 K

It is now well established that the neutron star (NS) merger is at the origin of the production of trans-iron heavy elements in the universe. These elements are therefore present in large quantities in the ejected matter, whose electromagnetic radiation, called kilonova, is characterized by a significant opacity due to the high density of spectral lines belonging to many heavy ions. Among these, the lanthanide ions play an essential role since, with their open 4f subshell, they have a considerable number of transitions that can absorb emitted light. The knowledge of the atomic structure and the radiative parameters of these ions as well as the determination of the corresponding opacities is therefore of paramount importance for the spectral analysis of kilonovae. The main goal of the present work is to determine the relative contributions of the different lanthanide elements to the opacity of the emission spectrum of a kilonova in its early phase, that is, a few hours after the NS merger, where the conditions are such that the temperature is between 25000 and 40000 K. At these temperatures, the lanthanide ions whose charge states are between V and VII are predominant. We used the pseudo-relativistic Hartree-Fock (HFR) method extensively to calculate the relevant atomic data (energy levels, wavelengths, and oscillator strengths) in La-Lu V-VII ions. The corresponding monochromatic opacities were estimated from the expansion formalism. We calculated the spectroscopic parameters for a total of more than 800 million radiative transitions in all the ions considered. These data were used to estimate the expansion opacities and Planck mean opacities for all the lanthanide elements at early-phase kilonova conditions between 25000 and 40000 K, making it possible to deduce the respective contributions of each element as a function of temperature. Atomic calculations were also carried out with the fully relativistic Multiconfiguration Dirac-Hartree-Fock (MCDHF) method in the specific case of the Yb V ion, as the available experimental data had not yet been compared with the theoretical calculations in our previous studies on lanthanide ions.

Targeted optimization in small-scale atomic structure calculations: application to Au I

The lack of reliable atomic data can be a severe limitation in astrophysical modelling, in particular of events such as kilonovae that require information on all neutron-capture elements across a wide range of ionization stages. Notably, the presence of non-orthonormalities between electron orbitals representing configurations that are close in energy can introduce significant inaccuracies in computed energies and transition probabilities. Here, we propose an explicit targeted optimization (TO) method that can effectively circumvent this concern while retaining an orthonormal orbital basis set. We illustrate this method within the framework of small-scale atomic structure models of Au I, using the Grasp2018 multiconfigurational Dirac–Hartree–Fock atomic structure code. By comparing to conventional optimization schemes we show how a TO approach improves the energy level positioning and ordering. TO also leads to better agreement with experimental data for the strongest E1 transitions. This illustrates how small-scale models can be significantly improved with minor computational costs if orbital non-orthonormalities are considered carefully. These results should prove useful to multi-element atomic structure calculations in, for example, astrophysical opacity applications involving neutron-capture elements.

Determination of the radiative transition rates in Ta VII using a multiplatform approach

Tantalum (Z=73) is an element that is produced in the neutron-induced transmutation of tungsten (Z=74) which in turn will compose the divertors in Tokamaks. As a consequence, their sputtering may generate ionic impurities of all possible charge states in the deuterium-tritium plasma that could contribute to radiation losses in controlled nuclear devices. The radiative properties of these ions have therefore potential important applications in this field. In this context, a multiplatform approach has been adopted in order to compute the Ta VII radiative rates and estimate their accuracy. The oscillator strengths and transition probabilities have been calculated for the 237 electric dipole (E1) transitions of the Ta VII spectrum as classified by Ryabtev et al. (2014). Three independent atomic structure models have been used; one based on the semi-empirical pseudo-relativistic Hartree–Fock (HFR) method and two based on the fully relativistic ab initio multiconfiguration Dirac–Hartree–Fock (MCDHF) method.

Energies and radiative properties of 1s22l2l′ and 1s(2l)22l′ levels in tungsten ion, W70+

Multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations of energy levels, oscillator strengths and transition rates of open K-shell transitions in beryllium-like tungsten ion, W[Formula: see text], are performed using the fully relativistic GRASP2018 code. For only principal quantum number [Formula: see text], energy levels of 1[Formula: see text] 2[Formula: see text], 1[Formula: see text]2[Formula: see text], 1[Formula: see text]2[Formula: see text], 1[Formula: see text]2p, 1[Formula: see text] and 1[Formula: see text] at different angular momenta and parity ([Formula: see text] are presented. Excitations of up to four electrons from the ground level, 1[Formula: see text] 2[Formula: see text], to excited levels are allowed. Correlations up to 5l orbitals are included in the configuration state function (CSF), [Formula: see text], p, d, f and g. The fine-structure calculations of E1, E2, M1 and M2 oscillator strengths and radiative rates between intercombination transitions in W[Formula: see text] ions are evaluated. The accuracy of these results is estimated using different ways, such as the comparison with previously published results and calculating the uncertainty of the transition data. The uncertainty of the transition probabilities showed low values for most of transitions.

Calculations of energy levels, transition rates, lifetimes and Landé g factors for silicon-like Kr XXIII

The multiconfiguration Dirac–Hartree–Fock (MCDHF) method is employed to calculate excitation energies, transition rates, lifetimes and Landé g factors for the lowest 700 levels belonging to the 22 configurations 3s23p{3l,4l′}, 3s3p2{3l,4l′}, 3s23d{3d,4s,4p}, 3s{3p3d2,3d3}, 3p{3p3,3p23d,3p3d2,3d3}, 3d4 with l = 1, 2 and l′ = 0, 1, 2, 3 in Kr XXIII. The present excitation energies are compared with available experimental and theoretical values. The mean relative difference between our results and the values provided by the National Institute of Standards and Technology (NIST) is only 0.05%, which suggests a good agreement. The uncertainties of the transition rates are estimated based on quantitative and qualitative evaluation method which analyzes the dependencies of the line strength S on the gauge parameter G. It is observed that 49.6% of E1 S values have uncertainties of ≤ 1% (AA) and over 82% have uncertainties of ≤ 3% (A). The present wavelengths and transition rates are compared with the experimental values and generally good agreements have been achieved. For lifetime, the present MCDHF values fall well within the range of experimental error. Comparison of the computed Landé g factors is also made with the Landé g factors in pure LS-coupling. These accurate data can be useful for fusion plasma research and astrophysical applications.

Extended calculations of energy levels and transition rates for Yb LVII

Abstract Extended energy levels and transition data for the Yb LVII are calculated with the GRASP2018 package, which is based on the multiconfiguration Dirac–Hartree–Fock and relativistic configuration methods. Complete and consistent data sets of energy levels, transition rates and lifetimes for electric-dipole (E1), electric-quadrupole (E2), magnetic-dipole (M1), and magnetic-quadrupole (M2) transitions among all these levels are given in this calculation. Three methods of uncertainty estimators are used to evaluate the accuracy of transition data. The computed results are also compared with other theoretical computations. The present results are reported as benchmarks for future calculations and measurements.

Extended calculations of energy levels, radiative properties, and lifetimes for oxygen-like Ge XXV

The calculations are performed for the lowest 427 fine-structure levels arising from the 2s22p4, 2s2p5, 2p6, 2s22p3nl (n=3−4, l≤n−1), 2s2p4nl (n=3−4, l≤n−1), and 2p5nl (n=3, l≤n−1) configurations in O-like Ge XXV using two state-of-the-art methods, namely the many-body perturbation theory (MBPT) method and the multiconfiguration Dirac–Hartree–Fock (MCDHF) method. A comprehensive set of atomic data for these 427 levels is presented, encompassing excitation energies, wavelengths, E1, E2, M1, M2 radiative transition data (line strengths, oscillator strengths, transition rates), and lifetimes. Thorough comparisons are made between the results obtained from the two methods, as well as with existing data. The accuracy of the present data set is deemed sufficient for precise identification and deblending of emission lines associated with the n=3,4 levels. Furthermore, these data can contribute to the modeling and diagnosis of fusion plasmas.

Formula omitted][formula omitted] MCDHF/RCI calculations of mass- and field shifts isotopes parameters of the [formula omitted][formula omitted][formula omitted] and [formula omitted][formula omitted][formula omitted] transitions in He-like ions for the sequence 2 [formula omitted][formula omitted][formula omitted] 83

Based on the multiconfiguration Dirac–Hartree–Fock method, the field shift and mass shift parameters of the 1s21S0−1s2p1P1o and 1s21S0−1s2p3P0,1,2o transitions in He-like ions for the sequence 2 ≤Z≤ 83 are calculated with high precision. The total value of the isotope shift is determined by the sum of the mass- and field-shifts. With the inclusion of the Breit interaction and the leading QED corrections, we find that the mass shift parameters of these transitions do not change monotonously along the isoelectronic sequence in the high-Z range due to the relativistic nuclear recoil effects. In addition, the field shifts and mass shifts of these four transitions are estimated and compared along the isoelectronic sequence.