Multiconfiguration Dirac-Fock Results Research Articles

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

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

Calculation of energy levels, lifetimes and radiative data for La XXIX to Sm XXXIV

We present the most comprehensive atomic data for La XXIX to Sm XXXIV with single electron excitation from M-shell to N-shell and N-shell to higher shells. We have presented energy levels, lifetimes and radiative data using Multi-configuration Dirac–Fock (MCDF) method for the lowest 27 states belonging to the configuration 3d104l (l=0,1,2,3), 3d105l (l=0,1,2,3,4), 3d106l (l=0,1,2,3,4) and 3d94s2. We have also considered relativistic effects by incorporating quantum electrodynamics (QED) and Breit corrections. We have made comparisons of our presented results with available theoretical as well as experimental results and a good agreement is achieved. Further, we have also reported energy levels by performing distorted wave calculations with fully relativistic flexible atomic code (FAC). The calculations match well with MCDF results. Additionally, we have investigated the effect of nuclear charge on transition wavelength and radiative rates for strong Extreme Ultraviolet (EUV) transitions from n=4→4. We believe that our reported data in this work may be useful in various applications of lanthanide ions related to broad area of research such as applied physics, laser physics and astrophysics etc.

Energy levels and oscillator strengths for Mg-like copper

Energy levels and oscillator strengths for electric-dipole (E1), electric-quadrupole (E2), magnetic-dipole (M1), and magnetic-quadrupole (M2) transitions among the lowest 185 levels arising from the n≤5 configurations in Cu XVIII are calculated through second-order many-body perturbation theory (MBPT). To illustrate the improvement of many-body perturbation corrections, we have also carried out the parallel calculations using the standard relativistic configuration-interaction (RCI) approach. Furthermore, to confirm the accuracy of the present MBPT results and show further the importance of valence–valence and core–valence correlation effects, we have performed another independent calculation using the multiconfiguration Dirac–Fock (MCDF) method within the GRASP code in the active space approximation. The accuracies of the present level energies, wavelengths, transition rates and lifetimes are assessed by comparing to available experimental and other theoretical results. The present MBPT and MCDF results are believed to be the most comprehensive and accurate ones to date.

Dielectronic Recombination of Fe xxi and Fe xxii via N = 2→ N ′ = 2 Core Excitations

We have measured dielectronic recombination (DR) resonance strengths and energies for carbon-like Fe XXI forming Fe XX and for boron-like Fe XXII forming Fe XXI via N = 2 → N' = 2 core excitations. All measurements were carried out using the heavy-ion Test Storage Ring at the Max-Planck-Institute for Nuclear Physics in Heidelberg, Germany. We have also calculated these resonance strengths and energies using three independent, state-of-the-art perturbative techniques: a multiconfiguration Breit-Pauli (MCBP) method using the code AUTOSTRUCTURE, a multiconfiguration Dirac-Fock (MCDF) method, and a relativistic configuration interaction method using the Flexible Atomic Code (FAC). Overall, reasonable agreement is found between our experimental results and our theoretical calculations. The most notable discrepancies tend to occur for relative collision energies 3 eV. We have used our measured 2 → 2 results to produce Maxwellian-averaged rate coefficients for Fe XXI and Fe XXII. Our experimentally derived rate coefficients are estimated to be accurate to better than ≈20% both for Fe XXI at kBTe > 0.5 eV and for Fe XXII at kBTe > 0.001 eV. For these results, we provide fits that are accurate to better than 0.5% for Fe XXI at 0.001 eV ≤ kBTe ≤ 10,000 eV and for Fe XXII at 0.02 eV kBTe ≤ 10,000 eV. Our fitted rate coefficients are suitable for ionization balance calculations involving Fe XXI and Fe XXII in photoionized plasmas. Previous published Burgess formula and LS-coupling calculations are in poor agreement with our experimentally derived rate coefficients. None of these published calculations reliably reproduce the magnitude or temperature dependence of our experimental results. Our previously published Fe XXI MCDF results are in good agreement with our experimental results for kBTe 0.07 eV. For both ions in this temperature range our new MCBP, MCDF, and FAC results are in excellent agreement with our experimentally derived rate coefficient.

Experimental andtheoretical studies of lifetimes and transition probabilitiesfor Au II

We report lifetime measurements for three of the 5d96plevels in Au II and relativistic multiconfigurationDirac-Fock (MCDF) calculations oflifetimes and transitions probabilities in this ion. The workwas motivated by significant disagreements between previousexperimental 5d96p lifetimes, obtained by means of thebeam-foil (BF) method and theoretical data based on Hartree-Fock calculations in which relativistic effects were included asperturbations. The new measurements, based on laser-inducedfluorescence, support the BF data and are also inexcellent agreement with the MCDF results. We confirm that,while computational methods which include perturbative relativistic corrections appear to be adequate for moderatelyheavy elements such as Ag, fully relativistic calculations areessential for describing systems as heavy as Au.

Dielectronic Recombination (via N = 2→ N ′ = 2 Core Excitations) and Radiative Recombination of Fe xx : Laboratory Measurements and Theoretical Calculations

We have measured the resonance strengths and energies for dielectronic recombination (DR) of Fe xx forming Fe xix via N ¼ 2 ! N 0 ¼ 2( DN ¼ 0) core excitations. We have also calculated the DR resonance strengths and energies using the AUTOSTRUCTURE, Hebrew University Lawrence Livermore Atomic Code (HULLAC), Multiconfiguration Dirac-Fock (MCDF), and R-matrix methods, four different state-ofthe-art theoretical techniques. On average the theoretical resonance strengths agree to within .10% with experiment. The AUTOSTRUCTURE, MCDF, and R-matrix results are in better agreement with experiment than are the HULLAC results. However, in all cases the 1 � standard deviation for the ratios of the theoretical-to-experimental resonance strengths is &30%, which is significantly larger than the estimated relative experimental uncertainty of .10%. This suggests that similar errors exist in the calculated level populations and line emission spectrum of the recombined ion. We confirm that theoretical methods based on inverse-photoionization calculations (e.g., undamped R-matrix methods) will severely overestimate the strength of the DR process unless they include the effects of radiation damping. We also find that the coupling between the DR and radiative recombination (RR) channels is small. Below 2 eV the theoretical resonance energies can be up to � 30% larger than experiment. This is larger than the estimated uncertainty in the experimental energy scale (.0.5% below � 25 eV and .0.2% for higher energies) and is attributed to uncertainties in the calculations. These discrepancies makes DR of Fe xx an excellent case for testing atomic structure calculations of ions with partially filled shells. Above 2 eV, agreement between the theoretical and measured energies improves dramatically with the AUTOSTRUCTURE and MCDF results falling within 2% of experiment, the R-matrix results within 3%, and HULLAC within 5%. Agreement for all four calculations improves as the resonance energy increases. We have used our experimental and theoretical results to produce Maxwellian-averaged rate coefficients for DN ¼ 0D R of Fexx. For kBTe & 1 eV, which includes the predicted formation temperatures for Fe xx in an optically thin, low-density photoionized plasma with cosmic abundances, the experimental and theoretical results agree to better than � 15%. This is within the total estimated experimental uncertainty limits of .20%. Agreement below � 1 eV is difficult to quantify due to current theoretical and experimental limitations. Agreement with previously published LS-coupling rate coefficients is poor, particularly for kBTe . 80 eV. This is attributed to errors in the resonance energies of these calculations as well as the omission of DR via 2p1=2 ! 2p3=2 core excitations. We have also used our R-matrix results, topped off using AUTOSTRUCTURE for RR into J � 25 levels, to calculate the rate coefficient for RR of Fe xx. Our RR results are in good agreement with previously published calculations. We find that for temperatures as low as kBTe � 10 � 3 eV, DR still dominates over RR for this system. Subject headings: atomic data — atomic processes — methods: laboratory On-line material: machine-readable tables

MCDF calculations of the specific mass shift inhelium-like ions

An extension of the GRASP92 (Parpia F A, Froese Fischer C andGrant I P 1996 Comput. Phys. Commun. 94 249)multi-configuration Dirac-Fock (MCDF) program describedpreviously (Perger W F and Idrees M 1995 Phys. Commun.85 389-97) is used for the calculation of the specificmass shift (SMS) of the helium 1S ground stateisoelectronic sequence. We also employ a multi-configurationHartree-Fock (MCHF) method to calculate the ground state SMS forcomparison with MCDF results. The SMS matrix elements fortwo-electron systems obtained from the relativistic program areshown to exhibit a trend: the larger the atomic number Z, thelarger the relativistic contributions to the SMS matrix elementsfor the ions. The SMS matrix elements approximately vary asZ3 along the isoelectronic sequence from Z = 2 to 92.In addition, it is shown that the relativistic effects increaseapproximately as Z3/A2 in the SMS values for all theions considered confirming some previous observations(Parpia F A, Tong M and Froese Fischer C 1992 Phys. Rev. A 463717-24).Excellent agreement is found between the present ab initio calculations and the available semi-relativisticcalculations for the small values of Z along the helium-likeions. Furthermore, a large set of configuration state functionsused in the calculations has revealed larger disagreements forhigh-Z ions between both relativistic (MCDF-optimized-level) andnonrelativistic (MCHF) calculations suggesting that the SMS forhelium-like ions with Z>40 relativistic and correlationeffects are increasingly important.

Ab initio calculation of 4fN6s2 hyperfine structure in neutral rare-earth atoms.

The multiconfiguration Dirac-Fock (MCDF) method is used to calculate excitation energies, Land\'e g values, and hyperfine-structure (hfs) constants for the lowest multiplets of the 4${f}^{N}$6${s}^{2}$ configurations of neutral rare-earth atoms. Although no adjustable parameters are used, the results are in rather good agreement with experiment. The calculated excitation energies and dipole hfs constants (using the known moment values) differ from experiment by typically 5%, and the g values by 0.1%. Relative to quadrupole moment values determined from muonic-atom hfs or Coulomb excitation, the calculated electric-quadrupole hfs is typically (30\ifmmode\pm\else\textpm\fi{}2)% too large, consistent with a Sternheimer shielding factor (not included in the MCDF calculations) of ${R}_{4f}$=+0.23. The calculated J dependence for all four observables is generally in good agreement with experiment for the ground multiplets. Particular cases where the MCDF results are less accurate are identified and discussed.

Intershell correlation corrections to the energy levels of the n=2 states of Li-like to F-like ions

The leading intershell correlation corrections to the energy levels of the 2sm2pk (m0-2, k=0-6) configurations of three- to nine-electron ions are calculated on the basis of the Z-expansion theory. These intershell correlations are leading corrections to the multiconfiguration Dirac-Fock (MCDF) results of Cheng and co-workers (1979) and the present study shows that they substantially improve the agreement between the MCDF results and experimental measurements.