Multiconfiguration Dirac-Fock Research Articles

Calculations of Atomic Parameters of Highly Charged Fe Ions for Interpreting Astrophysical Spectra

Study of physical processes in astrophysical and fusion plasmas consists of detail analysis of high resolution atomic spectra obtained from such plasmas. The X-ray spectra from iron K-shell and L-shell ions are particularly important for astrophysics as they are in wavelength range covered by telescopes on board space observatories like Chandra and XMM-Newton. To conduct the astrophysical plasma diagnostic studies of Active galactic nuclei (AGN), solar corona and other similar astronomical entities, a large number of accurate transition data both from theory and experiment are indispensable. Here we have calculated similar atomic data in use for these studies by multi-configuration Dirac-Fock (MCDF) formalism used in Grasp2K code. Calculations consists of ground and few low level excited states in He-like and Li-like Fe ions and some important transitions connecting these levels.

Non-dipole effects in the angular distributions of photoelectrons on sodium-like ions

Photoionization processes widely exist in the astrophysical plasma and the high temperature laboratory plasma. Compared with the traditional photoelectron energy spectrum, the photoelectron angular distribution is not only related to the amplitude of the photoionization channels, but also sensitive to the phases of these channels. So the photoelectron angular distribution contains much more quantum information about the photoionization processes and is used to provide stringent tests of our understanding of basic physical processes underlying gas- and condensed-phase interaction with radiation, as well as a tool to probe physical and chemical structure in solids and surfaces. For a long time, the dipole approximation has been the basis in the study of the photoelectron angular distribution, but with the progress of light source, such as the fourth generation synchrotron facilities, more and more attention is paid to the non-dipole effect of the photoelectron angular distribution. In thispresent work, the photoionization processes of sodium-like ions (20Z92) are studied for the different incident photon energies based on the multiconfiguration Dirac-Fock method and the density matrix theory. The influences of the non-dipole terms on the photoelectron angular distributions, which arise from the multipole expansion of the electron-photon interaction, are discussed in detail. The relationship between the dipole and non-dipole parameters of the photoelectron angular distribution along with the atomic number is given. It is found that the influence of non-dipole terms on the photoelectron angular distribution is related to the incident photon energy and the atomic number of the target ion and the subshell of the ionized electron. In general, the influences of the non-dipole terms on the photoelectron angular distribution of p subshell are larger than those of the s subshell. In the electric dipole approximation, the s subshell photoelectron angular distribution is nearly independent of the photon energy and nuclear charge number, but this situation is not for the p subshell. With the increase of photon energy, an abnormal angular distribution is found for the p subshell photoelectron. However, if the non-dipole effects are included, the abnormal photoelectron angular distribution of p subshell disappears and the photoelectron distribution has maximum values respectively near 45o and 135o with respect to the polarization vector of incident light, that is, the photoelectron distribution has an obvious forward scattering characteristic.

Charge Radii of Neutron Deficient ^{52,53}Fe Produced by Projectile Fragmentation.

Bunched-beam collinear laser spectroscopy is performed on neutron deficient ^{52,53}Fe prepared through in-flight separation followed by a gas stopping. This novel scheme is a major step to reach nuclides far from the stability line in laser spectroscopy. Differential mean-square charge radii δ⟨r^{2}⟩ of ^{52,53}Fe are determined relative to stable ^{56}Fe as δ⟨r^{2}⟩^{56,52}=-0.034(13) fm^{2} and δ⟨r^{2}⟩^{56,53}=-0.218(13) fm^{2}, respectively, from the isotope shift of atomic hyperfine structures. The multiconfiguration Dirac-Fock method is used to calculate atomic factors to deduce δ⟨r^{2}⟩. The values of δ⟨r^{2}⟩ exhibit a minimum at the N=28 neutron shell closure. The nuclear density functional theory with Fayans and Skyrme energy density functionals is used to interpret the data. The trend of δ⟨r^{2}⟩ along the Fe isotopic chain results from an interplay between single-particle shell structure, pairing, and polarization effects and provides important data for understanding the intricate trend in the δ⟨r^{2}⟩ of closed-shell Ca isotopes.

Changes in nuclear structure along the Mn isotopic chain studied via charge radii

The hyperfine spectra of $^{51,53-64}$Mn were measured in two experimental runs using collinear laser spectroscopy at ISOLDE, CERN. Laser spectroscopy was performed on the atomic $3d^5\ 4s^2\ ^{6}\text{S}_{5/2}\rightarrow 3d^5\ 4s4p\ ^{6}\text{P}_{3/2}$ and ionic $3d^5\ 4s\ ^{5}\text{S}_2 \rightarrow 3d^5\ 4p\ ^{5}\text{P}_3$ transitions, yielding two sets of isotope shifts. The mass and field shift factors for both transitions have been calculated in the multiconfiguration Dirac-Fock framework and were combined with a King plot analysis in order to obtain a consistent set of mean-square charge radii which, together with earlier work on neutron-deficient Mn, allow the study of nuclear structure changes from $N=25$ across $N=28$ up to $N=39$. A clear development of deformation is observed towards $N=40$, confirming the conclusions of the nuclear moments studies. From a Monte Carlo Shell Model study of the shape in the Mn isotopic chain, it is suggested that the observed development of deformation is not only due to an increase in static prolate deformation but also due to shape fluctuations and triaxiality. The changes in mean-square charge radii are well reproduced using the Duflo-Zuker formula except in the case of large deformation.

Energy levels, lifetimes, and transition rates for the selenium isoelectronic sequence Pd XIII–Te XIX, Xe XXI–Nd XXVII, W XLI

Energy levels, wavelengths, lifetimes, oscillator strengths, and electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), magnetic quadrupole (M2) transition rates among the 46 fine structure levels belonging to the ([Ar]3d10)4s24p4, ([Ar]3d10)4s24p34d, and ([Ar]3d10)4s4p5 configurations for the selenium isoelectronic sequence Pd XIII–Te XIX, Xe XXI–Nd XXVII, W XLI are reported. These data are determined in the multi-configuration Dirac–Fock (MCDF) approach, in which relativistic effects, main electron correlations within the n=7 complex, Breit interaction (BI), and quantum electrodynamic (QED) corrections are included. The many-body perturbation theory (MBPT) method is also employed as an independent calculation to confirm the present accuracy, taking W XLI as an example. Comparisons and analysis are made between the present results and available experimental and theoretical ones, and good agreements are obtained. These accurate data are expected to be useful in nuclear fusion research and astrophysical applications.

Calculation of levels, transition rates, and lifetimes for the arsenic isoelectronic sequence Sn XVIII-Ba XXIV, W XLII

Multi-configuration Dirac–Fock (MCDF) calculations of energy levels, wavelengths, oscillator strengths, lifetimes, and electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), magnetic quadrupole (M2) transition rates are reported for the arsenic isoelectronic sequence Sn XVIII-Ba XXIV, W XLII. Results are presented among the 86 levels of the 4s24p3, 4s4p4, 4p5, 4s24p24d, and 4s4p34d configurations in each ion. The relativistic atomic structure package GRASP2K is adopted for the calculations, in which the contributions from the correlations within the n≤7 complexes, Breit interaction (BI) and quantum electrodynamics (QED) effects are taking into account. The many-body perturbation theory (MBPT) method is also employed as an independent calculation for comparison purposes, taking W XLII as an example. Calculated results are compared with data from other calculations and the observed values from the Atomic Spectra Database (ASD) of the National Institute of Standards and Technology (NIST). Good agreements are obtained. i.e, the accuracy of our energy levels is assessed to be better than 0.6%. These accurate theoretical data should be useful for diagnostics of hot plasmas in fusion devices.

Energies and radiative transitions (E1, E2, and M1) for hydrogen-like thorium

Hydrogen-like ions with high Z present unique opportunities to promote the understanding of atomic structure. On the other hand, determining the atomic structure of hydrogen-like atoms provides us the test of relativistic effects as well as accurate values of the spectral characteristics required for many applications. For this reason we have calculated level energies of hydrogen like thorium (Th89+, Z = 90) with both multiconfiguration Hartree–Fock (MCHF) and multiconfiguration Dirac–Fock (MCDF) methods. These calculations have contained the Breit–Pauli relativistic corrections in MCHF calculation and quantum electrodynamics effects in MCDF calculations besides electron correlations. The wavelengths, λ, weighted oscillator strengths, gf-value, and transition probabilities, Aki, have been also represented for allowed (E1) and forbidden (E2 and M1) transitions. We have compared our results with only theoretical work results because there is no available experimental data for Th89+.

Diagnostics of the plasma parameters based on the K X-ray line positions for various 4d and 4f metals

Abstract This paper shows the theoretical predictions of the outer-shell ionization effect on the positions of Kα1,2, Kβ1,3, and K β2 X-ray lines for some 4d-transition metals (molybdenum and palladium) and 4f rare-earth elements (dysprosium and ytterbium). The ionization energy shifts have been evaluated using the multiconfiguration Dirac-Fock method, containing Breit interaction and quantum electrodynamic (QED) corrections. The presented results are important for obtaining the information about some parameters of plasma generated by different sources, especially by pulsed power machine and short-pulse lasers.

Calculations with spectroscopic accuracy for energies, transition rates, hyperfine interaction constants, and Landé gJ-factors in nitrogen-like Kr XXX

Extensive self-consistent multi-configuration Dirac-Fock (MCDF) calculations and second-order many-body perturbation theory (MBPT) calculations are performed for the lowest 272 states belonging to the 2s22p3, 2s2p4, 2p5, 2s22p23l, and 2s2p33l (l=s, p, d) configurations of N-like Kr XXX. Complete and consistent data sets of level energies, wavelengths, line strengths, oscillator strengths, lifetimes, AJ, BJ hyperfine interaction constants, Landé gJ-factors, and electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), magnetic quadrupole (M2) transition rates among all these levels are given. The present MCDF and MBPT results are compared with each other and with other available experimental and theoretical results. The mean relative difference between our two sets of level energies is only about 0.003% for these 272 levels. The accuracy of the present calculations are high enough to facilitate identification of many observed spectral lines. These accurate data can be served as benchmark for other calculations and can be useful for fusion plasma research and astrophysical applications.

Kα1,2x-ray linewidths, asymmetry indices, and[KM]shake probabilities in elements Ca to Ge and comparison with theory for Ca, Ti, and Ge

We have investigated systematically the $K\ensuremath{\alpha}$ x-ray spectra in elements from Ca to Ge within Berger's two-Lorentzian functions model, using a high-resolution antiparallel double-crystal x-ray spectrometer, in order to obtain in detail the physical meaning of the asymmetry in the spectral profiles. The overall tendency of the corrected full width at half maximum of the $K{\ensuremath{\alpha}}_{1}$ and $K{\ensuremath{\alpha}}_{2}$ lines as a function of $Z$, as well as the linewidths, are in good agreement with the data reported in the literature. It is found, from both the experiments and calculation, that satellite lines arising from shake-off appear between the $K{\ensuremath{\alpha}}_{1}$ and $K{\ensuremath{\alpha}}_{2}$ lines. The asymmetry index of $K{\ensuremath{\alpha}}_{1}$ in $3d$ elements from Sc to Zn is ascribed to the existence of a $3d$ spectator hole. Moreover, the observed Sc $K{\ensuremath{\alpha}}_{1}$ line shows a symmetric profile unlike the Ti $K{\ensuremath{\alpha}}_{1}$ line profile, this discrepancy being explained by the existence of satellite lines on both sides of the Sc profile. Our experimental results yielded around 25% probability for the probability of shake processes creating a second hole in the $3p$ or $3d$ subshells in Sc and around 18% probability for creating a second hole the in the $3p$ in Ca. For the latter process our calculated value, using multiconfiguration Dirac-Fock wave functions and the sudden approximation yielded a 10% probability.

Prominent role of multielectron processes inK-shell double and triple photodetachment of oxygen anions

The photon-ion merged-beams technique was used at a synchrotron light source for measuring absolute cross sections of double and triple photodetachment of O$^{-}$ ions. The experimental photon energy range of 524-543 eV comprised the threshold for K-shell ionization. Using resolving powers of up to 13,000, the position, strength and width of the below-threshold 1s 2s2 2p6 2S resonance as well as the positions of the 1s 2s2 2p5 3P and 1s 2s2 2p5 1P thresholds for K-shell ionization were determined with high precision. In addition, systematically enlarged multi-configuration Dirac-Fock calculations have been performed for the resonant detachment cross sections. Results from these ab-initio computations agree very well with the measurements for the widths and branching fractions for double and triple detachment, if double shake-up (and -down) of the valence electrons and the rearrangement of the electron density is taken into account. For the absolute cross sections, however, a previously found discrepancy between measurements and theory is confirmed.

Revised and extended calculations of level energies, M1 and E2 radiative rates for highly charged tungsten ions from W57+ to W60+

We have applied systematically enlarged multiconfiguration Dirac–Fock wavefunctions using Grasp2K to calculate the transition energies, oscillator strengths and transition probabilities for fine structure M1 and E2 transitions between the low-lying levels of the 3s23p5, 3s23p4, 3s23p3 and 3s23p2 configurations of highly charged tungsten ions from to . Large wavefunction expansions are applied to calculate the transition probabilities, which are indispensable for calculating various plasma parameters accurately. In the present calculations, our theoretical data agrees well with that obtained in precise electron beam ion trap measurements, and is therefore important for the identification of weak forbidden lines for plasma diagnostic applications.

Ground-state Landégfactors for selected ions along the boron isoelectronic sequence

Land\'e $g$ factors for the fine-structure $1{s}^{2}2{s}^{2}2p\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2}$ and $^{2}P_{3/2}$ levels in the boron isoelectronic sequence for selected $Z$ values have been calculated using the multiconfiguration Dirac-Fock method with both quantum-electrodynamic and electronic correlation corrections included. All-order Breit and vacuum polarization corrections were included in the calculation, with a fully optimized active set wave function. The results are compared with the available theoretical data, showing a very good agreement.

Atomic structure calculations and study of EUV and SXR spectral lines in Cu-like ions

In the present work, we provide a most extensive and detailed study of highly ionized Cu-like ions and diagnose extreme ultraviolet (EUV) and soft X-ray (SXR) transitions with N-shell electron excitation to M-shell and higher shells. We have determined energy levels and lifetimes for lowest 27 fine-structure levels by adopting multiconfiguration Dirac–Fock (MCDF) with the inclusion of quantum electrodynamics (QED) as well as Breit corrections as a first-order perturbation theory. We have also reported complete radiative data for strong electric dipole transitions within lowest 27 levels. We have compared our calculated results with theoretically calculated and experimentally measured results available in the literature, to measure the credibility and genuineness of our results, and achieve good agreement. Further, because of insufficiency of adequate and complete atomic data for higher levels of highly ionized Cu-like ions in the literature, we have performed other equivalent parallel calculations by implementing fully relativistic distorted wave flexible atomic code (FAC) to ensure the accuracy of our results. Additionally, we have also presented transition wavelengths of Nα transitions of high-Z Cu-like ions by using Moseley’s law. We believe that the large amount of atomic data presented in this paper may be useful in fusion and astrophysical plasma and in several applications, especially in lithography and cell biology.

4d → 4f resonance in photoabsorption of cerium ion Ce3+ and endohedral cerium in fullerene complex

The theoretical investigation of the single-photoionization spectra in the 4d-resonance region (120–150 eV) for the ionic cerium Ce3+ and cerium in the endohedral complex (in practice, is presented. The fullerene cage is modeled by ab initio spherical jellium shell with an accurate account for the real distribution of carbon electron density. The oscillator strengths are calculated within the multiconfiguration Dirac–Fock (MCDF) approach for phototransitions from the outermost shells of the ion Ce3+ with and without the influence of the potential generated by a fullerene cage. It is shown that the integrated oscillator strengths have the main contribution from the Ce3+ 4d → 4f (ten possible from the phototransitions resonance photoexcitations. The corresponding precise MCDF values for the oscillator strengths and the transition energies are presented for the first time. It is demonstrated that the resonance oscillator strengths are slightly affected by the presence of the cage potential, despite the fact that the spectral levels structure is changed when the effect of this potential is included. The Auger 4d −1 decay from the cerium free ion Ce3+ and the encapsulated endohedral ion Ce3+@ are considered within the two-step model and the corresponding Lorentzian profiles are presented. This model clearly reveals the correspondence of the complex resonance profile in the Ce3+ photoabsorption to the fine structure of ion energy levels. The smoothing of the resonance profile in the photoabsorption of the endohedral system compared with the free ion Ce3+ is attributed to increasing the linewidths of the Auger transitions. This increase is estimated from the relevant experiment (Müller et al 2008 Phys. Rev. Lett. 101 133001) to be strong; as at least three times the value for an isolated ion. The presence of the confining fullerene cage decreases the autoionizing giant resonance lifetime for endohedral cerium in due to the opening of additional decay channels involving electrons of the fullerene shell, which cannot be accounted as a static potential. From consideration of the two-step model, it is clear that these processes are important. However, they lead only to broadening of the resonance. The dramatic reduction in the integrated oscillator strength in the cerium 4d resonance region can only occur when additional processes besides photoionization come into play.

Multiconfigurational Dirac-Fock Energy Levels and Radiative Rates for Kr XX

In present calculations, energy levels and radiative properties are reported for transitions in Cl-like Kr. For these calculations, the fully relativistic multiconfigurational Dirac-Fock (MCDF) approach is employed by including 54 configurations (generating 5370 levels) and the Breit and quantum electrodynamics effects. To assess the accuracy of presented results, calculations have also been performed for energy levels using the fully relativistic flexible atomic code (FAC) and comparisons are made with the existing experimental and theoretical data. Energies are reported for the lowest 100 levels corresponding to the configurations 3s 2 3p 5 , 3s3p6, 3s 2 3p 4 3d, 3s3p 5 3d, 3s 2 3p 3 3d 2 and radiative rates are provided for E1 and M2 transitions from ground state.

Atomic structure calculations and study of line intensity ratio for Kr XXIV

In this work, we provide a detailed and elaborate theoretical study of atomic data along with plasma parameters for Kr XXIV. We have computed energy levels, lifetimes, and wave-function compositions for the lowest 148 fine-structure levels by implementing the multi-configuration Dirac–Fock method with the addition of quantum electrodynamics as well as Breit corrections. We have also given the radiative data among 148 levels for electric dipole (E1) transition, which lie in the extreme ultraviolet range. We have compared our calculated results with NIST and other theoretical results available in the literature and attain a good agreement. Because of the unavailability of sufficient and complete data for higher excited levels for Kr XXIV in the literature, a similar calculation has also been compiled using fully relativistic flexible atomic code (FAC) to access the credibility and integrity of our results. On the other hand, we have also presented the line intensity ratio and plasma parameters for optically thin plasma, which are not published anywhere in the literature, and we believe that our presented results may be advantageous in plasma modeling and astrophysical and fusion plasma research applications.

E1, E2 and M1 transition parameters for some levels over ionization limit of Ne III

We have reported the level energies and radiative transition (E1 , E2 and M1 parameters, such as wavelengths, transition rates, oscillator strengths and line strengths for some levels over the ionization limit of Ne III (oxygen-like). The calculations have been performed using the general-purpose relativistic atomic structure package (GRASP) based on the fully relativistic multiconfiguration Dirac-Fock (MCDF) method. The results obtained have been compared with the available theoretical and experimental values in the literature.

The K x-ray line structures of the 3d-transition metals in warm dense plasma

The shapes and positions of the Kα1 and Kα2 x-ray lines for 3d-transition metals can vary substantially as electrons are stripped from the outer-shells. This paper shows the detailed line shapes for nickel and zinc, obtained by calculations with a multiconfiguration Dirac–Fock method that includes Breit interaction and quantum electrodynamics corrections. The line shapes can be useful in interpreting hot, dense plasmas with energetic electrons for which the K x-ray lines are optically thin, as may be produced by pulsed power machines such as the plasma-filled rod pinch diode or the plasma focus, or in short-pulsed high power laser plasmas.

Probing electron correlation through radiative lifetime measurements upon inner-valence photoionization of Ne and Ar

This work demonstrates that electron correlation can have a strong effect on the radiative lifetime of atoms. We report measurements of the radiative lifetimes of inner-valence hole states, the 3s3p6 2S1/2 state of Ar+ and the 2s2p6 2S1/2 state of Ne+ by using the time-correlated single photon counting technique combined with photoionization by synchrotron radiation. Theoretical calculations utilizing the multi-configuration Dirac–Fock method agreed well with the experimental results. In particular, the radiative lifetime was found to depend very sensitively on the mixing of valence excited state configurations. While the Ne+ 2s2p6 2S1/2 state only has relatively weak inter-shell correlation, Ar+ 3s3p6 2S1/2 state has strong intra-shell correlation within the M-shell. This intra-shell correlation enhances configuration mixing and causes the radiative lifetime of the Ar+ 3s3p6 2S1/2 state to become very much longer than that of the Ne+ 2s2p6 2S1/2 state.