Multiconfiguration Dirac-Fock Research Articles

Accurate ab initio calculation and neural network prediction of the atomic properties of Os LXXIII, Ir LXXIV, Pt LXXV, and Au LXXVI

In this paper, we present an ab initio theoretical calculation of the atomic parameters, including energy levels, wavelengths, lifetimes, and transition parameters, associated with the 1s22snl and 1s22pnl (n= 2–4, l≤n−1) configurations of Be-like sequence: Os LXXIII, Ir LXXIV, Pt LXXV, and Au LXXVI. Our analysis is based on the relativistic wavefunctions derived from the multi-configuration Dirac–Fock (MCDF) method, which are implemented in the relativistic atomic structure package GRASP2018. The correlations within the (principal quantum number) n= 10 complex are accounted for. The Breit interaction and quantum electrodynamical effects are added in the relativistic configuration interaction (RCI) calculation. Our results are compared with the existing data. The uncertainties of the dipole transition line strengths are assessed. In addition, we propose a feed forward neural network to predict the energy levels of Au LXXVI. This is a powerful machine learning tool capable of learning from existing data and predicting unknown data. The network is trained using theoretical energy levels of Os LXXIII, Ir LXXIV, and Pt LXXV obtained from the MCDF method. Our neural network exhibits average relative deviations of approximately 0.01% and 0.02% for trained and predicted energy levels, respectively, when compared to the MCDF results. This level of deviation suggests that our results are reasonably accurate. The data set presented in this study is useful for modeling fusion plasmas.

Relativistic atomic structure calculations of Li-like ions used for plasma diagnostic studies

We have carried out atomic structure calculations using systematically enlarged multiconfiguration Dirac-Fock wavefunctions of Li-like ions of the most prominent plasma impurities (Ar, Ti, Fe, Ni, Kr and W) found in presently working tokamaks. Relativistic Breit interaction and quantum electrodynamic (QED) corrections such as vacuum polarization and self-energy corrections are also included in the calculations prior to the evaluation of low lying energy levels, transition probabilities, oscillator strengths and line strengths. Selective radiative data for electric dipole and magnetic quadrupole transitions are also reported. Special emphasis is given in the computations of fundamental quantities such as oscillator strengths as they are widely used in atomic data and analysis structure (ADAS) databases to evaluate quantities such as effective collision strengths. Present computed values are compared with existing available results on NIST database and few similar earlier computations and a good agreement has been found. We believe that the detailed atomic data with the relativistic and QED corrections will assist in spectroscopic studies such as accurate line identification and plasma modelling work in tokamak plasma, laser induced breakdown spectroscopy (LIBS), highly charged ions clocks and astrophysical observations.

Large-scale relativistic calculations of spectral data in Zr XXVIII, Nb XXIX and Tc XXXI of tokamak interest

Large-scale relativistic multiconfiguration Dirac–Fock calculations of energy levels and lifetimes of the 206 states arising from the 3s23p, 3p3, 3s3p3d, 3p3d2, 3s24p, 3s24f, 3s3p2, 3s23d, 3s3d2, 3s24d, 3s24s, 3s3p4s, 3s3p4d, 3p23d, 3d3, and 3s3p4p configurations of Zr XXVIII, Nb XXIX, and Tc XXXI of tokamak interest are carried out. The active space approximation is employed for the calculations. To obtain accurate and convergent results, the calculations take into account the valence and core-valence correlations within the n= 9 complex, as well as the Breit interaction, self-energy corrections, and vacuum polarization corrections. Detailed information regarding the decay properties of these ions is provided, including the transition wavelengths, line strengths, and radiative transition rates for various types (electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole transitions) of transitions among the levels of the aforementioned configurations. The uncertainties of each dipole transition are evaluated. The present data sets are compared to previous results and a good agreement is observed, which is valuable for emission line identification and fusion modeling, especially in situations where experimental data are scarce.

Semi-Empirical and Theoretical Calculation of L1, L2, and L3 Subshell Fluorescence Yields

In this study, semi-empirical Li subshells fluorescence yields (ωLi) were calculated from the available experimental data covering the period from 1955 to 2022 for elements with 28 ≤ Z ≤ 96 for L1 subshell, and 23 ≤ Z ≤ 96 for L2 and L3 subshells. First, we critically examine these data and obtain weighted average values (ωL1W,ωL2W,andωL3W) using a formula based on experimental (ωEXP) values and measurement errors. New recommended values ωWR are obtained by calculating the ratio S = ωEXP/ωW and removing out-of-range values (less than 0.8 or greater than 1.2). Semi-empirical values were derived for the three subshells using two interpolations: the analytical function [ωWR/(1 − ωWR)]1/4 and the fitting ratio S = ωEXP/ωWR, both as function of the atomic number Z. Furthermore, new theoretical calculations based on the Multiconfiguration Dirac-Fock Method have been performed for some elements and are presented in this work. Finally, our semi-empirically and theorical calculated Li subshell fluorescence yields were compared with other theoretical, experimental, and empirical values from the literature.

Fine structure resolved excitation cross sections of singly ionized Ga for the modeling and diagnostics of Ga plasmas

Calculation of electron impact excitation cross sections for singly charged Ga ions plays a crucial role in plasma modeling, facilitating the comprehension of plasma behavior, characteristics, and dynamics in diverse domains, such as astrophysics, fusion research, the semiconductor industry, etc. In the available literature, there is a notable scarcity of, or even a complete absence of, these cross sections. Hence, in the present work, electron impact excitation cross sections are calculated for the transitions from the fine structure resolved energy levels of the configurations 4s2 and 4s4p to the fine structure resolved energy levels of the configurations 4s4p , 4s5s , 4p2 and 4s4d of the singly charged Ga ion (Ga+) using the relativistic distorted wave approximation theory with the target states represented by multi configurational Dirac Fock wavefunctions. The cross sections are calculated for projectile electron energy varying from threshold to 500 eV. Furthermore, the electron impact excitation rate coefficients for all the transitions under investigation are also calculated for electron temperatures ranging from 0.5 to 5 eV. In addition, analytic fitting of the rate coefficients is also performed, providing a practical resource for directly utilizing in plasma modeling applications.

Lisbon Atomic Database (LISA): a compilation of calculated fundamental atomic parameters

The Lisbon Atomic Database (LISA) has a dedicated mission of compiling and providing a comprehensive collection of atomic parameters for the study of the interaction of X-rays with matter. This encompassing array of parameters spans a broad spectrum, extending from the calculation of electron impact ionization cross sections (EIICS) using the Modified Relativistic Binary Encounter Bethe model (MRBEB) , to pivotal data such as fluorescence and Coster–Kronig yields of atomic subshells, binding energies, and the full suite of radiative and non-radiative atomic transition parameters. Except for the EIICS values, all these parameters are obtained through ab initio calculations. These calculations are carried out using a self-consistent ab initio Multi-Configuration Dirac–Fock approach, supported by a specialized code developed by Desclaux, Indelicato, and others (MCDFGME).Graphical abstract

Fully relativistic distorted wave calculations of electron impact excitation of gallium atom: Cross sections relevant for plasma kinetic modeling

Electron impact excitation cross sections of neutral Ga are calculated using the relativistic distorted wave approximation with the aid of multiconfigurational Dirac-Fock wavefunctions. The cross sections are calculated from the fine structure resolved levels of the 4s24p manifold, i.e., from the ground 2P1/2 and the first excited state 2P3/2, to the fine structure resolved levels of the manifolds 4s24pdf, 4s4p2(4P1/2,4P3/2, and 4P5/2), 4s25spdf, 4s26spdf, 4s27spdf, and 4s28spdf for incident electron energies ranging from threshold to 500 eV. Where available, a comparison of the calculated oscillator strengths, transition probabilities, and cross sections with the previously reported results has been performed. The cross sections for the excitation from 4s24p2P1/2 to 4s24f, 4s4p2(4P1/2,4P3/2, and 4P5/2), 4s25f, 4s26f, 4s27df, and 4s28spdf and all the excitation cross sections from 4s24p2P3/2 are calculated and reported for the first time for a wide range of electron energies. Furthermore, the rate coefficients are also calculated using the present cross sections for an electron temperature varying from 0.5 to 5 eV. An analytic fitting of the calculated rate coefficients is provided to facilitate their inclusion in various plasma kinetic models.

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.

A Study of the Atomic Processes of Highly Charged Ions Embedded in Dense Plasma

The study of atomic spectroscopy and collision processes in a dense plasma environment has gained a considerable interest in the past few years due to its several applications in various branches of physics. The multiconfiguration Dirac-Fock (MCDF) method and relativistic configuration interaction (RCI) technique incorporating the uniform electron gas model (UEGM) and analytical plasma screening (APS) potentials have been employed for characterizing the interactions among the charged particles in plasma. The bound and continuum state wavefunctions are determined using the aforementioned potentials within a relativistic Dirac-Coulomb atomic structure framework. The present approach is applied for the calculation of electronic structures, radiative properties, electron impact excitation cross sections and photoionization cross sections of many electron systems confined in a plasma environment. The present study not only extends our knowledge of the plasma-screening effect but also opens the door for the modelling and diagnostics of astrophysical and laboratory plasmas.

Hyperfine-induced effects on linear polarization following electron-impact excitation of heliumlike Tl79+ ions with nuclear spin

A most general density-matrix formalism is presented to investigate linear polarization of characteristic lines following electron-impact excitation of atoms or ions with arbitrary nuclear spin, which can account for depolarization of energy levels and multipole mixing of radiation fields. It is then applied to the linear polarization of the line radiated from heliumlike ions with nuclear spin . As an example, detailed calculations are performed for Tl79+ ions using the multi-configurational Dirac-Fock method and relativistic distorted-wave theory. It is found that the effect of the hyperfine interaction on the linear polarization depends dominantly on impact electron energy. For low impact energies close to the excitation threshold, the hyperfine interaction results in an enhancement of the linear polarization, especially for those photons emitted perpendicularly to the impact electron beam. In contrast, such a hyperfine-induced effect diminishes quickly with increasing impact energy and vanishes at medium and high energies, which is very different from the results for the case of radiative electron capture (Surzhykov et al 2013 Phys. Rev. A 87 052507). The present study is experimentally accessible at both electron-beam ion traps and ion storage rings and, thus, accurate polarization measurements at low energies can be utilized to probe the hyperfine interaction in highly charged few-electron ions.

Measurement and modelling of resonant inelastic X-ray scattering and many-body processes using extended-range high energy resolution fluorescence detection and multiconfigurational Dirac–Fock calculations

Measurement and modelling of resonant inelastic X-ray scattering and many-body processes using extended-range high energy resolution fluorescence detection and multiconfigurational Dirac–Fock calculations

Electron impact fine-structure cross-section calculations of Cu and their applications in the diagnostics of laser-produced Cu-plasma through the collisional radiative model

We present the calculations of electron impact excitation cross-sections for the transitions from the ground state of Cu 3d104sS1/22 to the excited fine structure energy levels of the configurations 3d94s2,3d94s4p,3d104l,(l=p,d,f),3d105l,(l=s,p,d),3d10nl,(n=6,7;l=s,p) using the fully relativistic distorted wave theory. In addition, cross-sections for the transitions from the metastable states 3d94s2D5/2,3/22 to the upper excited levels are also presented. For calculating these cross-sections, we have obtained the atomic wave functions of copper using the multi-configuration Dirac–Fock approximation theory. To ensure the accuracy of these wave functions, we compared our calculated oscillator strengths of some dipole-allowed transitions of Cu with the available earlier reported values. We have utilized all the calculated electron impact fine-structure level excitation cross-sections from the ground as well as the metastable states of Cu to develop a fine structure-resolved collisional-radiative (CR) model for the diagnostics of laser-produced Cu plasma at atmospheric pressure. The model has been applied for diagnostics by coupling it with the spatially resolved optical emission spectroscopy (OES) measurements of Singh and Sharma [Phys. Plasmas 23 122104 (2016)] in the presence and absence of a static magnetic field. For diagnostics, the intensities of three OES observed strong atomic emission lines of Cu viz, 510.5, 515.3, and 521.8 nm have been utilized in the absence and presence of a magnetic field at different axial lengths (z = 0.5–6.5 mm) from the Cu target. Also, these intensities are corrected using the internal reference self-absorption method to overcome the effect of radiation trapping. The normalized intensities of the considered lines obtained from the CR model have been compared with their corresponding OES-measured values to extract the plasma parameters, i.e., electron temperature and electron density. Further, the obtained electron temperatures from the CR model are compared with the corresponding values reported in the experimental paper of Singh and Sharma [Phys. Plasmas 23 122104 (2016)] obtained using the Boltzmann plot method.

Calculations of energy levels, radiative transition parameters, hyperfine structure constants [formula omitted] - [formula omitted], Landé [formula omitted] factors and isotope shifts for Sc XX using the MCDF-RCI method

Large scale calculations for the energy levels, transition rates, oscillator strengths, lifetimes, hyperfine interaction constants, Landé gJ factors, and isotope shift factors have been performed for 1s2 and 1snl(n=2−8andl≤n−1) levels of He-like Sc XX ion. The general-purpose relativistic atomic structure package (GRASP2018) based on the fully relativistic multiconfiguration Dirac–Fock (MCDF) method is used to carry out the calculations. The leading quantum electrodynamic corrections, Breit interaction and nuclear recoil effects are also included in the succeeding relativistic configuration interaction (RCI) calculations. The relativistic isotope shift (RIS4) programme is used to determine the mass and field shifts factors. Furthermore, the percentage uncertainty in the transition parameters and lifetimes is estimated. A detailed comparison of the present results with the corresponding values from the NIST database and other theoretical and experimental works, wherever available, has been done, and an excellent agreement is achieved. A large section of the results is reported for the first time in the present work.

Calculations of term energies, radiative transition wavelengths and Auger electron energies for resonances of F4+

In this work, the saddle-point variation combined with complex-rotation methods are used to calculate term energies, radiative transition wavelengths and Auger transition energies of the 1s2s22p2 (2S, 2P, 2D, 4P), 1s2s22p3p (2S, 2P, 2D), 1s2s2p3 (2,4S°, 2,4P°, 2,4D°), and 1s2p4 (2S, 2P, 2D, 4P) resonances for F4+. The present term energies, radiative rates, radiative transition wavelengths, Auger rates and corresponding transition energies agree well with the multiconfiguration Dirac-Fock calculation results listed in the literature. Other transition data in this work are expected to offer reference values for future studies.

Multipole mixing effects on the angular distribution and polarization of dielectronic hypersatellite lines from highly charged helium-like ions

The angular distribution and the degree of linear polarization of the dielectronic hypersatellite lines of highly charged helium-like ions are studied by using the multiconfiguration Dirac-Fock method and density matrix theory with a focus on the multipole mixing effects. Detailed calculations have been carried out for the emission of characteristic X-rays from the (2s2p)P1,23 and P11 resonant states decay to the (1s2s)S13 state following the KLL dielectronic recombination of initial hydrogen-like ions with atomic nuclear charge from Z=22 to Z=100. It is shown that the mixing of electric dipole (E1) and magnetic quadrupole (M2) radiations significantly alters the angular distribution and the degree of linear polarization, in which the shifts are dependent on the resonant capture states and the atomic nuclear charges. The E1+M2 mixing has opposite effects for the (2s2p)P23 and (2s2p)P11 resonant states, except for the (2s2p)P11 resonance of the heavy ions with Z≳90, where the profile of angular distribution is reversed by strong mixing effects due to the contribution of the M2 term and its interference with the E1 radiative channel. The results should be of particular interest to the diagnosis of anisotropic plasmas and the test of fundamental physics in few-electron heavy ions.

L-Shell Photoionization of Magnesium-like Ions with New Results for Cl5+

This study reports on the absolute photoionization cross sections for the magnesium-like Cl5+ ion over the 190–370 eV photon energy range, corresponding to the L-shell (2s and 2p subshells) excitation regime. The experiments were performed using the Multi-Analysis Ion Apparatus (MAIA) on the PLéIADES beamline at the SOLEIL synchrotron radiation storage ring facility. Single and double ionization ion yields, produced by photoionization of the 2p subshell of the Cl5+ ion from the 2p63s2 1S0 ground state and the 2p63s3p 3P0,1,2 metastable levels, were observed, as well as 2s excitations. Theoretical calculations of the photoionization cross sections using the Multi-Configuration Dirac-Fock and R-matrix approaches were carried out, and the results were compared with the experimental data. The Cl5+ results were examined within the overall evolution of L-shell excitation for the early members of the Mg-like isoelectronic sequence (Mg, Al+, Si2+, S4+, Cl5+). Characteristic photon energies for P3+ were estimated by interpolation.

Detailed Analysis of Spectra from Ga-like Ions of Heavy Elements Observed in High-Temperature Plasmas

This study has systematically investigated the atomic number (Z) dependence of spectra from gallium-like (Ga-like) ions of heavy elements. We have mainly analyzed the experimental spectra recorded in high-temperature plasmas produced in the Large Helical Device (LHD) for various elements with atomic numbers from 57 onward. The measured wavelengths are compared with theoretical values calculated with a multi-configuration Dirac Fock code. As a result, we have successfully obtained Z-dependent wavelengths of several prominent transitions of Ga-like ions, including a magnetic dipole (M1) transition. Many of them have been experimentally identified for the first time in this study. The present results manifest the significant effects of configuration interaction and spin–orbit interaction for highly charged heavy ions.

Theoretical investigation on extreme ultraviolet radiative opacity and emissivity of Sn plasmas at local-thermodynamic equilibrium

Sn is the material for an extreme ultraviolet (EUV) light source working at 13.5 nm, therefore the radiative properties of Sn plasma are of great importance in designing light source. The radiative opacity and emissivity of Sn plasma at local thermodynamic equilibrium are investigated by using a detailed-level-accounting model. In order to obtain precise atomic data, a multi-configuration Dirac-Fock method is used to calculate energy levels and oscillator strengths of <inline-formula><tex-math id="M3">\begin{document}${\rm{Sn}}^{6+}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M3.png"/></alternatives></inline-formula>-<inline-formula><tex-math id="M4">\begin{document}${\rm{Sn}}^{14+}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M4.png"/></alternatives></inline-formula>. The electronic correlation effects of <inline-formula><tex-math id="M5">\begin{document}$4{\rm d}^m\text{-}4{\rm f}^m$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M5.png"/></alternatives></inline-formula>(<inline-formula><tex-math id="M6">\begin{document}$m=1, 2, 3, 4$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M6.png"/></alternatives></inline-formula>) and <inline-formula><tex-math id="M7">\begin{document}$ 4\mathrm{p}^n\text{-}4\mathrm{d}^n $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M7.png"/></alternatives></inline-formula>(<inline-formula><tex-math id="M8">\begin{document}$n=1, 2, 3$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20230455_M8.png"/></alternatives></inline-formula>) are mainly considered, which dominate the radiation near 13.5 nm. The number of fine-structure levels reaches about 200000 for each ionization stage in the present large-scale configuration interaction calculations. For the large oscillator strengths (> 0.01), the length form is in accord with the velocity form and their relative difference is about 20%–30%. The calculated transmission spectra of Sn plasma at 30 eV and 0.01 g/cm<sup>3</sup> are compared with the experimental result, respectively, showing that they have both good consistency. The radiative opacity and emissivity of Sn plasma at the temperature in a range of 16–30 eV and density in a scope of of 0.0001–0.1 g/cm<sup>3</sup> are investigated systematically. The effects of the plasma temperature and plasma density on radiation characteristics are studied. The results show that the radiative properties near 13.5 nm are broadened with the increase of density at a specific temperature, while it is narrowed with the increase of temperature for a specific density. The present investigation should be helpful in designing and studying EUV light source in the future.

Single and double electron excitation transition rates and oscillator strengths calculations in the study of the x-ray absorption spectrum of Neon

We report a new study of the x-ray absorption spectrum of Neon near the K-edge and near the KL-edge. The study is performed by calculating the transition probabilities and oscillator strengths for excitations from the ground state to singly and doubly excited states, the calculations were performed using multi-configurational Dirac-Fock (MCDF) method. Breit interaction between electrons and finite nuclear size effects were taken into account during the calculations, the transition probabilities were convoluted into Lorentzian line shape profiles. The results of the calculations were then compared to previous measurements of the x-ray absorption spectrum of Neon, good agreement was observed and many features in the spectrum were explained.

Detection of cesium in the atmosphere of the hot He-rich white dwarf HD 149499B

ABSTRACT We report the first detection of cesium (Z = 55) in the atmosphere of a white dwarf. Around a dozen absorption lines of Cs iv, Cs v, and Cs vi have been identified in the Far Ultraviolet Spectroscopic Explorer spectrum of the He-rich white dwarf HD 149499B (Teff = 49 500 K, log g = 7.97). The lines have equivalent widths ranging from 2.3 to 26.9 mÅ. We performed a spectral synthesis analysis to determine the cesium content in the atmosphere. Non-local thermodynamic equilibrium atmosphere models were computed by considering cesium explicitly in the calculations. For this purpose we calculated oscillator strengths for the bound–bound transitions of Cs iv–Cs vi with both autostructure (multiconfiguration Breit–Pauli) and grasp2k (multiconfiguration Dirac–Fock) atomic structure codes as neither measured nor theoretical values are reported in the literature. We determined a cesium abundance of log N(Cs)/N(He) = −5.45 ± 0.35, which can also be expressed in terms of the mass fraction log XCs = −3.95 ± 0.35.