Multiconfiguration Dirac Hartree Fock Research Articles

Extended calculations of energy levels, radiative properties, and lifetimes for P-like Ge XVIII

Using the multiconfiguration Dirac-Hartree-Fock (MCDHF) and the relativistic configuration interaction (RCI) methods, a consistent set of transition energies and radiative transition data for the lowest 150 states of the 3s23p3,3s3p4,3s23p23d,3s3p33d,3p5, and 3s23p3d2 configurations in P-like Ge XVIII is provided. To assess the accuracy of the MCDHF transition energies, we have also performed calculations using the many-body perturbation theory (MBPT). Comparisons are made between the present MCDHF and MBPT data sets, as well as with other available experimental and theoretical values. The resulting accurate and consistent MCDHF data set will be useful for line identification and modeling purposes. These data can be considered as a benchmark for other calculations.

The fully relativistic multi-configuration Dirac–Hartree–Fock method for atomic structure calculations for multiply charged ions: the example of Ca XV

In this work, fully relativistic multi-configuration Dirac–Hartree–Fock approach for calculating atomic structure parameters has been presented and compared to other approaches such as Hartree–Fock pseudo-Relativistic (HFR) method. As an example of application, results of fully relativistic calculations for the ion Ca XV have been obtained and compared to Hartree–Fock pseudo-relativistic calculations and to NIST database values.This example is important for plasma diagnostic and astrophysical studies because Ca XV atomic data of high accuracy are still very scarce.

Crystal field module for the general relativistic atomic structure package

The latest version of the grasp2018 package [Froese Fischer et al. (2019)], based on the multiconfigurational Dirac–Hartree–Fock method, is extended to account for effects of crystal fields in complex systems. Instead of using the simplified treatment of the crystal field effects based on the Stevens’ operator-equivalent method the program uses the fully ab-initio method in which the external ions are treated as point charges at fixed positions. In addition, examples of how to use the CF_Hamiltonian program are given in source directory grasp2018/src/appl/CF_Hamiltonian/Sample_Runs. Program summaryProgram Title:CF_HamiltonianCPC Library link to program files:https://doi.org/10.17632/fksxwwjbx6.1Licensing provisions: MIT licenseProgramming language: Fortran 95.External routines/libraries used:Grasp2018 modules: Libmod, Lib9290, Librang90; Grasp2018 routines: starttime, setdbg, getmixblock, getmixa, getmixc, setmc, factt, setcon, setcsla, stoptime; and Lapack library.Nature of problem: The CF_Hamiltonian program is designed as a part of the Grasp2018 package for the computation of Stark splitting in crystal field in the point charge crystal field approximation.Solution method: The point charge crystal field approach is used. It allows user to include different Atomic State Functions (ASF) mixing such as ASF mix with the same total J values, ASF mixing with different total J values, ASF mixing with different parities.Additional comments including restrictions and unusual features: The restrictions of the program are coming from the restrictions of Grasp2018 package and it is suitable for systems for which the point charge crystal field approximation is appropriate. The Stark level splitting of the atomic energy terms in the point-charge crystal field approach is performed by the program CF_Hamiltonian.

Multiconfiguration Dirac–Hartree–Fock radiative parameters for emission lines in Ce ii–ivions and cerium opacity calculations for kilonovae

ABSTRACTLarge-scale calculations of atomic structures and radiative properties have been carried out for singly, doubly, and trebly ionized cerium. For this purpose, the purely relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) method was used, taking into account the effects of valence–valence and core–valence electronic correlations in detail. The results obtained were then used to calculate the expansion opacities characterizing the kilonovae observed as a result of neutron star mergers. Comparisons with previously published experimental and theoretical studies have shown that the results presented in this work are the most complete currently available, in terms of quantity and quality, concerning the atomic data and monochromatic opacities for Ce ii, Ce iii, and Ce iv ions.

Theoretical study on radii of neutral atoms and singly charged negative ions

Systematic theoretical calculations of the ground state of atomic radii and singly charged negative ionic radii for elements with 1 ≤ Z ≤ 118 have been performed in a multi-configuration Dirac–Hartree–Fock method including all relativistic effects. Three radii of atoms and singly charged negative ions are computed in this work. They are the radii of the maximum radial charge density of every subshell, the total mean radius and total mean spherical radius based on the total charge density. Results are compared with the radii of the maximum radial charge density calculated by Waber et al. and the experimental ionic radii from Shannon. This work is the first systematic study of singly charged negative ionic radii for all elements in the periodic table (if the corresponding singly charged negative ion exists).

Numerical Procedures for Relativistic Atomic Structure Calculations

Variational methods are used extensively in the calculation of transition rates for numerous lines in a spectrum. In the GRASP code, solutions of the multiconfiguration Dirac–Hartree–Fock (MCDHF) equations that optimize the orbitals are represented by numerical values on a grid using finite differences for integration and differentiation. The numerical accuracy and efficiency of existing procedures are evaluated and some modifications proposed with heavy elements in mind.

Energies and E1, M1, E2, and M2 line strengths for Nb XXXIV

The multiconfiguration Dirac-Hartree-Fock (MCDHF) method is used to calculate energies, lifetimes, wavelengths, transition probabilities, weighted oscillator strengths, and line strengths for electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among the lowest 226 fine-structure levels arising from the 2s22p4, 2s2p5, 2p6, 2s22p33l, 2s2p43l, and 2p53l (l = s, p, d) configurations in O-like Nb XXXIV. The valence and core-valence correlation effects are included in the calculations. The Breit-interaction and the leading quantum electrodynamics contributions are taken into account in the relativistic configuration interaction calculations. The present energies, wavelengths, line strengths, and oscillator strengths are compared with the available experimental and other theoretical results. The accuracy of the present results is estimated using the comparison between the results from the two largest layers in the present MCDHF calculations.

Extended calculations with spectroscopic accuracy: Energy levels and radiative rates for O-like ions between Ar XI and Cr XVII

Using the multiconfiguration Dirac–Hartree–Fock and the relativistic configuration interaction methods, a consistent set of transition energies and radiative transition data for the main states of the 2s22p4, 2s2p5, 2p6, 2s22p33s, 2s22p33p, 2s22p33d, 2s2p43s, 2s2p43p, and 2s2p43d configurations in O-like Ions between Ar XI (Z=18) and Cr XVII (Z=24) is provided. Our data set is compared with the NIST compiled values and previous calculations. The data are accurate enough for identification and deblending of new emission lines from hot astrophysical and laboratory plasmas. The amount of data of high accuracy is significantly increased for the n=3 states of several O-like ions, where experimental data are very scarce.

Isotope shift of the 2s 2S1/2 → 2p 2P1/2,3/2 transitions of Li-like Ca ions* *Project supported by the National Natural Science Foundation of China (Grant No. 11864036) and the Funds for Creative Research Groups of Gansu Province, China (Grant No. 20JR5RA541).

The mass- and field-shift parameters of the two 2s 2S1/2 → 2p 2P1/2,3/2 transitions in the Li-like Ca ions are calculated by using multi-configuration Dirac–Hartree–Fock (MCDHF) and the relativistic configuration interaction (RCI) methods with the inclusion of the transverse photon (Breit) interaction, vacuum polarization and self-energy corrections. In addition, the mass shift and field shift of these two transitions are calculated, where the field shift is calculated by using the evaluated value δ〈 r 2〉 obtained by [Atomic Data and Nuclear Data Tables 99 69 (2013)]. It is found that the mass shift of Li-like Ca ions is greater than the field shift.

Theoretical study of the hyperfine interaction constants, Landé g-factors, and electric quadrupole moments for the low-lying states of the 61Ni q+ (q = 11,12,14, and 15) ions* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11704398 and 11934014), the National Key Research and Development Program of China (Grant No. 2017YFA0304402), and the Strategic Priority Research Program

Highly charged nickel ions have been suggested as candidates for the ultra-precise optical clock, meanwhile the relevant experiment has been carried out. In the framework of the multiconfiguration Dirac–Hartree–Fock (MCDHF) method, we calculated the hyperfine interaction constants, the Landé g-factors, and the electric quadrupole moments for the low-lying states in the 61Ni11+, 61Ni12+, 61Ni14+, and 61Ni15+ ions. These states are clock states of the selected clock transitions in highly charged nickel ions (see Fig. ). Based on discussing the effects of the electron correlations, the Breit interaction, and quantum electrodynamics (QED) effect on these physical quantities, reasonable uncertainties were obtained for our calculated results. In addition, the electric quadrupole frequency shifts and the Zeeman frequency shifts of the clock transitions concerned were analyzed.

Theoretical investigation of oscillator strengths and lifetimes in Ti II

Aims. Accurate atomic data for Ti II are essential for abundance analyses in astronomical objects. The aim of this work is to provide accurate and extensive results of oscillator strengths and lifetimes for Ti II. Methods. The multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction (RCI) methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2018, were used in the present work. In the final RCI calculations, the transverse-photon (Breit) interaction, the vacuum polarisation, and the self-energy corrections were included. Results. Energy levels and transition data were calculated for the 99 lowest states in Ti II. Calculated excitation energies are found to be in good agreement with experimental data from the Atomic Spectra Database of the National Institute of Standards and Technology based on the study by Huldt et al. Lifetimes and transition data, for example, line strengths, weighted oscillator strengths, and transition probabilities for radiative electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) transitions, are given and extensively compared with the results from previous calculations and measurements, when available. The present theoretical results of the oscillator strengths are, overall, in better agreement with values from the experiments than the other theoretical predictions. The computed lifetimes of the odd states are in excellent agreement with the measured lifetimes. Finally, we suggest a relabelling of the 3d2(12D)4p y2 D3/2o and z2 P3/2o levels.

Theoretical level energies, radiative lifetimes and transitions in W IX

The atomic states of the W IX (W8+) tungsten ion lying below the W9+ ionisation threshold have been studied theoretically, employing the multiconfiguration Dirac–Hartree–Fock method with configuration interaction. The level electronic structures and their energies are presented. The electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) radiative transitions have been computed in order to calculate the radiative lifetimes of given states. Transition wavelengths, energies, and decay rates are also presented for selected high-intensity E1 transitions. The configuration interaction method was applied to estimate electron correlation effects. The aim of the present research was to fill a lack of atomic data for low-charged tungsten ions, which may be useful in low-temperature plasma diagnostics and may form the base for collisional–radiative modelling of spectra for low-charged tungsten ions.

Energy levels and spectral lines for Ge-like Zr, Nb, and Tc ions

The energy levels, transition probabilities, oscillator strengths, line strengths, and wavelengths of Ge-like Zr, Nb, and Tc ions have been calculated using the multi-configuration Dirac–Hartree–Fock method. The Breit interactions and quantum electrodynamics correction were taken into account. The calculated values of energy levels and wavelengths have been compared with other theoretical calculations and available experimental values; good agreement is achieved for most of the energy levels and wavelengths calculated. The number of energy levels and wavelengths considered is larger than that of any other theoretical calculations, and the transition probabilities and line strengths are also given where no other theoretical results and experimental values are available.

Energy levels and transition probabilities for transitions in Zr XXXV

Excitation energies, wavelengths, transition probabilities, weighted oscillator strengths, and line strengths for electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions between the states of the 2s22p2, 2s2p3, 2p4, 2s22p3l, 2s2p23l, and 2p33l(l = s, p, d) configurations are calculated using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method for C-like Zr XXXV. The Breit interaction and quantum electrodynamics (QED) contributions are included in the relativistic configuration interaction calculations. The calculated energies, wavelengths, and oscillator strengths are compared with the other theoretical results.

Energy levels, wavelengths, and transition probabilities for transitions in Pd XLII

Energy levels and lifetimes for the lowest 204 fine-structure levels belonging to the 2s22p, 2s2p2, 2p3, 2s23l, 2s2p3l, 2p23l, 2s24l, 2s2p4l, and 2p24l (l = s, p, d, f) configurations of B-like Pd XLII are calculated using the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, as well as wavelengths, transition probabilities, weighted oscillator strengths, and line strengths for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among these levels. In the calculations, the contributions from Breit interaction and quantum electrodynamics (QED) corrections are taken into account. Comparisons are made with available theoretical energies and electric dipole oscillator strengths.

MCDHF/RCI extended calculations of energy levels, radiative properties, [formula omitted], [formula omitted] hyperfine interaction constants, and Landé [formula omitted]-factors for [formula omitted][formula omitted

Energy levels, weighted oscillator strength, transition probabilities, AJ, BJ hyperfine interaction constants, and Landé gJ-factors have been calculated for all levels of 1s2 and 1snl (n=1−7, 0≤l≤n−1) configurations of He-like Argon ion (ArXVII). Multiconfigurational Dirac-Hartree-Fock (MCDHF) method has been adopted for calculating the mentioned parameters. Transition probabilities are reported for all allowed and forbidden transitions (E1, E2, M1 and M2) from the ground level. Breit interactions and quantum electrodynamics effects are estimated in subsequent relativistic configuration interaction calculations (RCI). The present calculations, namely MCDHF/RCI, have been compared with other theoretical results. Our results are in reasonable agreement with the published experimental data and theoretical values. Also, lifetimes for all excited levels were calculated. Most of the data presented here are published for the first time.

A theoretical calculation of atomic parameters for the transitions of Si II

Energy levels, wavelengths, transition probabilities, oscillator strengths and line strengths of transitions between computed levels are reported for Si II by using the multiconfiguration Dirac–Hartree–Fock method. The contributions of Breit interaction and quantum electrodynamics correction are taken into consideration. Comprehensive comparisons are made with available experimental and theoretical values, and the accuracy of the present results is assessed to be better than that of other values, which is much closer to the experimental values. The atomic structure parameters of some higher excited states that have no other theoretical values are also calculated and listed in this paper. We came to the conclusion that the contributions of Breit interaction and quantum electrodynamics correction cannot be ignored for high-precision excitation and transition energy calculations.

Spectral line list of potential cosmochronological interest deduced from new calculations of radiative transition rates in singly ionized thorium (Th ii)

ABSTRACTIn this work, we report a list of 91 strong Th ii spectral lines in the visible wavelength region that could be used as cosmochronometers in future investigations to determine stellar ages from thorium radioactive decay. This list was established on the basis of a pseudo-relativistic Hartree–Fock model including core-polarization corrections (HFR+CPOL) allowing us to compute the corresponding radiative decay parameters, the latter being found to be in good overall agreement with the most accurate experimental data when available. Besides this semi-empirical approach, the fully relativistic ab initio multiconfiguration Dirac–Hartree–Fock (MCDHF) method was attempted, showing large discrepancies with both the present HFR+CPOL and the most recent experimental oscillator strengths, although the calculated wavelengths from theoretical energy levels agreed with observed spectral line wavelengths within 2.4 per cent.

Energy levels, weighted oscillator strengths, transition rates, lifetimes of He-like-Pt deduced from the relativistic multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction theory calculations

We disclose relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) spectrum calculations for He-like-Pt. Energy levels and weighted oscillator strengths are calculated for 127 odd- and even-parity states as well as lifetimes and transition rates between these states. For comparative purpose, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the relativistic configuration interaction (RCI) method. Additionally, the Breit interaction and leading quantum electrodynamics effects (QED) are included as perturbations in extensive RCI calculations. We signal that, our calculations for He-like-Pt are made for the first time and they provide to date the most accurate and complete atomic data related to this ion.

Ionization potentials of the superheavy element livermorium (Z = 116).

Ionization potentials (IPs) of the superheavy element (SHE) livermorium (Lv) and its ions Lvn+ (n = 1, …, 6) are obtained using the multiconfiguration Dirac-Hartree-Fock method. The effects of electron correlation in the subshells {6s, 6p, 6d, 7s, 7p} are taken into account, together with the Breit interaction and quantum electrodynamic (QED) effects. In Lv, the strong relativistic effect causes a large splitting between the energies of the 7p1/2 and 7p3/2 orbitals, which results in a large difference between IP3 and IP2. As a consequence, the behavior of the IPs of Lv differs from that of the lighter oxygen group elements: among the IPn Z (Z = Se, Te, Po, Lv; n = 1, …, 6), IP1,2 Lv are the smallest, whereas IP3,4,5,6 Lv are the second largest among the IP3,4,5,6 Z. This jump in IP can be taken to be a natural characteristic of SHEs because the calculations of the difference between IP3 and IP2 are only weakly affected by electron correlation, the Breit interaction, and QED effects, with only the relativistic effect being significant. We also show that the energies and IPs of neutral Lv and Lv+ are clearly influenced by the electron correlation effect in the subshells {6s, 6p, 6d}. The Breit interaction and QED have an effect on the energies that has an exponential dependence on the atomic number, although they have only a weak influence on the IPs. The analysis of the stabilities of the 2+, 4+, and 6 + states of Lv shows good agreement with predictions from other studies.