Dirac Hartree Fock Calculations Research Articles

Energy Levels and Transition Rates for Laser Cooling Os− and a General Approach to Produce Cold Atoms and Molecules

High-resolution photoelectron energy spectra of osmium anions are obtained using the slow-electron velocity-map imaging method. The energy levels of excited states 4 F 7/2, 4 F 5/2 and 4 F 3/2 of Os− are determined to be 148.730(13), 155.69(15), and 176.76(13) THz [or 4961.09(41), 5193.4(49), and 5896.1(42) cm−1], respectively. The lifetime of the opposite-parity excited state is determined to be 201(10) μs using a cold ion trap, about 15 times shorter than the previous result 3(1) ms. Our high-level multi-configuration Dirac–Hartree–Fock calculations yield a theoretical lifetime 527 μs. Our work shows that the laser cooling rate of Os− is as fast as that of Th−. The advantages of Os− are its near-IR range cooling transition and simple electronic structure, which make Os− a promising candidate for laser cooling of negative ions. We propose a general approach to produce cold atoms and molecules based on the sympathetic cooling of negative ions in combination with a threshold photodetachment.

Pseudo-Relativistic Hartree–Fock and Fully Relativistic Dirac–Hartree–Fock Calculations of Radiative Parameters in the Fifth Spectrum of Lutetium (Lu V)

Using two independent theoretical methods based on the pseudo-relativistic Hartree–Fock (HFR) and the fully relativistic Multiconfigurational Dirac–Hartree–Fock (MCDHF) approaches, we computed the radiative parameters (transition probabilities and oscillator strengths) corresponding to the spectrum of quadruply ionized lutetium (Lu V). The agreement observed between both sets of results allowed us to deduce the radiative rates for a large amount of transitions in order to calculate the contribution of this ion to the opacity of kilonovae in their early phases, i.e., for T = 25,000 K. The results obtained were compared to previous data computed for other quadruply ionized lanthanide atoms, namely La V, Ce V, Pr V, Nd V and Pm V, in order to highlight the main contributors to the opacity among these ions under kilonovae conditions where the Vth spectra are predominant.

Large-scale Multiconfiguration Dirac–Hartree–Fock Calculations for Astrophysics: C-like Ions from O iii to Mg vii

Large-scale multiconfiguration Dirac–Hartree–Fock calculations are provided for the n ≤ 5 states in C-like ions from O iii to Mg vii. Electron correlation effects are accounted for by using large configuration state function expansions, built from sets of orbitals with principal quantum numbers n ≤ 10. An accurate and complete data set of excitation energies, wavelengths, radiative transition parameters, and lifetimes is offered for the 156 (196, 215, 272, 318) lowest states of the 2s 22p 2, 2s2p 3, 2p 4, 2s 22p3s, 2s 22p3p, 2s 22p3d, 2s2p 23s, 2s2p 23p, 2s2p 23d, 2p 33s, 2p 33p, 2p 33d, 2s 22p4s, 2s 22p4p, 2s 22p4d, 2s 22p4f, 2s2p 24s, 2s2p 24p, 2s2p 24d, 2s2p 24f, 2s 22p5s, 2s 22p5p, 2s 22p5d, 2s 22p5f, and 2s 22p5g configurations in O iii (F iv, Ne v, Na vi, Mg vii). By comparing available experimental wavelengths with the MCDHF results, the previous line identifications for the n = 5, 4, 3 → n = 2 transitions of Na vi in the X-ray and EUV wavelength range are revised. For several previous identifications discrepancies are found, and tentative new (or revised) identifications are proposed. A consistent atomic data set including both energy and transition data with spectroscopic accuracy is provided for the lowest hundreds of states for C-like ions from O iii to Mg vii.

Near K-edge Photoionization and Photoabsorption of Singly, Doubly, and Triply Charged Silicon Ions

Experimental and theoretical results are presented for double, triple, and quadruple photoionization of Si+ and Si2+ ions and for double photoionization of Si3+ ions by a single photon. The experiments employed the photon–ion merged-beams technique at a synchrotron light source. The experimental photon-energy range 1835–1900 eV comprises resonances associated with the excitation of a 1s electron to higher subshells and subsequent autoionization. Energies, widths, and strengths of these resonances are extracted from high-resolution photoionization measurements, and the core-hole lifetime of K-shell ionized neutral silicon is inferred. In addition, theoretical cross sections for photoabsorption and multiple photoionization were obtained from large-scale multiconfiguration Dirac–Hartree–Fock calculations. The present calculations agree with the experiment much better than previously published theoretical results. The importance of an accurate energy calibration of laboratory data is pointed out. The present benchmark results are particularly useful for discriminating between silicon absorption in the gaseous and in the solid component (dust grains) of the interstellar medium.

Theoretical calculation of characteristic radiation: multiconfiguration Dirac–Hartree–Fock calculations in scandium K α and K β

The characteristic x-ray spectra of 3d transition metals are a constant source of advances in atomic physics, x-ray spectrometry, and quantum mechanics. Prior to this work, there was a discrepancy of 0.549 eV between theoretical and experimental results for the scandium Kα 1 peak energy, representing a 55σ discrepancy using the experimental uncertainty. This work improves this to a 0.330 eV discrepancy with only a 4σ error between experiment and theory. Furthermore, we add considerable evidence that asymmetries in x-ray spectra are described by shake events. This work provides ab initio calculations for the diagram and shake-off satellite lines of Sc Kα and Kβ and makes significant improvement on the previous fitting between theory and experiment, from a of 7.35 and 20.85 to 1.60 and 1.45 for Kα and Kβ, respectively. Therefore, we make a strong claim that the asymmetries in scandium x-ray lines exist due to satellite lines with very little room for other hypothesised phenomena to exist, such as Kondo-like interactions and Doniac–Sunjic asymmetries. By fitting to the best experimental data for Sc Kα, β we obtain values for the width and intensity of the satellite lines which enable us to reconstruct the Kα, Kβ profiles.

Multiconfiguration Dirac–Hartree–Fock calculations of energy levels, wavelengths, weighted oscillator strengths, transitions probabilities and lifetimes of Cd XLVII

Abstract Energy levels, wavelengths, weighted oscillator strengths, transition probabilities and lifetimes are calculated for all levels of 1s 2 and 1snl (n = 2–6) configurations of He-like cadmium ion (Cd XLVII). The calculations were carried out using three codes GRASP2018, FAC and AMBiT in order to provide theoretically the most accurate data. Transition probabilities are reported for all the E1, E2, M1 and M2 transitions. Breit interactions and quantum electrodynamics effects are included in the RCI calculations. Comparisons were made with other calculations and a good agreement was found which confirms the reliability of our results. We present some missing data for the He-like cadmium in this paper for the first time.

Benchmarking Multiconfiguration Dirac–Hartree–Fock Calculations for Astrophysics: Si-like Ions from Cr xi to Zn xvii

Abstract The multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction methods are used to provide excitation energies, lifetimes, and radiative transition data for the 604 (699, 702, 704, 704, 704, and 699) lowest levels of the 3s 23p 2, 3s3p 3, 3s 23p3d, 3p 4, 3s3p 23d, 3s 23d 2, 3p 33d, 3s3p3d 2, 3s3d 3, 3p3d 3, 3p 23d 2, 3s 23p4s, 3s 23p4p, 3s 23p4d, 3s 23p4f, 3s3p 24s, 3s3p 24p, 3s3p 24d, 3s3p 24f, 3s 23d4s, 3s 23d4p, 3p 34s, 3p 34p, 3s3p3d4s, 3s 23p5s, and 3s 23p5p configurations in Cr xi, (Mn xii, Fe xiii, Co xiv, Ni xv, Cu xvi, and Zn xvii). Previous line identifications of Fe xiii and Ni xv in the EUV and X-ray wavelength ranges are reviewed by comprehensively comparing the MCDHF theoretical results with available experimental data. Many recent identifications of Fe xiii and Ni xv lines are confirmed, and several new identifications for these two ions are proposed. A consistent atomic data set with spectroscopic accuracy is provided for the lowest hundreds of levels for Si-like ions of iron-group elements of astrophysical interest, for which experimental values are scarce. The uncertainty estimation method suggested by Kramida, applied to the comparison of the length and velocity line strength values, is used for ranking the transition data. The correlation of the latter with the gauge dependency patterns of the line strengths is investigated.

Large-scale Multiconfiguration Dirac–Hartree–Fock Calculations for Astrophysics: n = 4 Levels in P-like Ions from Mn xi to Ni xiv

Using the multiconfiguration Dirac-Hartree-Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the lowest 546 (623, 701, 745) states of the $3p^4 3d$, $3s 3p^2 3d^2$, $3s 3p^3 4p$, $3s 3p^4$, $3s^2 3d^3$, $3s^2 3p^2 3d$, $3s^2 3p^2 4d$, $3s^2 3p^2 4s$, $3p^3 3d^2$, $3p^5$, $3s 3p 3d^3$, $3s 3p^3 3d$, $3s 3p^3 4s$, $3s^2 3p 3d^2$, %$3s^2 3p^2 4f$, $3s^2 3p^2 4p$, $3s^2 3p^3$ configurations in Mn~XI (Fe~XII, Co~XIII, Ni~XIV) is provided. The comparison between calculated excitation energies for the $n=4$ states and available experimental values for Fe XII indicate that the calculations are highly accurate, with uncertainties of only a few hundred cm$^{-1}$. Lines from these states are prominent in the soft X-rays. With the present calculations, several recent new identifications are confirmed. Other identifications involving $3p^2 4d$ levels in Fe~XII that were found questionable are discussed and a few new assignments are recommended. As some $n=4$ states of the other ions also show large discrepancies between experimental and calculated energies, we reassess their identification. The present study provides highly accurate atomic data for the $n=4$ states of P-like ions of astrophysical interest, for which experimental data are scarce.

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.

The structure and radiative lifetimes of negative ions homologous to N−

Negative ions homologous to N− are interesting systems, since there are several bound terms within the ground configuration. The forbidden transitions between them, often dominated by the magnetic dipole contributions, are affected by term mixing—a relativistic effect. When increasing the nuclear charge in the homologous sequence of negative ions, this effect increases. In this paper we use systematic multiconfiguration Dirac–Hartree–Fock calculations to study these effects and predict affinities, level splittings and transition rates between bound states of N−, P−, As−, Sb− and Bi−. By monitoring the line strengths we are able to predict the deviation from the non-relativistic LS-coupled values for transitions between levels of the lowest 3P term. For Sb− the 1D term is also bound, and the prediction for the rates of its transition to the 3P-levels is a challenge for theory. For Bi− less is known experimentally and we analyze its structure and the relativistic contributions to it.

Radiative Transition Parameters in Atomic Lanthanum from Pseudo-Relativistic Hartree–Fock and Fully Relativistic Dirac–Hartree–Fock Calculations

Calculated radiative transition probabilities and oscillator strengths are reported for 392 lines of neutral lanthanum (La I) atom in the spectral range from the near ultraviolet to the mid infrared. They were obtained using two different theoretical methods based on the pseudo-relativistic Hartree–Fock (HFR) and the fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) approaches, both including the most important intravalence and core-valence electron correlations. The quality of these radiative parameters was assessed through detailed comparisons between the results obtained using different physical models and between our theoretical results and the experimental data, where available. Of the total number of La I lines listed in the present work, about 60% have gf- and gA-values determined for the first time.

Benchmarking Atomic Data from Large-scale Multiconfiguration Dirac–Hartree–Fock Calculations for Astrophysics: S-like Ions from Cr ix to Cu xiv

Abstract We present a consistent set of calculated energies and E1, M1, E2, M2 radiative transition data for the main n = 3 levels from the 3s 23p 4, 3p 6, , , , , and configurations for S-like ions from Cr ix to Cu xiv. The fully relativistic multiconfiguration Dirac–Hartree–Fock method implemented in the GRASP2K code is used to perform the present calculations. The excitation energies of the lowest 47 levels from the , , and configurations, producing the strongest lines, are found to be in good agreement, reaching spectroscopic accuracy, with the latest experimental values for Fe xi evaluated by Del Zanna. Our energies can reliably be used to identify in astrophysical and laboratory spectra the levels in other S-like ions, which are mostly unknown. On the contrary, significant discrepancies with the 3s3p 43d levels were found, emphasizing the need for more detailed experimental studies. A few new tentative identifications are suggested. The benchmarks we present indicate that our consistent set of radiative data is accurate and can be used for spectral line modeling.

Energy Levels, Transition Rates and Electron Impact Excitation Rates for the B-like Isoelectronic Sequence with Z = 24–30

Abstract We report calculations of spectroscopic accuracy for 513 states in the B-like ions with Z = 24–30. The energy levels and transition rates are calculated using the second-order many-body perturbation theory, while multiconfiguration Dirac–Hartree–Fock calculations are performed to support the former results. The present two sets of results agree excellently with each other, and can be used as benchmarks in the future. The electron-impact excitation (EIE) collision strengths are calculated based on independent processes and isolated resonances approximation using the distorted wave method. Based on the present atomic data, the spectral lines of these ions are simulated using a collisional radiative model. The amount of energy, transition data, and EIE collision strengths of high accuracy are significantly increased for several B-like ions of astrophysical interest, where experimental data are still very scarce. The results can be used in line identification, plasma modeling, and diagnostics of astrophysical plasmas.

Multiconfiguration Dirac–Hartree–Fock calculations of energy levels and radiative rates of Fe VII

Detailed calculations arc performed for 134 fine-structure levels of the 3p(6)3d(2), 3p(6)3d4s, 3p(5)3d(3) and 3p(6)3d4p configurations in Fe ViT using the multiconfiguration Dirac-Hartree-Fock (MC ...

High-accuracy multi-configuration Dirac–Hartree–Fock calculations of the energy levels and transition properties of Ga-like to Br-like gadolinium ions

Theoretical calculations of Ga-like to Br-like gadolinium ions were performed by using the fully relativistic multi-configuration Dirac–Hartree–Fock (MCDHF) method. Extensive lists of excitation energies, wavelengths, line and oscillator strengths, and E1, M1, E2, M2, and E3 transition rates are presented. The effects of core–valence electron correlation from the deep subshells 3d and 3p are investigated and the accuracy of the results is confirmed by comparing with available theoretical and experimental data sets.

Lifetimes and oscillator strengths for ultraviolet transitions in singly-ionized germanium

The results of lifetime measurements using beam-foil techniques for the levels in Ge ii are presented. The corresponding oscillator strengths for transitions at 1237.1, 1264.7 and 1261.9 Å are derived and reported. These levels, as well as the levels, are studied with multi-configuration Dirac–Hartree–Fock calculations using a development version of the GRASP2K package. The resulting energy levels from our calculations are reported in this paper. These calculations aid and extend the laboratory results. Our experimental and theoretical results are compared with other available studies.

The KLM + KLN Auger electron spectrum of rubidium in different matrices

The KLM + KLN Auger electron spectrum of rubidium (Z = 37) emitted in the electron capture decay of radioactive 83Sr in a polycrystalline platinum matrix and also 85Sr in polycrystalline platinum and carbon matrices as well as in an evaporated layer onto a carbon backing were experimentally studied in detail for the first time using a combined electrostatic electron spectrometer. Energies, relative intensities, and natural widths of fifteen basic spectrum components were determined and compared with both theoretical predictions and experimental data for krypton (Z = 36). Relative spectrum line energies obtained from the semi-empirical calculations in intermediate coupling scheme were found to agree within 3σ with the measured values while disagreement with experiment exceeding 3σ was often observed for values obtained from our multiconfiguration Dirac–Hartree–Fock calculations. The absolute energy of the dominant spectrum component given by the semi-empirical approach agrees within 1σ with the measured value. Shifts of +(0.2 ± 0.2) and −(1.9 ± 0.2) eV were measured for the dominant KLM spectrum components between the 85Sr sources prepared by vacuum evaporation on and implanted into the carbon foil, respectively, relative to 85Sr implanted into the platinum foil. A value of (713 ± 2) eV was determined for the energy difference of the dominant components of the KLM + KLN Auger electron spectra of rubidium and krypton generated in the polycrystalline platinum matrix. From the detailed analysis of the measured data and available theoretical results, the general conclusion can be drawn that the proper description of the KLM + KLN Auger electron spectrum for Z around 37 should still be based on the intermediate coupling of angular momenta taking into account relativistic effects.

Multi-configuration Dirac–Hartree–Fock calculations of forbidden transitions within the [formula omitted] ground configurations of highly charged ions ([formula omitted

Extensive self-consistent multi-configuration Dirac–Hartree–Fock (MCDHF) calculations are performed for the 3s23p63dk (k=1–9) ground configurations of highly charged ions (Z=72–83). Complete and consistent datasets of excitation energies, wavelengths, line strengths, oscillator strengths, and magnetic dipole (M1) and electric quadrupole (E2) transition rates among all these levels are given. We have compared our results with the results available in the literature and the accuracy of the data is assessed. We predict new energy levels and transition probabilities where no other experimental or theoretical results are available, which will form the basis for future experimental work.

Resolving a discrepancy between experimental and theoretical lifetimes in atomic negative ions

A recent measurement of the lifetime of the excited 3p5 state in the S− negative ion, which is dominated by a forbidden magnetic dipole transition to the ground state, reveals a discrepancy with earlier theoretical predictions. To investigate this we have performed systematic and large-scale multiconfiguration Dirac–Hartree–Fock calculations for this system. After including a careful treatment of correlation and relativistic effects, we predict a well-converged value for this lifetime, with an uncertainty considerably less than 1%, thereby removing the apparent conflict between theory and experiment. We also show that this result corresponds to the non-relativistic limit in the LS coupling approximation for the magnetic dipole transition within this 2P term. In addition we demonstrate the usefulness of the latter approach for 2P transitions in O−, Se− and Te−, as well as for analogous M1 transitions within 2D terms in Ni− and Pt− ions.

EXTENDED CALCULATIONS WITH SPECTROSCOPIC ACCURACY: ENERGY LEVELS AND TRANSITION PROPERTIES FOR THE FLUORINE-LIKE ISOELECTRONIC SEQUENCE WITH Z = 24–30

ABSTRACT We have performed extensive multiconfiguration Dirac–Hartree–Fock calculations and second-order many-body perturbation calculations for F-like ions with Z = 24–30. Energy levels and transition rates for electric dipole (E1), electric-quadrupole (E2), electric-octupole (E3), magnetic dipole (M1), and magnetic-quadrupole (M2) transitions, as well as radiative lifetimes, are provided for the lowest 200 levels belonging to the , , , , , and configurations of each ion. The results from the two sets of calculations are in excellent agreement. Extensive comparisons are also made with other theoretical results and observed data from the CHIANTI and NIST databases. The present energies and wavelengths are believed to be accurate enough to aid line identifications involving the n = 3 and n = 4 configurations, for which observations are largely missing. The calculated wavelengths and transition data will be useful in the modeling and diagnostics of astrophysical and fusion plasmas.