Multiconfiguration Dirac-Fock Research Articles

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.

Transition energies and transition probabilities for the core-excited state [formula omitted] of Li-like ions with [formula omitted] 6–92

The transition energies and radiative transition probabilities for the transition from the (1s2s2p)3/2 group to the ground state 1s22s involving the electric dipole (E1) and magnetic quadrupole (M2) transitions have been systematically calculated for ions along the Li isoelectronic sequence from Z=6 to Z=92. The calculations are performed by using the full relativistic multi-configuration Dirac–Fock (MCDF) method, in which the leading quantum electrodynamics (QED) shifts and the frequency dependence of the Breit interaction are also considered. The present calculation results are in good agreement with available previous results. It is found that the transition probabilities generally increase along with nuclear number Z; however, the abnormal behavior with the minima transition probabilities at Z=28 and Z=25 emerges in the [(1s2s)02p3/2]3/2→1s22s via E1 transition and the [(1s2s)12p3/2]3/2→1s22s via M2 transition, respectively; the M2 transition probabilities become comparable with that of E1 in mid-Z ions, and particularly for the q line of Z=28 ion, the M2 and E1 transition probabilities would be of the same order of magnitude. In addition, the present results show that the electron correlations impact on the energy levels and transition probabilities mainly work on the low-Z ions, while, the QED and Breit effects mainly work on the high-Z ions. This work should be of particular interest to the analysis of the spectrum and the effects of multipole mixing on the X-ray properties.

Updated database, semi-empirical and theoretical calculation of K[formula omitted]/K[formula omitted] intensity ratios for elements ranging from [formula omitted]Na to [formula omitted]Cm

A collection of 1118 experimental Kβ/Kα X-ray intensity ratios induced by photon impact was published recently by Daoudi et al. [1]. There were errors in some tabulated values. These errors are corrected here, as well as a substantial update including all experimental Kβ/Kα X-ray intensity ratios obtained from various sources for elements ranging from 11Na to 96Cm, when bombarded with photons, protons, deuterons, alpha particles, and electrons. More than 2100 experimental Kβ/Kα X-ray intensity ratios published between 1969 and 2020 (196 papers) are summarized in a table. A thorough analysis of these data is provided, as well as a table with weighted average intensity ratio values Kβ/KαW. Subsequently new semi-empirical average Kβ/Kα X-ray intensity ratios for elements in the range 11 ≤ Z ≤ 96 have been determined using an interpolation procedure which involves the analytical function Kβ/KαW/1−Kβ/KαW1/4 as a function of the atomic number Z and then fitting the experimental to weighted average ratios S=Kβ/KαEXP/Kβ/KαW. Furthermore, new theoretical calculations based on the Multiconfiguration Dirac–Fock Method have been performed for some elements and are presented in this work. The compilation provides a snapshot of the current status of Kβ/Kα X-ray atomic data. The need for additional quality measurements with detailed uncertainty assessments is clear. Considerable expert judgment will be needed in the future to shift through the database to create a statistically robust evaluation.

K- and L-shell theoretical fluorescence yields for the Fe isonuclear sequence

In this work, we present K- and L- shell fluorescence yield values of the full isonuclear sequence of Fe ions, using a state-of-the-art multiconfiguration Dirac–Fock approach. These results may be of importance for spectral fitting and plasma modeling, both in laboratory and astrophysical studies, where Fe is an important benchmark element. The K-shell fluorescence yields were found to be very similar up to the removal of 14 electrons.

Satellite and hypersatellite structure of Mα1,2 x‐ray transitions in thorium excited by fast oxygen ions

AbstractThe high‐resolution spectra of thorium Mα1,2 (M5 → N6,7) and Mβ1 (M4 → N6) x‐ray lines induced by an impact of O ions with energy 376.0 MeV were measured using a von Hamos crystal spectrometer in order to study the x‐ray emission from multiple ionized atoms. The observed x‐rays have been interpreted in terms of the relativistic multiconfiguration Dirac‐Fock (MCDF) calculations performed for dominating vacancy configurations expected to contribute to the measured spectra. Due to the complexity of such calculations for selected multi‐vacancy configurations the simplified average <MCDF> model, combining the MCDF calculations and binomial distribution of vacancies has been used. The measured spectra clearly exhibit a rich structure of Mα1,2 x‐ray satellites of thorium, including the transitions from the multivacancy initial configurations M−1N−n as well as the hypersatellites corresponding to the transitions in complex multivacancy initial configurations M−mN−n (m,n ≤ 4). The present interpretation of the measured satellite/hypersatellite structure of Mα1,2 (M5 → N6,7) x‐ray transitions allows us to determine the ionization probabilities for the M‐ and N‐shell in central collisions. The measured ionization probabilities are compared with the theoretical predictions of the geometrical model (GM), and the semiclassical approximation (SCA) using both the Dirac hydrogenic and Dirac‐Hartree‐Fock selfconsistent wave functions.

L -shell photoionization of Mg-like S4+ in ground and metastable states: Experiment and theory

We report measurements of the absolute photoionization cross sections of magnesiumlike ${\mathrm{S}}^{4+}$ over the 158--280 eV photon energy range. The experiments were performed with the multianalysis ion apparatus at the SOLEIL synchrotron radiation facility. Single- and double-ionization ion yields produced by the photoionization of the $2p$ subshell of the ${\mathrm{S}}^{4+}$ both from the $2{p}^{6}3{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ ground state and the $2{p}^{5}3s3p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1,2}$ metastable levels were observed, as well as $2s$ excitations. Theoretical calculations of the photoionization cross sections were carried out using multiconfiguration Dirac-Fock and $R$-matrix computer codes and the results are compared with the experimental data. While in general reasonably good agreement was found, notable differences in the strengths and positions of predicted resonances were observed and significant systematic energy shifts of the theoretical predictions were required.

Diagnosing the electron density of channel plasma in artificially triggered lightning

Transition rates, collision excitation cross sections, and collision excitation rate coefficients of neutral N I atom and N II ions were calculated by Flexible Atomic Code that is based on the multiconfiguration Dirac-Fock method. The line intensity of some strong spectral lines were calculated. Then the dependent relationship among the ratio of line intensity I′I, the electron density ne and the electron temperature T were obtained. The calculation shows that the electron density has some dependence on the temperature and the ratio of line intensity. Furthermore, through applying the theoretical calculations to the channel plasma spectra of artificially triggered lightning, the electron densities were diagnosed at different channel locations and times. The accuracy of the electron density was estimated using the degree of accordance, which can pick out the diagnostic data that can best reflect the real state of plasma from a large number of statistical data.

Experimental and theoretical approaches for determining the K-shell fluorescence yield of carbon

The knowledge of atomic fundamental parameters, such as the fluorescence yields with low uncertainties, is of decisive importance in elemental quantification involving X-ray fluorescence analysis techniques. However, especially for the low-Z elements, the available data in the literature is either of poor quality, of unknown or very large uncertainty, or both. For this reason, the K-shell fluorescence yield of carbon was determined in the PTB laboratory at the synchrotron radiation facility BESSY II. In addition, theoretical calculations of the same parameter were performed using the multiconfiguration Dirac–Fock method, including relativistic and quantum electrodynamics (QED) corrections. Both values obtained in this work are compared to the corresponding available published data.

Electron impact excitation cross section calculations of the fine structure transitions of Mo and their applications in the diagnostics of the laser induced Mo plasma

The current work reports a detailed calculation of electron impact excitation cross sections for the fine structure transitions of Mo from the manifolds 4d 55s, 4d 45s 2, 4d 6 and 4d 55p to the manifolds 4d 55s, 4d 45s 2, 4d 6, 4d 55p, 4d 45s5p, 4d 55d, 4d 56s, 4d 45s6s, and 4d 57s, using the relativistic distorted wave approximation for the applications in plasma modelling. Multi-configurational Dirac–Fock wave functions are used in the calculations. The oscillator strength and cross section results are compared with the previous calculations and measurements. A comprehensive collisional radiative (CR) model is developed and used to characterize laser induced molybdenum plasma to ensure that the calculated cross sections can be used for various plasma modelling applications. The current CR model has taken into account the electron impact excitation and de-excitation processes using the calculated consistent cross sections. The electron induced processes are dominant kinetic processes in the laser induced plasma. Furthermore, the diagnostics of the laser induced Mo plasma is done by coupling the current CR model with the experimental laser induced breakdown spectroscopic measurements of Mal et al (2021 Appl. Phys. B 127 52). The plasma parameter, i.e., electron temperature has been calculated using nine measured intensities of the emission lines of Mo, with wavelengths 406.9, 423.3, 438.2, 453.7, 476.0, 550.7, 553.3, 557.0 and 592.9 nm. The results are also compared with the values reported in the Boltzmann plot at various delay times ranging from 0.5 to 5.0 μs.

Energy Levels and Radiative Lifetimes for Four Times Ionized Xenon (Xe V)

By employing the general-purpose relativistic atomic structure package (GRASP) based on the fully relativistic multiconfiguration Dirac-Fock (MCDF) method, energies and radiative lifetimes of levels have been reported for four times ionized xenon (Xe V). In calculations, the Breit interactions for relativistic effects, quantum electrodynamical (QED) contributions have been included as a perturbation, as well as electron correlation effects (VV, CV, and CC). We have compared the results obtained from this work with other available experimental and theoretical values in available literature for Xe V. We have obtained good agreement with previous works.

Photoelectron spectra of shake-up processes from the 2p subshell of sodium atoms in the excited states 2p 63p

The 2p photoionization of sodium atoms from the initial states 2p 63p 1/2,3/2 have been investigated, with special emphasis placed on the relaxation and correlation effects. To understand the details of the spectra, a series of ab initio calculations based on the multi-configuration Dirac–Fock method have been performed. Theoretical predictions have been compared with the high-resolution spectra measured using a synchrotron radiation source, and suitable agreement between experiment and theory has enabled the identification of fine-structure spectra. The prominent influence of the relaxation and correlation effects on the photoelectron spectra has been analysed according to the detailed calculations.

Study of excitation energies of doubly excited states and identification of EUV, SXR and HXR spectral lines in M1 transitions of W LXXIII and Au LXXVIII

We present excitation energies, wavelength of emitted photon during the transition from upper level to lower level, transitions rates and other transition parameters for doubly excited states of W LXXIII and Au LXXVIII by employing Multi-Configuration Dirac-Fock (MCDF) scheme with the inclusion of relativistic effects. We endorse that contribution of QED and Breit corrections in energies of levels is significant. We have also shown that our results of energies from both, FAC and GRASP matches with each other. We have predicted that 37 Hard X-ray (HXR), 25 Soft X-ray (SXR) and 20 Extreme Ultraviolet (EUV) magnetic dipole (M1) transitions among relativistic levels generated from doubly excited states in W LXXIII and Au LXXVIII. Further, we have studied the convergence in excitation energies and lifetime of excited states and analysed the improvement in accuracy of results by estimation of uncertainty percentage in line strength. Besides, fresh atomic data of W LXXIII and Au LXXVII which is not published in the literature have been reported and can be advantageous in diagnosis and modelling of fusion and astrophysical plasmas.

Z -dependent crossing of excited-state energy levels in highly charged galliumlike lanthanide atomic ions

Extreme ultraviolet (EUV) optical transitions of lanthanide highly charged ions have been studied. The $[\mathrm{Ni}]4{s}^{2}4p--[\mathrm{Ni}]4{s}^{2}4d$ and $[\mathrm{Ni}]4{s}^{2}4p--[\mathrm{Ni}]4s4{p}^{2}$ transition lines of galliumlike lanthanide elements have been spectroscopically measured in large helical device (LHD) plasma and electron-beam ion trap (EBIT) plasma. The wavelengths for Eu ions agreed within $0.03%$ between the LHD and EBIT measurements. Due to the enhancement of spin-orbit interactions along with the increase of atomic number $Z$ in $4p$ atomic orbitals, energy splitting between $4{p}_{1/2}$ and $4{p}_{3/2}$ orbitals increases significantly from lanthanum to lutetium, causing the crossing of $Z$-dependent wavelength curves. The spectral line positions and strengths are theoretically calculated by means of the multiconfiguration Dirac-Fock method. The mixing of the $[\mathrm{Ni}]4{s}^{2}4d$ and $[\mathrm{Ni}]4s4{p}^{2}$ configurations leads to an avoided crossing in the apparent wavelength curves. The configuration mixing makes both the $[\mathrm{Ni}]4{s}^{2}4p--[\mathrm{Ni}]4{s}^{2}4d$ and $[\mathrm{Ni}]4{s}^{2}4p--[\mathrm{Ni}]4s4{p}^{2}$ lines well visible in the EUV spectra near the level crossing point. The levels are found to cross between $Z=62$ and 63.

Electron Impact Excitation of Ge-like Te20+–Cd16+ Ions

We study electron impact excitation of dipole allowed transitions in the extreme ultraviolet range—8–55 nm—for the germanium isoelectronic sequence Te20+–Cd16+. The fine structure transitions between the ground state having configuration 4s24p2 and the excited states with configurations 4s4p3 and 4s24p4d are considered for these ions. We employ the relativistic distorted wave method to calculate the excitation cross sections in the incident electron energy range from the excitation threshold to 5000 eV. To obtain the required ionic bound state wavefunctions we have used the multi-configuration Dirac-Fock method with correlations within the n = 5 complexes as well as performed relativistic configuration interaction calculations to include the quantum electrodynamic effects. The accuracy of these wavefunctions is established by comparing our calculated wavelengths and oscillator strengths of the considered transitions with the previously reported measurements and other available theoretical results. We also provide the fitting parameters of the calculated cross sections and the excitation rate coefficients for their direct applications in plasma modeling.

Plasma environment effects on K lines of astrophysical interest

Aims. We calculate the plasma environment effects on the ionization potentials (IPs) and K-thresholds used in the modeling of K lines for all the ions belonging to the isonuclear sequences of abundant elements apart from oxygen and iron, namely: carbon, silicon, calcium, chromium, and nickel. These calculations are used to extend the data points for the fits of the universal formulae, first proposed in our fourth paper of this series, to predict the IP and K-threshold lowerings in any elemental ion. Methods. We used the fully relativistic multi-configuration Dirac–Fock method and approximated the plasma electron-nucleus and electron-electron screenings with a time-averaged Debye–Hückel potential. Results. We report the modified ionization potentials and K-threshold energies for plasmas characterized by electron temperatures and densities in the ranges of 105−107 K and 1018−1022 cm−3. In addition, the improved universal fitting formulae are obtained. Conclusions. We conclude that since explicit calculations of the atomic structures for each ion of each element under different plasma conditions is impractical, the use of these universal formulae for predicting the IP and K-threshold lowerings in plasma modeling codes is still recommended. However, their comparatively moderate to low accuracies may affect the predicted opacities with regard to certain cases under extreme plasma conditions that are characterized by a plasma screening parameter of μ > 0.2 a.u., especially for the K-thresholds.

Non-dipole effects on angular distribution of photoelectrons in sequential two-photon double ionization of Ar atom and K<sup>+</sup> ion

Owing to the development of XUV and X ray of the free-electron lasers, the photoelectron angular distribution in the sequential two-photon double ionization has received increasing attention of theorists and experimentalists, because it provides the valuable information about the electronic structure of atom or molecule systems and allows the obtaining of additional information about mechanisms and pathways of the two-photon double ionization. In this paper, the expression of the sequential two-photon double ionization process of the photoelectron angular distributions, including the non-dipole effects, is obtained based on the multi-configuration Dirac-Fock method and the density matrix theory, and the corresponding calculation code is also developed. Based on the code, the sequential two-photon double ionization process of the 3p and 2p shells of Ar atom and K<sup>+</sup> ion are studied, in which, the dipole and the non-dipole parameters of photoelectron angular distribution are investigated systematically. It is found that the angular distributions of the first- and second-step electrons in sequential two-photon double ionization are similar and the two photoionization processes affect each other. Near the ionization threshold, the photoionization cross-sections and anisotropy parameters for the 3p shell and the 2p shell show a large difference. While away from the threshold, the cross-section and angular anisotropy parameters of the 3p and 2p shells show similar behaviors. At the position of Cooper minimum of the photoionization cross section, the contribution of the electric dipole is suppressed, and the non-dipole effect is obvious. The non-dipole effect leads to a forward-backward asymmetric distribution of photoelectrons relative to the direction of incident light. The results of this paper will be helpful in studying the nonlinear processes of photon and matter interaction in the XUV range.

Kβ-to-Kα X-ray intensity ratio studies on changes of valance electron structures of nickel in Ni–B/hBN composite coatings

In this study, Kβ/Kα X-ray intensity ratio values of nickel in Ni coating and Ni–B/hBN (hBN: hexagonal Boron Nitride) composite coatings have been determined by the Energy Dispersive X-ray fluorescence spectroscopy (EDXRF) method. The Kβ/Kα X-ray intensity ratios of nickel in the Ni coating and Ni–B/hBN composite coatings have been compared with theoretical, experimental, and fitted data of the pure nickel. X-ray Diffraction (XRD) and Scanning Electron Microscopy (SEM) measurements have been performed to observe how hBN particles with different bath concentrations affected the crystal structure and microstructure, respectively. The valence electronic structure of Ni in the coatings has been determined by comparing the experimental Kβ/Kα X-ray intensity ratios with Multiconfiguration Dirac-Fock (MCDF) predictions for various electron structures of Ni. The results show that while the values of the Kβ/Kα X-ray intensity ratio of the Ni–B/hBN composite coatings over pure Ni coatings increases, the 3d electron populations decreases. The change in the valence electronic structure were interpreted through charge transfer and rearrangement processes.

Atomic Compton scattering effect on direct dark matter detection

Atomic Compton scattering effect significantly contributes to low-energy electronic recoils below its k-shell energy for the direct dark matter detection. Searches on ADM models, dark photon models, leptophilic dark matter models as well as the conventional WIMPs for background understandings are vitally required to clarify the effect. We employed the relativistic impulse approximation (RIA) together with the ab initio Multi-Configuration Dirac-Fock (MCDF) theory to obtain the atomic Compton scattering for Germanium (Ge) Silicon (Si) and Xenon (Xe) atoms. Comparisons on low momentum transfer regions with our calculations for Ge and Si are achieved. In addition, millicharged dark matter particles estimated by RIA in the atomic ionization for Ge and Xe have been evaluated. A factor-of-two discrepancy on the incoherent-scattering factor (a.k.a. scattering function) near 100 eV/c momentum transfer with the Ge system between our calculation and the latest version of Geant4 (10.07.02) simulation data is observed. Plans on the experimental verification and the perspectives of the atomic Compton scattering effect for the direct detections will be discussed.

Development of various methods to the investigation of the spectral properties and collision dynamics of H‐like ions taking place in dense and hot plasma environments

AbstractThe correct understanding of the behavior of highly stripped ions immersed in a dense plasma environment is a hitherto challenge for theory and it is of importance in various applications. Here, we developed four kinds of novel theoretical models to the determination of the spectral properties and collision dynamics of H‐like ions in dense and hot plasmas by employing the analytical potential [Li et al., Phys. Plasmas 2019, 26, 033301] to describe the interactions among the charged particles: (i) The electron photon processes in plasma model within the relativistic scheme; (ii) The multiconfiguration Dirac–Fock model within the framework of relativistic self‐consistent iteration approximation; (iii) The generalized pseudospectral method within the relativistic framework; and (iv) An analytic formula based on the Hartree–Fock method and the irreducible tensor theory within the non‐relativistic regime, derived from a solution of Schrödinger equation. As a typical example, energy eigenvalues, radiative transition properties, spectral line shifts, and electron impact excitation and ionization cross sections of the selected N6+ and Ne9+ ions are determined for several temperature‐density cases, characteristic of inertial confinement fusion plasmas. A comparison of these results with each other and the results from earlier calculations as well as with the available experimental data is provided. Systematic trend is determined for all the properties under study concerning increased screening. The present study not only extends our understanding of the dense plasma shielding effects, but also opens the way for future investigations allowing accurate predictions of spectral properties of ions in dense and hot plasmas aimed at providing precision data for various practical applications.

Multiple photodetachment of silicon anions via K -shell excitation and ionization

Experimental cross sections for $m$-fold photodetachment ($m=3-6$) of silicon anions via $K$-shell excitation and ionization were measured in the photon-energy range of 1830-1900 eV using the photon-ion merged-beams technique at a synchrotron light source. All cross sections exhibit a threshold behavior that is masked by pre-threshold resonances associated with the excitation of a $1s$ electron to higher, either partly occupied or unoccupied atomic subshells. Results from multi-configuration Dirac-Fock (MCDF) calculations agree with the experimentally derived cross sections for photo-absorption if small energy shifts are applied to the calculated resonance positions and detachment thresholds. Moreover, a systematic approach is applied for modeling the deexcitation cascades that set in after the initial creation of a $K$-shell hole. The resulting product charge-state distributions compare well with the measured ones for direct $K$-shell detachment but less well for resonant $K$-shell excitation. The present results are potentially useful for identifying silicon anions in cold plasmas such as interstellar gas clouds.