Multiconfiguration Dirac-Fock Research Articles

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.

Electron Impact Excitation of Extreme Ultra-Violet Transitions in Xe7–Xe10 Ions

In the present work, a detailed study on the electron impact excitation of Xe7+, Xe8+, Xe9+ and Xe10+ ions for the dipole allowed (E1) transitions in the EUV range of 8–19 nm is presented. The multi-configuration Dirac–Fock method is used for the atomic structure calculation including the Breit and QED corrections along with the relativistic configuration interaction approach. We have compared our calculated energy levels, wavelengths and transition rates with other reported experimental and theoretical results. Further, the relativistic distorted wave method is used to calculate the cross sections from the excitation threshold to 3000 eV electron energy. For plasma physics applications, we have reported the fitting parameters of these cross sections using two different formulae for low and high energy ranges. The rate coefficients are also obtained using our calculated cross sections and considering the Maxwellian electron energy distribution function in the electron temperature range from 5 eV to 100 eV.

Fully relativistic study on electron impact elastic scattering from Nq+ (q = 1–3), Na+, Arq+ (q = 1–3, 7–8), and Xeq+ (q = 2–6, 8)

AbstractA study is presented on the elastic scattering of electrons from Nq+ (q = 1–3), Na+, Arq+ (q = 1–3, 7–8), Xeq+ (q = 2–6, 8) to understand the available experimental differential cross section results. A model potential approach has been utilized to describe the scattering process. The model potential includes the static, exchange, polarization and absorption potentials. The static potentialis obtained through the charge density calculated by obtaining ionic wave functions using multi‐configuration Dirac‐Fock (MCDF) approximation. Thereafter, the static potential is added to the suitable exchange, polarisation and absorption potentials to construct the spherically averaged complex optical potential. Using the obtained potential in the Dirac equations,these are solved with the partial wave phase shift analysis method and the differential cross sections are calculated. Results for different ions exhibit prominent interference structures in the energy versus cross section curves and show good agreement on comparison with the experimental results available in the selected energy ranges.

Fine structure calculations of excitation energies, lifetimes and radiative properties of S-like Kr XXI

Extensive and systematic calculations for energy levels and lifetimes are carried out for the lowest 145 levels arising from the 3s23p4, 3s3p5, 3s23p33d, 3p6, 3s3p43d and 3s23p23 d2 configurations in S-like Kr XXI ion using the multiconfiguration Dirac-Fock (MCDF) method. Additionally, radiative data such as transition wavelengths, absorption oscillator strengths, line strengths and radiative decay rates have also been computed for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1) and magnetic quadrupole (M2) transitions from the ground state. The importance of Breit interaction (BI) and quantum electrodynamics (QED) corrections on the energy levels has also been estimated. To assess the credibility and integrity of our MCDF energies, independent calculations using the relativistic configuration interaction (RCI) approach have also been performed. Detailed comparisons are made between our two sets of results, as well as with other existing experimental and theoretical values, and a good agreement is achieved. The present results will be helpful for the modeling and diagnostics of fusion plasmas.

Forbidden transitions between the 2p3/2 and 2p1/2 states of ground B-like ions with 14 ≤ Z ≤ 92

The magnetic-dipole M1 and electric quadrupole E2 transition energies and rates between the two fine structure states of 1s22s22p configuration for B-like ions with 14 92 have been calculated using the multi-configuration Dirac-Fock (MCDF) method. The interactions with atomic core have been considered and the core-valence correlation contributions to the level energies are evaluated in the active space approximation. The finite nuclear size, the frequency dependent and independent Breit interaction and quantum electrodynamics (QED) corrections have been included in the calculations. To improve the accuracy of the present data on the forbidden line energies and rates, the QED corrections to the transition energies have been adjusted using QEDMOD code with MCDF wavefunctions. The sensitivity of the transition parameters on the nature of the spin orbitals has been probed by considering two sets of calculations, one with fully relaxed and the other with a common set of radial functions. The present line energies and lifetime of the 2s22p 2 p 3/2 state are found to be in excellent agreement with available experimental and theoretical data.

Sensitivity of correlation effects and Shannon entropy in Be@C60 to the nature of confinement potentials

The multi-configuration Dirac-Fock (MCDF) method is used to study the correlation effects in Be@C60 by investigating the localization properties of the electronic probability density distribution. The confinement environment is simulated by two types of model potentials: (A) the commonly employed compact annular square well (ASW) and (B) the diffusive Gaussian annular square well (GASW). The present work aims to investigate the sensitivity of correlation effects and localization properties to the contrasting nature of the confinement potentials. To accomplish this, the variation of the correlation energy and Shannon’s correlation information entropy with the depth of both confinement potentials are presented to give an idea of the sensitivity of these parameters to the nature of the confining potential. The present work concludes that the correlation energy and the associated electronic structure attributes are extremely susceptible to the nature of the confining potential.

Proton-neutron pairing correlations in the self-conjugate nucleus 42Sc

Collinear laser spectroscopy of the N=Z=21 self-conjugate nucleus 42Sc has been performed at the JYFL IGISOL IV facility in order to determine the change in nuclear mean-square charge radius between the Iπ=0+ ground state and the Iπ=7+ isomer via the measurement of the 42g,42mSc isomer shift. New multi-configurational Dirac-Fock calculations for the atomic mass shift and field shift factors have enabled a recalibration of the charge radii of the 42−46Sc isotopes which were measured previously. While consistent with the treatment of proton-neutron, proton-proton and neutron-neutron pairing on an equal footing, the reduction in size for the isomer is observed to be of a significantly larger magnitude than that expected from both shell-model and ab-initio calculations. The measured nuclear magnetic dipole moment and electric quadruple moment, on the other hand, are in good agreement with simple empirical estimates and shell-model calculations.

Comprehensive Laboratory Measurements Resolving the LMM Dielectronic Recombination Satellite Lines in Ne-like Fe xvii Ions

Abstract We investigated experimentally and theoretically dielectronic recombination (DR) populating doubly excited configurations (LMM) in Fe xvii, the strongest channel for soft X-ray line formation in this ubiquitous species. We used two different electron beam ion traps and two complementary measurement schemes for preparing the Fe xvii samples and evaluating their purity, observing negligible contamination effects. This allowed us to diagnose the electron density in both EBITs. We compared our experimental resonant energies and strengths with those of previous independent work at a storage ring as well as those of configuration interaction, multiconfiguration Dirac–Fock calculations, and many-body perturbation theory. This last approach showed outstanding predictive power in the comparison with the combined independent experimental results. From these we also inferred DR rate coefficients, unveiling discrepancies from those compiled in the OPEN-ADAS and AtomDB databases.

Photoionization Cross-Sections of Carbon-Like N+ Near the K-Edge (390–440 eV)

High-resolution K-shell photoionization cross-sections for the C-like atomic nitrogen ion (N+) are reported in the 398 eV (31.15 Å) to 450 eV (27.55 Å) energy (wavelength) range. The results were obtained from absolute ion-yield measurements using the SOLEIL synchrotron radiation facility for spectral bandpasses of 65 meV or 250 meV. In the photon energy region 398–403 eV, 1s⟶2p autoionizing resonance states dominated the cross section spectrum. Analyses of the experimental profiles yielded resonance strengths and Auger widths. In the 415–440 eV photon region 1s⟶(1s2s22p2 4P)np and 1s⟶(1s2s22p2 2P)np resonances forming well-developed Rydberg series up n=7 and n=8 , respectively, were identified in both the single and double ionization spectra. Theoretical photoionization cross-section calculations, performed using the R-matrix plus pseudo-states (RMPS) method and the multiconfiguration Dirac-Fock (MCDF) approach were bench marked against these high-resolution experimental results. Comparison of the state-of-the-art theoretical work with the experimental studies allowed the identification of new resonance features. Resonance strengths, energies and Auger widths (where available) are compared quantitatively with the theoretical values. Contributions from excited metastable states of the N+ ions were carefully considered throughout.

Exploring the x-ray photoabsorption spectrum of sodium in the energy range 1070–1090 eV by elucidating the inner shell excitation transition probabilities

The researchers report on a new study of the x-ray photoabsorption spectrum of sodium near the K-edge, involving the calculations of the excitation energies and the excitation transition probabilities for K-shell and M-shell electron excitations transitions in atomic sodium. The calculations were carried out by employing the ‘multi configuration Dirac–Fock method’, Breit interactions and ‘finite nuclear size corrections’ are included in the calculations, the transition probabilities were convoluted into ‘Breit–Wigner’ line shapes, and single 1s photoionization was also taken into account. In addition, the [1s]np and the [1s3s]ns n′p singlet–triplet energy splitting was calculated. Results of the calculations were compared with previous measurements of the photoabsorption spectrum of sodium near the K-edge, and a very good agreement was observed.

Angular Distribution and Polarization of the 3C and 3D Lines Following Electron-impact Excitation of Fe16+ Ions

Abstract The electron-impact excitations from the ground state to the excited levels and as well as the subsequent radiative decays of neonlike Fe16+ ions have been investigated within the framework of the multiconfigurational Dirac–Fock method and the relativistic distorted-wave theory. Special attention has been paid to emission behaviors of the astrophysically relevant resonance 3C and intercombination 3D lines emitted in the radiative decays of Fe16+ ions. To this end, we calculate the angular distribution and linear polarization of both of the lines for a series of impact electron energies. It is found that the angular and polarization behaviors of the resonance 3C line are nearly the same as those of the intercombination 3D line. Nevertheless, the angular and polarization behaviors of both of the lines are found to be very sensitive to the impact electron energy, especially at low impact energies. Based on such a sensitivity, it is expected that high-precision angular and polarization measurements of the 3C and 3D lines could be served as a tool for revealing detailed information such as electron energy of relevant laboratory and astrophysical plasmas.

Relativistic R-matrix calculations of the photoionization of W63+ ions

The direct and resonant single-photon photoionization of W63+ ions from their ground state 1s 22s 22p 63s 2 S 1/2 and four lowly-excited states 1s 22s 22p 63p 2 P 1/2,3/2 and 1s 22s 22p 63d 2 D 3/2,5/2 has been studied within the framework of the relativistic R-matrix method and the multiconfigurational Dirac–Fock method. Special attention has been paid to obtaining direct and resonant ionization limits and to identifying possible resonant symmetries of W63+ ions. To this end, the photoionization cross-sections have been calculated using the Dirac Atomic R-matrix Code package. Direct and resonant ionization limits were obtained for the ground-state photoionization of W63+ ions, and the resonant peaks identified were found to be associated with the resonances 1s 22s 22p 53lnl′ and 1s 22s2p 63lnl′ (l, l′ = s, p, d) for the fine-structured energy level or configuration at the level of fine structure or configuration. For excited-state photoionization, however, the resonant ionization limits and resonant peaks were hardly distinguishable due to much more densely spaced resonant peaks and a complicated resonant structure, although the respective direct ionization limits are obtained. We expect that this work will remedy the current lack of fundamental studies of the photoionization of W63+ ions and be helpful in the diagnosis and simulation of fusion plasmas in conjunction with the available photoionization data for tungsten ions in other charge states.

Auger decay of the 3d hole in the isoelectronic series of Br, Kr+ , and Rb2+

The Auger decay process of the $3{d}_{5/2}$ hole is studied experimentally and theoretically along the isoelectronic Br, ${\mathrm{Kr}}^{+}$, and ${\mathrm{Rb}}^{2+}$ series with electron configuration [Ar] $3{d}^{9}4{s}^{2}4{p}^{6}$. The experimental results consist of multielectron coincidence data measured from all three elements and conventional high-resolution Auger spectrum for the Br case. Theoretical interpretation was done by using multiconfiguration Dirac-Fock calculations. It is found that the decay rate of two-Auger-electron emission increases along the series in the direction of decreasing nuclear charge. Also, complexity of the Auger spectrum follows the same trend, requiring a drastic increase to the size of the configuration space for describing the observed spectra.

Spectroscopic study of EUV and SXR spectral lines with partition function and level population of W LVI

We present a comprehensive and elaborate study of W LVI (K-like W55+) by using multi-configuration Dirac–Fock method (MCDF). We have included relativistic corrections, QED (quantum electrodynamics) and Breit corrections in our computation. We have reported energy levels and radiative data for multipole transitions (i.e., electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2)) within the lowest 142 fine-structure levels and predicted soft X-ray transition (SXR) and extreme ultraviolet transitions (EUV) from higher excited states to the ground state. We have compared our calculated data with energy levels compiled by NIST and other available results in the literature and the small discrepancies found with them are discussed. Because only a few of the lowest levels are available in the literature, for checking excitation energies of higher excited states we have performed the same calculations with the distorted wave method. Furthermore, we have also provided relative population for the first five excited states, with both the partition function and thermodynamic quantities for W LVI and studied their variations with temperature. We believe that our reported new atomic data of W LVI may be useful in identification and analysis of spectral lines from various astrophysical and fusion plasma sources and may also be beneficial in plasma modeling.

Theoretical determination of level delocalizations, plasma shifts and radiative properties of fusion relevant Ni XXII in finite temperature dense plasmas using a generalized analytical b-potential

We propose a novel relativistic method to explore the atomic structure of highly charged ions perturbed by a dense plasma. The calculations are performed within the general framework of the ion sphere theory and application of the generalized analytical b-potential combined with the multi-configuration Dirac-Fock approximation. In the method, the relativistic effects provided by the Dirac-Coulomb Hamiltonian, Breit interaction and two kinds of quantum electrodynamics corrections, self-energy and vacuum polarization, are accounted for systematically via perturbation theory. The level delocalizations, line shifts and radiative properties among the levels of the 2sx2py (x+y=5) configurations of Ni XXII under the finite temperature dense plasma conditions are demonstrated for illustrative purposes. Such ions can exist in inertial confinement devices or in laser-produced plasmas. Systematic changes are determined for the properties under study in respect of increased temperature and electron density. The obtained atomic structure, line shift, and level delocalization are essential fundamental properties for advanced diagnostics, equation of state calculations, line identifications, and benchmark data for ionization balance calculations ect.

Fundamental Parameters Related to Selenium Kα and Kβ Emission X-ray Spectra

We present relativistic ab initio calculations of fundamental parameters for atomic selenium, based on the Multiconfiguration Dirac-Fock method. In detail, fluorescence yields and subshell linewidths, both of K shell, as well as Kβ to Kα intensity ratio are provided, showing overall agreement with previous theoretical calculations and experimental values. Relative intensities were evaluated assuming the same ionization cross-section for the K-shell hole states, leading to a statistical distribution of these initial states. A method for estimating theoretical linewidths of X-ray lines, where the lines are composed by a multiplet of fine-structure levels that are spread in energy, is proposed. This method provides results that are closer to Kα1,2 experimental width values than the usual method, although slightly higher discrepancies occur for the Kβ1,3 lines. This indicates some inaccuracies in the calculation of Auger rates that have a higher contribution for partial linewidths of the subshells involved in the Kβ1,3 profile. Apart from this, the calculated value of Kβ to Kα intensity ratio, which is less sensitive to Auger rates issues, is in excellent agreement with recommended values.

Relaxation effects on the magnetic cross section and fluorescence radiation polarization after 4d inner-shell photoionization of Ba-like ions

On the basis of the multi-configuration Dirac–Fock method and the density matrix theory treatment of photoionization (PI) dynamics, a systematic investigation for 4d inner-shell PI of exemplary Ba atom and Ba-like Nd4+, Gd8+ and Yb14+ ions is performed. Starting from the general framework of the relativistic, the relaxation effects are considered by using a set of relaxed one-electron orbitals in solving the coupled Dirac equations. Our results uncover for the first time that the relaxation effects, arising from the overlap integrals between orbitals of the initial state and the relaxed final state, may play a paramount role in determining the magnetic sublevel cross sections, the photoelectron angular-distribution asymmetry parameters, and the fluorescence polarizations of the subsequent x-ray radiation, particularly for neutral atoms close to the threshold regime. Yet the importance of inclusion of the orbital relaxation weakens as the incoming photon energy and/or the degree of atom ionization increases. The nature of these influences is explored, which allows us to get more insight on the physical process and mechanism involved. Our results are consistent with those obtained by the experiments and other theoretical predictions.