Relativistic Configuration Interaction Method Research Articles

Second order Rayleigh–Schrödinger perturbation theory for the Grasp2018 package: Core–core correlations

GRASP package is based on the relativistic configuration interaction in which accurate calculations, accounting for valence, valence–valence, core–valence, core and core–core electron correlations, often rely on massive CSF expansions. This paper presents a further development of the method based on the second-order perturbation theory for finding the most important CSFs that have the greatest influence on the core–valence, core and core–core correlations. This method is based on a combination of the relativistic configuration interaction method and the stationary second-order Rayleigh–Schrödinger many-body perturbation theory in an irreducible tensorial form [G. Gaigalas, P. Rynkun, and L. Kitovienė, Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core–valence correlations, Lith. J. Phys. 64(1), 20–39 (2024), https://doi.org/10.3952/physics.2024.64.1.3, and G. Gaigalas, P. Rynkun, and L. Kitovienė, Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core correlations, Lith. J. Phys. 64(2), 73–81 (2024), https://doi.org/10.3952/physics.2024.64.2.1]. In this extension, the perturbation theory takes into account electron core–valence, core and core–core correlations, where an atom or ion has any number of valence electrons, for calculation of energy spectra and other properties. Meanwhile, the rest of the correlations are taken into account in a traditional way. This allows a significant reduction of the space of the configuration state function for complex atoms and ions. We also demonstrate how this method works for calculations of the energy structure and E1 transition properties of Fe XV ion.

Atomic Data for Astrophysically Important Spectral Lines of Singly Ionized Nitrogen

Nitrogen lines are widely observed in astrophysical spectra and provide important diagnostics for plasma properties. In this work, we present extended calculations for accurate energy levels, electric dipole radiative transition parameters, and lifetimes for the lowest 102 states of the 2s 22p 2, 2s2p 3, 2s2p 23s, 2s 22p{n 1 l, n 2 d, 4f}(n 1 = 3–5, l = s, p, n 2 = 3, 4), and 2p 4 configurations of N ii within the framework of the fully relativistic multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods. These data are useful for modeling astrophysical spectra, for example, for nitrogen abundance determinations in early B-type stars, and for studying the compositions and plasma properties of H ii regions and planetary nebulae. Our computed transition parameters are compared with available experimental and theoretical data. The accuracy of the calculations is also assessed via a statistical analysis of the differences between the transition rates in the Babushkin and Coulomb gauges and by consideration of cancellation factors. In this way, 201 of the 1656 transitions computed in this work are estimated to be from accurate to better than 3%, corresponding to an accuracy class of A.

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.

Effect of dense plasma environment and external magnetic field on atomic structure and radiative properties of Ar XVII

Atomic structures and radiative properties of He like Ar XVII in the presence of dense plasma environments and external magnetic field have been presented within the framework of the relativistic theory. For this purpose, the relativistic configuration interaction method by incorporating the generalized b-potential and external magnetic field has been implemented. Plasma screening effect on 1s2 1S0 → 1s2p 3P1 transitions of Ar XVII ion in the presence of an external magnetic field has been investigated. We also studied the Zeeman splitted energies and predicted the excitation energies of Ar XVII ion for the magnetic sublevels 1s2p 3P0 (MJ = 0), 3P1 (MJ = 0, ±1), 3P2 (MJ = 0, ±1, ±2), 1P1 (MJ =0, ±1). Our calculated results are in excellent agreement with National Institute of Science and Technology (NIST) database and other theoretical available data.

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.

Second-order Rayleigh–Schrödinger perturbation theory for the GRASP2018 package: Core–valence correlations

The General Relativistic Atomic Structure package [GRASP2018, C. Froese Fischer, G. Gaigalas, P. Jönsson, and J. Bieroń, Comput. Phys. Commun. (2019), DOI: 10.1016/j.cpc.2018.10.032] is based on multiconfiguration Dirac– Hartree–Fock and relativistic configuration interaction (RCI) methods for energy structure calculations. The atomic state function used in the program is built from the set of configuration state functions (CSFs). The valence–valence, core–valence and core–core correlations are explicitly included through expansions over CSFs in RCI. We present a combination of RCI and the stationary second-order Rayleigh–Schrödinger many-body perturbation theory in an irreducible tensorial form to account for electron core–valence correlations when an atom or ion has any number of valence electrons. This newly developed method, which offers two ways of use, allows a significant reduction of the CSF space for complex atoms and ions. We also demonstrate how the method and program works for the energy structure calculation of Cl III ion.

Theoretical investigation of magnetic-field and hyperfine-induced transition parameters for magnesium-like and chlorine-like ions

In this paper, we report an extensive theoretical study of the magnetic-field and hyperfine-induced transition parameters for magnesium-like ions from Cr XIII to Zn XIX and chlorine-like ions from Mn IX to Co XI. These ions have a high abundance in the astrophysical plasma. Zeeman splitting level energies, hyperfine- and/or magnetic-field dependent wavelengths, and transition rates of the 3s3p 3P2,1,0→3s21S0 (for magnesium-like ions) and the 3p43d 4D7/2→ 3p52P3/2 line (for chlorine-like ions), are computed using the multiconfiguration Dirac–Fock method. Some higher-order effects, such as the Breit interaction and quantum electrodynamics corrections, are included in the relativistic configuration interaction method, as this makes the results more accurate. A comparison between the our predictions and other theoretical and experimental values is made. A satisfactory agreement is achieved. Besides providing valuable information for spectral line analysis, the present work will have a variety of implications for fusion and astrophysical plasma sources, for example, in the determination of magnetic fields in solar coronas and other stars.

Calculations of the Binding-Energy Differences for Highly-Charged Ho and Dy Ions

The binding-energy differences for163Hoq+and163Dyq+ions with ionization degreesq=38, 39, and 40 are calculated. The calculations are performed using the large-scale relativistic configuration-interaction and relativistic coupled-clusters methods. The contributions from quantum-electrodynamics, nuclear-recoil, and frequency-dependent Breit-interaction effects are taken into account. The final uncertainty does not exceed 1 eV. Combining the obtained results with the binding-energy difference for neutral atoms calculated in [I.M.Savelyev, M.Y. Kaygorodov, Y.S. Kozhedub, I.I. Tupitsyn, and V.M. Shabaev, Phys. Rev. A105, 012806 (2022)], we get the secondary differences of the ion–atom binding energies. These values can be used to evaluate the amount of energy released in the electron capture process in163Hoatom (theQvalue), provided mass differences of highly charged ions163Hoq+and163Dyq+is known from experiment. TheQvalue is required by experiments on the determination of the absolute scale of the electron neutrino mass by studying the beta-decay process.

Study of Electron Impact Excitation of Na-like Kr Ion for Impurity Seeding Experiment in Large Helical Device

In this work, a krypton gas impurity seeding experiment was conducted in a Large Helical Device. Emission lines from the Na-like Kr ion in the extreme ultraviolet wavelength region, such as 22.00 nm, 17.89 nm, 16.51 nm, 15.99 nm, and 14.08 nm, respective to 2p63p(2P1/2o)−2p63s(2S1/2), 2p63p(2P3/2o)−2p63s(2S1/2), 2p63d(2D3/2)−2p63p(2P3/2o), 2p63d(2D5/2)−2p63p(2P3/2o), and 2p63d(2D3/2)−2p63p(2P1/2o) transitions, are observed. In order to generate a theoretical synthetic spectrum, an extensive calculation concerning the excitation of the Kr25+ ion through electron impact was performed for the development of a suitable plasma model. For this, the relativistic multiconfiguration Dirac–Hartree–Fock method was employed along with its extension to the relativistic configuration interaction method to compute the relativistic bound-state wave functions and excitation energies of the fine structure levels using the General Relativistic Atomic Structure Package-2018. In addition, another set of calculations was carried out utilizing the relativistic many-body perturbation theory and relativistic configuration interaction methods integrated within the Flexible Atomic Code. To investigate the reliability of our findings, the results of excitation energies, transition probabilities, and weighted oscillator strengths of different dipole-allowed transitions obtained from these different methods are presented and compared with the available data. Further, the detailed electron impact excitation cross-sections and their respective rate coefficients are obtained for various fine structure resolved transitions using the fully relativistic distorted wave method. Rate coefficients, calculated using the Flexible Atomic Code for population and de-population kinetic processes, are integrated into the collisional-radiative plasma model to generate a theoretical spectrum. Further, the emission lines observed from the Kr25+ ion in the impurity seeding experiment were compared with the present plasma model spectrum, demonstrating a noteworthy overall agreement between the measurement and the theoretical synthetic spectrum.

Partial identification of visible lines from W24+ ions in an electron-beam ion trap

To better understand the structure of the open shell, the spectroscopic data in the 420–600 nm range of the highly charged ions of W24+ obtained with an electron beam ion trap are presented. Detailed collisional-radiative (CR) modeling has been used to simulate the spectrum. The atomic structure data for the CR modeling were calculated using the relativistic many-body perturbation theory (RMBPT) and the large-scale relativistic configuration interaction (RCI) method implemented in the flexible atomic code. The two set theoretical calculation wavelengths for six observed lines are in reasonable agreement with the experimental observations, with average deviations of 0.61% for RMBPT and 1.75% for RCI. The relative intensities of the identified lines have also been investigated, revealing a strong correlation to electron density from = 109 to 1011 cm−3.

Extreme field calculations for Penning ion traps and corresponding strong laser field scenarios

The extreme forces of highly charged ions and their trapping within high-precision experimental devices allow for challenging fundamental theories in yet unexplored territory. Here we focus on the theoretical side employing ab initio fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods to precisely calculate the bound-state energies of complex atoms and ions, as well as on presenting state-of-the-art high-precision g-factor calculations. In combination with similarly accurate experiments, one can competitively determine fundamental constants like the masses of the neutrino and the electron as well as setting new limits for physics beyond the standard model. Scenarios involving extreme laser pulses hold comparable potential but still require especially advances in the precision of the associated experiments.

A relativistic configuration interaction method with general expansions and initial applications to electronic g-factors.

A new implementation of the orbital-based two-component relativistic configuration interaction approach is reported and applied to calculations of the electronic g-shifts of three diatomic radicals: AlO, HgF, and PdH. The new implementation augments efficient routines for the calculation of nonrelativistic Hamiltonians with new vectorized routines for the calculation of the action of the one-electron spin-orbit operator and allows efficient calculations for the expansion of generalized active space type. The program makes full use of double group as well as time-reversal symmetry. Particle-hole reorganization of the operators is used to improve the efficiency for expansions with nearly fully occupied orbital spaces. The flexibility of the algorithm and program is used to investigate the convergence of electronic g-shifts for the three diatomic radicals as functions of the active space, states included in the orbital optimization, and excitation levels. It was possible to converge to the valence limits within a few percent using expansions containing up to quadruple excitations. However, when excitations from the core orbitals were added, it was not possible to demonstrate convergence to within a few percent with expansions containing at most 10 × 109 determinants.

Calculations of the Binding-Energy Differences for Highly-Charged Ho and Dy Ions

The binding-energy differences for ^{{163}}{text{H}}{{{text{o}}}^{{q + }}} and ^{{163}}{text{D}}{{{text{y}}}^{{q + }}} ions with ionization degrees q = 38, 39, and 40 are calculated. The calculations are performed using the large-scale relativistic configuration-interaction and relativistic coupled-clusters methods. The contributions from quantum-electrodynamics, nuclear-recoil, and frequency-dependent Breit-interaction effects are taken into account. The final uncertainty does not exceed 1 eV. Combining the obtained results with the binding-energy difference for neutral atoms calculated in [I.M. Savelyev, M.Y. Kaygorodov, Y.S. Kozhedub, I.I. Tupitsyn, and V.M. Shabaev, Phys. Rev. A 105, 012806 (2022)], we get the secondary differences of the ion–atom binding energies. These values can be used to evaluate the amount of energy released in the electron capture process in ^{{163}}{text{Ho}} atom (the Q value), provided mass differences of highly charged ions ^{{163}}{text{H}}{{{text{o}}}^{{q + }}} and ^{{163}}{text{D}}{{{text{y}}}^{{q + }}} is known from experiment. The Q value is required by experiments on the determination of the absolute scale of the electron neutrino mass by studying the beta-decay process.

Extended atomic data for oxygen abundance analyses

As the most abundant element in the universe after hydrogen and helium, oxygen plays a key role in planetary, stellar, and galactic astrophysics. Its abundance is especially influential in terms of stellar structure and evolution, and as the dominant opacity contributor at the base of the Sun’s convection zone, it is central to the discussion on the solar modelling problem. However, abundance analyses require complete and reliable sets of atomic data. We present extensive atomic data for O I by using the multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods. We provide the lifetimes and transition probabilities for radiative electric dipole transitions and we compare them with results from previous calculations and available measurements. The accuracy of the computed transition rates is evaluated by the differences between the transition rates in Babushkin and Coulomb gauges, as well as via a cancellation factor analysis. Out of the 989 computed transitions in this work, 205 are assigned to the accuracy classes AA-B, that is, with uncertainties smaller than 10%, following the criteria defined by the Atomic Spectra Database from the National Institute of Standards and Technology. We discuss the influence of the new log(gf) values on the solar oxygen abundance, ultimately advocating for log єO = 8.70 ± 0.04.

Relativistic calculations of molecular electric dipole moments of singly charged aluminium monohalides

In this work, we have studied the permanent electric dipole moments of singly charged aluminum monohalides in their electronic ground state, , using Kramers-restricted relativistic configuration interaction method. We report our results from this method in the singles and doubles approximation with those of Dirac–Fock calculations. For our finite field computations, quadruple zeta basis sets were employed. We discuss the electron correlation trends that we find in our calculated properties and have compared our results with those from literature, wherever available.

Theoretical investigation of Sb-like sequence: Sb I, Te II, I III, Xe IV, and Cs V

We aim to investigate atomic properties of Sb-like sequence: Sb I, Te II, I III, Xe IV, and Cs V. The multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2018, are used in the present work. The lowest energy levels of the 5s25p3, 5s5p4, 5p5, 5s5p35d, and 5s25p2{6s,7s,6p,7p,5d,6d,4f} configurations and electric dipole, magnetic dipole, and electric quadrupole transitions between states of these configurations are computed. Accuracy of energy levels are evaluated by comparing it with the National Institute of Standards and Technology Atomic Spectra Database recommended values and with other methods. Accuracy of transitions data are investigated using quantitative and qualitative evaluation method.

Collisional-radiative modeling of the 2p3l(l = p,d) spectra of N II and application to lightning

The excitation energies, transition rates, collisional-excitation cross sections, and collisional-excitation rate coefficients of N II ions have been calculated by the relativistic configuration-interaction method with the implementation of the flexible atomic code. The population rate coefficients were subsequently investigated and shown that the net population rate coefficients of the 2p3d configuration are greater than those of the 2p3p configuration at an identical electron temperature. A reasonable collisional-radiative model has been constructed to simulate the 2p3s–2p3p and 2p3p–2p3d spectra, which were in reasonable agreement with the lightning data presently obtained in experimental measurements. A further application was implemented in effectively determining the lightning parameters, with the aid of a certain area surrounded by the intersections of contours of multiple line-intensity ratios on the two-dimensional plane of electron temperature and electron density.

Theoretical Investigation of Electron–Ion Recombination Process of Mg-like Gold

The L-shell dielectronic and trielectronic recombinations of highly charged Mg-like gold ions (Au67+) in the ground state 2s22p63s2 1S0 have been studied systematically. The recombination cross-sections and rate coefficients are carefully calculated for ∆n = 1 (2s/2p → 3l) transitions using a flexible atomic code based on the relativistic configuration interaction method and considering the Breit and QED corrections. Detailed resonance energies and resonance strengths are presented for the stronger resonances of the LMn (n = 3–12) series. It is found that the contributions of the trielectronic recombination to the total cross-section is about 13.75%, which cannot be neglected. For convenience of application, the plasma rate coefficients are also calculated and fitted to a semiempirical formula, and in the calculations, the contributions from the higher excited resonance groups n ≥ 13 are evaluated by an extrapolation method, which is about 2.93% of the total rate coefficient.

Be optical lattice clocks with the fractional Stark shift up to the level of 10−19

The energy levels and electric dipole () matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic , magnetic dipole () and electric quadrupole () polarizabilities as well as the hyperpolarizabilities of the and states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock transition at the magic wavelength are discussed in detail. We find that when the laser intensity I is in the range of 14.3–15.9 kW cm−2 and the detuning δ (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7–40.9 MHz, the fractional Stark shifts of the clock transition are less than 1.0 × 10−18. While, when I is in the range of 15.01–15.46 kW cm−2 and δ is in the range of 40.73–40.76 MHz, the fractional Stark shifts are lower than 1.0 × 10−19.