Multiconfiguration Dirac-Fock Calculations Research Articles

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.

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

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.

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.

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.

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.

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.

Relativistic multiconfiguration Dirac–Fock calculations of photoionization, electron-impact ionization, Auger decay, and relaxed-orbital oscillations of Cu ions

Core-hole creation and decay are of tremendous importance in both theory and applications. However, different ionization approaches and decay channels, especially at L-shell, bring many challenges to accurate simulation. In order to understand the ionization state effects on the creation and decay at L-shell hole, we performed a theoretical study of photon/electron-impact L-shell ionization of differently charged copper ions and the subsequent Auger electron and fluorescence emission by using the relativistic multiconfiguration Dirac–Fock approach. It was found that photoionization has much larger cross sections than electron-impact ionization near the ionization threshold, but smaller ones at higher impact energies. The ionization cross sections for 2s-sublevels are negligibly small compared with those for 2p-sublevels for both photon and electron impact ionizations. Additionally, the ionization cross sections decrease with the ionization state for both electron- and photon- impact L-shell ionizations. Similar to radiative (fluorescence) decay, Auger kinetic energy and yield decrease with ionization state, and the energy gaps and rate ratios between major Auger transitions change with ionization state. Furthermore, Auger rates from the L-shell decay are much larger than fluorescence rates, and the Auger-to-fluoresce decay ratio slightly decreases with increase in the ionization state of Cu ion.

Reference-free measurements of the1s2s2p2P1/2,3/2o→1s22s2S1/2and1s2s2p4P5/2→1s22s2S1/2transition energies and widths in lithiumlike sulfur and argon ions

We have measured the widths and energies of the 1s2s2p 2 P 1/2,3/2 → 1s 2 2s 2 S 1/2 transitions in lithiumlike sulfur and argon, as well as the energies of the forbidden 1s2s2p 4 P 5/2 → 1s 2 2s 2 S 1/2 M2 transition in both elements. All measurements were performed with a double-flat crystal spectrometer without the use of any reference line. The transition energy measurements have accuracies ranging from 2.3 ppm to 6.4 ppm depending on the element and line intensity. The widths and the intensity ratios of the 1s2s2p 2 P 1/2,3/2 → 1s 2 2s 2 S 1/2 lines have also been measured. These are the first reference-free measurements of transitions in core-excited lithiumlike ions, and have an accuracy comparable to the best relative measurements. We have also performed multi-configuration Dirac-Fock calculations of the widths, energies and intensity ratios. Extensive comparison between existing experimental results and theory is performed, and Bayesian techniques employed to extract the energy of the 1s 2p 2 4 P 1/2 → 1s 2 2p 2 P 1/2 transition in sulfur and identify contaminant transitions.

Theoretical study on the line shifts of He-like Al11+ ion immersed in a dense plasma

We present relativistic multi-configuration Dirac-Fock calculations for the energies and oscillator strengths of He-like Al11+ ion within a dense plasma. The average-atom ion-sphere potential and the uniform electron gas model potential are used to represent the interaction between the charge particles. Self-consistent calculations of dense plasma effects on the atomic structure, based on the above two potentials, are also carried out using EPPP package，based on the Flexible Atomic Code for comparison purposes. While we find consistency between our two kinds of theoretical predictions, a discrepancy persists with the calculations of Li and Rosmej [Europhys. Lett. 99, 33001 (2012)]. We also present the line shifts of 1s2p→1s2 transition to compare with the recent measurements of Stillman et al. [Phys. Rev. E 95, 063204 (2017)]. Agreement between theory and experiment is far from perfect, the experimental values are generally 2.2 times higher than our predictions. A qualitative analysis of the physical reasons for such differences is given. Further precise measurements and systematic elaborate calculations are needed to support spectral analysis.

Prominent enhancement on the radiative branching ratio of the doubly excited resonant states due to the Breit interaction induced ion-core energy inversion

The Breit interaction is the relativistic correction to the electron-electron interaction which mainly affects the level energies, and it is minor in general. We present a new manifestation of the Breit interaction effects in the highly charged Li- and B-like ions based on the multi-configuration Dirac-Fock calculations, where the strongly correlated many-body wavefunctions of the doubly excited resonant states [1s2p1/22p3/2]3/2 (or [1s(2s2)2p1/22p3/2]3/2) 4P3/2 and 2D3/2 are drastically influenced by the Breit interaction. The strong variation of wavefunctions results in a prominent enhancement of the radiative branching ratio between the two dominant transitions 2p3/2-1s and 2p1/2-1s of the doubly excited states. We elucidate the intrinsic mechanism of this effect is due to the ion-core energy inversion induced by the Breit interaction, and suggest that the possible experimental measurements can be achieved via the dielectronic recombination processes in an electron beam ion trap facility. Based on this effect, we also propose an alternative experimental determination of the fine structure splitting of [1s2p1/2]0,1 (or [1s(2s2)2p1/2]0,1) in heavy He-like (or Be-like) ions from the branching ratio of the doubly excited Li-like (or B-like) ions, which is sensitive to the fine structure level inversions and can be served as a complementary tool to the available hyperfine quenching experimental method aiming for the absolute value of the splitting.

Relativistic photoionization cross section calculations and resonance parameters for Mg-like Se XXIII

Photoionization cross sections of the ground state 2p63s2 (1S0) and the first three excited states 2p63s3p (3Po0,1,2) of Mg-like Se XXIII have been reported by employing the fully relativistic Dirac atomic R-matrix code (DARC). For construction of target wavefunctions, multiconfiguration Dirac-Fock calculations are performed for the lowest 21 fine structure energy levels belonging to 2p6nl (3 ≤ n ≤ 5) configurations. Our calculated target state energies of the core ion Se XXIV show close agreement with the energies tabulated in the NIST database. In order to assess the accuracy of our DARC results, photoionization cross section calculations of the ground state configuration have also been performed using the close-coupling Breit-Pauli R-matrix (BPRM) method. Our two independent calculations show a good agreement both in magnitude and resonant photoionization cross sections. The resonance energies (Er) and widths (Γ) of the 3pns (3P1,1P1), 3pnd (3D1, 3P1, 1P1), 3dnp (3D1, 3P1, 1P1) and 3dnf (3D1, 3P1, 1P1) series due to ejection of a 3s electron from the ground state 2p63s2 (1S0) have also been predicted by adopting Quigley and Berrington (QB) method. We believe that our results might be beneficial for the modelling and diagnostics of fusion and laser generated plasmas.

Multiconfiguration Dirac–Fock calculations of Zn K‐shell radiative and nonradiative transitions

Zinc K‐shell radiative and radiationless transition rates are calculated using the multiconfiguration Dirac–Fock method. Correlation up to the 4p orbital is included in almost all transition rate calculations. Calculated radiative transition rates and transition probabilities are compared with Scofield's Dirac–Hartree–Slater and Dirac–Hartree–Fock calculations, presenting good agreement with the later. Radiative transition intensity ratios involving the strongest lines are compared with theoretical, experimental, and empirical‐fit values. Most ratios are in close agreement with the empirical‐fit values from NIST's Fundamental Parameters database. Calculated radiationless transition rates and ratios are compared with Chen et al.'s Dirac–Fock values and Safronova et al.'s Dirac–Fock values. The K‐LL transition rates are overall lower than Chen et al.'s values, whereas the K‐LX and K‐XY transition rates are overall higher. Calculated K‐LX/K‐LL and K‐XY/K‐LL ratios are relatively close to the experimental values compared. Some calculated intensities relative to K‐L are in good agreement with the experimental values, whereas others present worse agreement. The calculated fluorescence yield is higher than all theoretical, experimental, and empirical‐fitted values compared, probably because the total radiationless transition rate value calculated in the present work is relatively low.

Fock-space multireference coupled cluster calculations of Auger energies of noble gas elements using relativistic spinors.

We report the Auger and Coster-Kronig transition energies (related to double ionization potentials) of noble gas elements obtained using the Fock-space multireference coupled cluster (FSMRCC) method with relativistic spinors. The resulting Auger and Coster-Kronig lines are found to be in agreement with the experimental data and with other reference theoretical estimates. To the best of our knowledge, no prior report of relativistic calculations is available for Auger transition energies at the FSMRCC level of theory. The ionization potentials resulted from this method with no extra cost are also found to be in agreement with experiment, particularly the outer-valence ones. Interestingly, the FSMRCC and the multiconfiguration Dirac-Fock calculations exhibit an inversion in the 3P energy levels of the xenon atom for N4,5-O23O23 Auger transitions, where the 3Pj state energies appear in the order J = 1, 0, 2, a feature which can be verified experimentally.

Diagram, valence‐to‐core, and hypersatellite Kβ X‐ray transitions in metallic chromium

We report on measurements of the Kβ diagram, valence‐to‐core (VtC), and hypersatellite X‐ray spectra induced in metallic Cr by photon single and double K‐shell ionization. The experiment was carried out at the Stanford Synchrotron Radiation Lightsource using the seven‐crystal Johann‐type hard X‐ray spectrometer of the beamline 6‐2. For the Kβ diagram and VtC transitions, the present study confirms the line shape features observed in previous works, whereas the Khβ hypersatellite transition was found to exhibit a complex spectral line shape and a characteristic low‐energy shoulder. The energy shift of the hypersatellite relative to the parent diagram line was deduced from the measurements and compared with the result of extensive multiconfiguration Dirac–Fock (MCDF) calculations. A very good agreement between experiment and theory was found. The MCDF calculations were also used to compute the theoretical line shape of the hypersatellite. A satisfactory agreement was obtained between the overall shapes of the experimental and theoretical spectra, but deviations were observed on the low‐ and high‐energy flanks of the hypersatellite line. The discrepancies were explained by chemical effects, which were not considered in the MCDF calculations performed for isolated atoms.

Collinear laser spectroscopy at ion-trap accuracy: Transition frequencies and isotope shifts in the 6s2S1/2→6p2P1/2,3/2 transitions in Ba+

The rest-frame transition frequencies of the $6s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}$ (${D}_{1}$) and $6s{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}6p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ (${D}_{2}$) lines in the stable isotopes of ${\mathrm{Ba}}^{+}$ were measured with an accuracy better than $200\phantom{\rule{4pt}{0ex}}\mathrm{kHz}$ through (quasi)simultaneous collinear and anticollinear laser spectroscopy, leading to an improvement in the accuracy of the isotope shifts by more than an order of magnitude compared to previous data. The ratio of the field-shift constants in the ${D}_{1}$, ${D}_{2}$ fine-structure doublet has been determined to $f=1.0186(9)$ through a King plot analysis. These collinear laser spectroscopy measurements have reached an accuracy comparable to ion-trap measurements on allowed dipole transitions. Our result provides an accurate benchmark for atomic many-body calculations and is compared to pure Dirac-Hartree-Fock calculations and to elaborate multiconfigurational Dirac-Fock calculations. The influence of correlation effects and the Breit interaction on the isotope shift in ${\mathrm{Ba}}^{+}$ are discussed.

Investigating XRF parameters and valance electronic structure of the Co, Ni, and Cu spinel ferrites

In the present study, K X-ray emission spectra of Cu, Ni, Co spinel ferrite (MFe2O4) alloys obtained with a HPGe detector by inducing 59.54 keV and 22.1 keV γ-rays emitted from 3 Ci 241Am annular source and 40 mCi 109Cd point source. The data obtained were evaluated in terms of the Kβ/Kα X-ray intensity ratios, the full width at half maximum (FWHM) values, asymmetry index (As), peak energies and chemical shifts (ΔE) depending on the alloying effect. In addition, calculated Kβ/Kα intensity ratios, which is used to determine the electron number changes in the orbitals for Cu, Ni, Co, Fe elements in the alloys, were compared with the results of Multiconfiguration Dirac-Fock (MCDF) calculations. It has been observed that chemical shifts in the spectra have been occurred upon alloying due to crystal structure, valence electron structure, bond type and length. It has been also concluded that the X-ray intensity ratios and the 3d electron densities of the pure ferrite have influenced by the alloying transition elements. It has been observed that the charge transfer mechanism predominates mainly due to the different electronegativity of the elements in the alloys.

A study for hydrogen-like lawrencium

Studying hydrogenic ions with high Z is an occasion to understand atomic structure. It also provides a reliable test of methods used to determine atomic structures. Many fields and applications require precise atomic data. For this reason, a hydrogen-like study is performed for lawrencium (Lr102+, Z = 103). The energy levels of hydrogen-like lawrencium are calculated with both multiconfiguration Hartree–Fock (MCHF) and multiconfiguration Dirac–Fock (MCDF) methods. The calculations contain Breit–Pauli relativistic corrections in MCHF calculation and the transverse photon and quantum electrodynamics (QED) effects in MCDF calculation along with electron correlations. In addition, some transition parameters (wavelengths, λ, logarithmic weighted oscillator strengths, log(gf) value, and transition probabilities, Aki) for allowed (E1) and forbidden (E2 and M1) transitions are investigated. The results from this study are compared with only a few theoretical works, but there is no available experimental data yet for Lr102+.

High-resolution tungsten spectroscopy relevant to the diagnostic of high-temperature tokamak plasmas

The x-ray transitions in Cu- and Ni-like tungsten ions in the 5.19--5.26 \AA{} wavelength range that are relevant as a high-temperature tokamak diagnostic, in particular for JET in the ITER-like wall configuration, have been studied. Tungsten spectra were measured at the upgraded Shanghai- Electron Beam Ion Trap operated with electron-beam energies from 3.16 to 4.55 keV. High-resolution measurements were performed by means of a flat Si 111 crystal spectrometer equipped by a CCD camera. The experimental wavelengths were determined with an accuracy of 0.3--0.4 m\AA{}. The wavelength of the ground-state transition in Cu-like tungsten from the $3{p}^{5}3{d}^{10}4s4d\phantom{\rule{4pt}{0ex}}[{(3/2,{(1/2,5/2)}_{2}]}_{1/2}$ level was measured. All measured wavelengths were compared with those measured from JET ITER-like wall plasmas and with other experiments and various theoretical predictions including cowan, relac, multiconfigurational Dirac-Fock (MCDF), and fac calculations. To obtain a higher accuracy from theoretical predictions, the MCDF calculations were extended by taking into account correlation effects (configuration-interaction approach). It was found that such an extension brings the calculations closer to the experimental values in comparison with other calculations.