Relativistic Configuration Interaction Calculations 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.

Relativistic configuration-interaction calculations on K α X-ray satellites of medium-charge Be-like ions

This study puts forward a calculation of the transitions of 1s2s22p 1P1−1s22s2 1S0 and 1s2s22p 3P1−1s22s2 1S0 for Be-like ions (Z = 6–30) using the multiconfiguration Dirac-Hartree–Fock (MCDHF) and relativistic configuration interaction methods. The computational results include transition wavelengths, transition probabilities, line strengths, and weighted oscillator strengths. The calculations also consider the contributions of the Breit interaction and quantum electrodynamics corrections (QED) to these levels. The results show that the contribution of the Breit interaction, self-energy, and vacuum polarization increase rapidly with increasing nuclear charge for certain configurations. The present calculated values are in good agreement with previous theoretical and experimental results, with errors better than 0.3%. A V/A L comparisons demonstrate the reliability of the data.

Benchmarking calculations of level energies, transition parameters and electron impact excitation cross sections of S-like Xe38+

Atomic structure parameters for levels corresponding to 2s22p63s23p4, 2s22p63s3p5, 2s22p63s23p23d2, 2s22p63s3p43d and 2s22p63s23p33d configurations of S-like Xe38+ are calculated using the fully relativistic multiconfiguration Dirac-Hatree-Fock (MCDHF) method followed by the subsequent relativistic configuration interaction (RCI) calculations. The parameters evaluated include energies of the lowest 75 levels and E1, M1, E2, and M2 transition parameters among these levels. The effect of the choice of virtual orbitals for generating the wavefunctions is discussed. The accuracy of our line strengths is established through the rigorous calculations of their associated uncertainties using three different methods. Another set of calculations using the many-body perturbation theory (MBPT) to validate the present MCDHF-RCI energies is carried out. Further, the electron impact excitation cross-sections using the relativistic distorted wave (RDW) theory are determined for all transitions from the ground and metastable states in the incident electron energy range from the excitation threshold to 10 keV. For plasma physics applications, the fitting parameters for these cross sections employing two distinct equations tailored for low and high-energy regimes are reported. Moreover, the rate coefficients are determined in the electron temperatures range of 15 eV to 100 eV by taking into account the Maxwellian electron energy distribution function and our computed cross-sections. In addition to addressing the atomic data gap in highly charged Xe ions, the present results are of good accuracy and can serve as benchmark tests for other theoretical evaluations. Moreover, they can also assist in line identification of the complex spectra of highly charged sulphur-like xenon ions.

Measuring the nuclear magnetic quadrupole moment of optically trapped ytterbium atoms in the metastable state

We propose a scheme to measure a nuclear magnetic quadrupole moment (MQM), a CP -violating electromagnetic moment that appears in the nuclear sector, using the long-lived 3P2 metastable state in neutral 173Yb atoms. Laser-cooling and trapping techniques enable us to prepare ultracold 173Yb atoms in the 3P2 state trapped in an optical lattice or an optical tweezer array, providing an ideal experimental platform with long spin coherence time. In addition, our relativistic configuration interaction calculation for the 3P2 electronic wavefunction reveals a large magnetic field gradient generated by the atomic electrons in this state, which amplifies the measurable effect of an MQM. Our scheme could lead to an improvement of more than one order of magnitude in MQM sensitivity compared to the best previous measurement (Murthy et al 1989 Phys. Rev. Lett. 63, 965).

Large-scale RCI calculation of energy levels in W9+

The Flexible Atomic Code (FAC) is developed to extend the computational scale based on the Relativistic Configuration Interaction (RCI) in the theoretical study of W9+ atomic structure. The results of the lowest 144 energy levels are consistent with the GRASP calculations, with a mean deviation of 2.11 %. The reference configuration selections for central potential optimization in the RCI calculations at different computational scales are studied. The contributions of the inner core 4d to the energy levels of the RCI calculations are also investigated. The mean deviation of the theoretical wavelengths of five M1 transitions of W9+ from the experimental results is within 0.86 %. This work demonstrates the feasibility of improving the accuracy of RCI calculations of complex atomic systems through large-scale computation based on FAC, which is helpful for experimental spectral line identifications and spectrum synthesis in many fields of plasma spectroscopy.

Calculations of energy levels, radiative transition parameters, hyperfine structure constants [formula omitted] - [formula omitted], Landé [formula omitted] factors and isotope shifts for Sc XX using the MCDF-RCI method

Large scale calculations for the energy levels, transition rates, oscillator strengths, lifetimes, hyperfine interaction constants, Landé gJ factors, and isotope shift factors have been performed for 1s2 and 1snl(n=2−8andl≤n−1) levels of He-like Sc XX ion. The general-purpose relativistic atomic structure package (GRASP2018) based on the fully relativistic multiconfiguration Dirac–Fock (MCDF) method is used to carry out the calculations. The leading quantum electrodynamic corrections, Breit interaction and nuclear recoil effects are also included in the succeeding relativistic configuration interaction (RCI) calculations. The relativistic isotope shift (RIS4) programme is used to determine the mass and field shifts factors. Furthermore, the percentage uncertainty in the transition parameters and lifetimes is estimated. A detailed comparison of the present results with the corresponding values from the NIST database and other theoretical and experimental works, wherever available, has been done, and an excellent agreement is achieved. A large section of the results is reported for the first time in the present work.

Performance Tests and Improvements on the rmcdhf and rci Programs of GRASP

The latest published version of GRASP (General-purpose Relativistic Atomic Structure Package), i.e., GRASP2018, retains a few suboptimal subroutines/algorithms, which reflect the limited memory and file storage of computers available in the 1980s. Here we show how the efficiency of the relativistic self-consistent-field (SCF) procedure of the multiconfiguration-Dirac–Hartree–Fock (MCDHF) method and the relativistic configuration-interaction (RCI) calculations can be improved significantly. Compared with the original GRASP codes, the present modified version reduces the CPU times by factors of a few tens or more. The MPI performances for all the original and modified codes are carefully analyzed. Except for diagonalization, all computational processes show good MPI scaling.

Theoretical studies of bound configuration levels and their radiative lifetimes in Pd− and Pt−

We performed multiconfiguration Dirac-Hartree-Fock and relativistic configuration-interaction calculations for states of the $4{d}^{9}5{s}^{2}$ and $4{d}^{10}5s$ configurations in ${\mathrm{Pd}}^{\ensuremath{-}}$ and for states of the $5{d}^{9}6{s}^{2}$ and $5{d}^{10}6s$ configurations in ${\mathrm{Pt}}^{\ensuremath{-}}$. Valence-valence, core-valence, and core-core electron correlation effects are accounted for in the present studies. The calculated excited energy levels agree within 2.5% with the available experimental values for both ${\mathrm{Pd}}^{\ensuremath{-}}$ and ${\mathrm{Pt}}^{\ensuremath{-}}$ and we confirm that ${\mathrm{Pd}}^{\ensuremath{-}}$ only has one bound excited state. We report a more precise value for the radiative lifetime of $5{d}^{9}6{s}^{2}{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{3/2}$ in ${\mathrm{Pt}}^{\ensuremath{-}}$ ($67.0\ifmmode\pm\else\textpm\fi{}0.3$ ms), which agrees within the experimental range (50--200 ms), but the radiative lifetime of $5{d}^{10}6s{\phantom{\rule{4pt}{0ex}}}^{2}{S}_{1/2}$ ($4.00\ifmmode\pm\else\textpm\fi{}0.16$ s) in ${\mathrm{Pt}}^{\ensuremath{-}}$ is 50% longer than the experimental measurement ($2.54\ifmmode\pm\else\textpm\fi{}0.10$ s). The radiative lifetimes for $4{d}^{9}5{s}^{2}{\phantom{\rule{4pt}{0ex}}}^{2}{D}_{3/2,5/2}$ in ${\mathrm{Pd}}^{\ensuremath{-}}$ are also discussed in detail.

Extended Calculations of Atomic Structure Parameters for Na-like Ar, Kr and Xe Ions Using Relativistic MCDHF and MBPT Methods

In this study, comprehensive calculations of energies, hyperfine structure constants, Landé gJ factors and isotope shifts have been performed for the lowest 71 states of Na-like Ar7+, Kr25+ and Xe43+ ions. Radiative parameters viz., wavelengths, transition rates, oscillator strengths and lifetimes are estimated for the electric dipole E1 transitions among these levels. The states under consideration include 1s22s22p6nl for n = 3–9, l = 0–6, and the fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) method integrated in the latest version of the general-purpose relativistic atomic structure package (GRASP2018) is used for the calculations. The additional corrections, such as the Breit interaction and quantum electrodynamics effects are included in the relativistic configuration interaction calculations, and their effects on energies and other parameters are analysed. We examined the impact of including the core–core and core–valence correlations on level energies. Furthermore, to inspect the reliability of our MCDHF results, we performed another set of calculations using the many-body perturbation theory built into the Flexible Atomic Code (FAC). Moreover, we estimated the uncertainties in the computed lifetimes and transition parameters and assigned their accuracy class. A thorough comparison between the two obtained calculations and with the previous theoretical and experimental results, wherever available, is carried out and a good agreement is observed.

Extended relativistic multiconfiguration calculations of energy levels and transition properties in singly ionized tin

Multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) calculations are performed for 22 states in singly ionized tin (Sn II) belonging to the 5s2ns(n=6,7), 5s2nd(n=5,6), 5s5p2 even parity configurations and the 5s2np(n=5,6,7), 5s24f odd parity configurations. Valence-valence and core-valence correlation effects are taken into account through configuration state function (CSF) expansions. Complete and consistent data sets of level energies, wavelengths, oscillator strengths, lifetimes and transition rates among all these states are given. The results are compared with existing theoretical and experimental results. There is an excellent agreement for calculated excitation energies with experimental data from the NIST database. Lifetimes and transition rates are also in agreement with the results from previous calculations and available measurements for most of the transitions.

Reducing the computational load – atomic multiconfiguration calculations based on configuration state function generators

In configuration interaction (CI) calculations the atomic wave functions are given as expansions over configuration state functions (CSFs) built on relativistic one-electron orbitals. The expansion coefficients of the configuration state functions are obtained by constructing and diagonalizing the Hamiltonian matrix. Here we show how a regrouping of the configuration state functions and the introduction of configuration state function generators (CSFGs) allow for a substantial reduction of the computational load in relativistic CI calculations. The computational methodology based on configuration state function generators, recently implemented in the General Relativistic Atomic Structure package (Grasp2018, Froese Fischer et al. (2019) [16]), is applied to a number of atomic systems and correlation models with increasing sets of one-electron orbitals. We demonstrate a reduction of the CPU time with factors between 10 and 14 for the largest CI calculations. The inclusion of the Breit interaction into the calculations is time consuming. By applying restrictions on the Breit integrals we show that it is possible to further reduce the CPU times with factors between 2 and 3, with negligible changes to the computed excitation energies. We also demonstrate that the introduction of configuration state function generators allows for efficient a priori condensation techniques, with reductions of the expansions sizes with factors between 1.5 and 2.5 and the CPU time with factors between 2.5 and 4.5, again with negligible changes to the excitation energies. In total we demonstrate reductions of the CPU time with factors up to 68 for CI calculations based on configuration state function generators, restrictions on the Breit integrals and with a priori condensed expansions compared to ordinary CI calculations without restrictions on the Breit integrals and with full expansions. Further perspectives of the new methodology based on configuration state function generators are given.

Wavelengths, transition rates, weight oscillator strengths and line strengths for He-like to Ne-like cobalt ions

The multi-configuration Dirac–Hartree–Fock (MCDHF) and Relativistic Configuration Interaction (RCI) methods have been used to calculate the wavelengths, transition rates, absorption oscillator strengths, and line strengths for the 2s-3p, 2p-3s, and 2p-3d electric dipole (E1) transitions in He-like to Ne-like cobalt ions. Breit interaction and quantum-electrodynamical (QED) contributions were estimated in extensive RCI calculations. The results are in good agreement with previous experimental and theoretical results. Our calculated wavelengths differ from wavelengths reported in other work mostly by less than 0.78%, with two exceptions, where our results differ by 1.63% and 1.91%, showing good overall confirmation of the accuracy of our results. Most importantly, we have predicted some theoretical data that, will be helpful in some plasma experiments.

Ab initio calculations of the hyperfine structure of 109Cd, 109Cd+ and reevaluation of the nuclear quadrupole moment Q(109Cd)

Large scale ab initio calculations of the electric contribution (i.e. the electric field gradient (EFG)) to the electric quadrupole hyperfine interaction constants B for the state of 109Cd+ ion and the states of neutral 109Cd atom were performed. To probe the sensitivity of B to different electron correlation effects, six sets of variational multi-configuration Dirac–Hartree–Fock and relativistic configuration interaction calculations employing different strategies were carried out. The calculated EFGs, together with experimental values of B, allow us to extract a new value of the nuclear electric quadrupole moment Q(109Cd) = 0.634(22) b which is about 5% larger than the recommended value (Stone 2016 At. Data Nucl. Data Tables 111–112 1; Pyykkö 2018 Mol. Phys. 116 1328). Efforts were made to provide a realistic theoretical uncertainty for the final Q value based on statistical principles and correlation with the magnetic dipole hyperfine interaction constant A.

Multiconfiguration Dirac–Hartree–Fock and Relativistic Many Body Perturbation Theory calculations of energy levels, wavelengths, weighted oscillator strengths, transitions rates, lifetimes, isotope shifts, hyperfine interaction constants and Landé g-factors of Zr XXXIX

An extensive and accurate data set of energy levels, wavelengths, weighted oscillator strengths, transitions rates, lifetimes, isotope shifts, hyperfine interaction constants and Landé g-factors have been calculated for the lowest 71 odd and even parity states arising from the 1s2 and 1snl(n=1−6,0≤l≤n−1) configurations of helium-like Zr. Calculations were performed using the Multiconfigurational Dirac–Hartree–Fock​ (MCDHF) followed by the Relativistic Configuration Interaction (RCI) method. Although no measurements or other theoretical results are available for comparison, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the Relativistic Many-Body Perturbation Theory (RMBPT) method. Transition rates for electric-multipole (dipole (E1), quadrupole (E2)) and magnetic-multipole (dipole (M1), quadrupole (M2)) have been also calculated. Breit interactions and quantum electrodynamics effects (QED) have been included as perturbations in extensive relativistic configuration interaction (RCI) calculations. The results arising from the two sets of calculations MCDHF/RCI and RMBPT are quite close. Almost all atomic data of helium-like Zr ion presented in this paper are calculated for the first time. We expect that our results can be used as a reference point for any further calculations of plasma processes (electron impact excitation, dielectronic recombination). Furthermore, our values can contribute to the NIST database by essentially providing the data for the lowest singly excited states of Zr XXXIX.

Energy levels and transition properties for As-like ions Se II, Br III, Kr IV, Rb V, and Sr VI

In this theoretical study, we aim to investigate atomic properties of As-like ions: Se II, Br III, Kr IV, Rb V, and Sr VI. The multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods, which are implemented in the general-purpose relativistic atomic structure package GRASP2018, are used in the present work. In the RCI calculations the transverse-photon (Breit) interaction, the vacuum polarization, and the self-energy corrections are included. By employing MCDHF method, we computed the lowest energy levels of the 4s4p4, 4s24p2{4d,5d,5s,6s} even and of the 4s24p3, 4s24p2{5p,6p,4f}, 4s4p34d odd configurations. Accuracy of energy levels is​ evaluated by comparing it with the National Institute of Standards and Technology Atomic Spectra Database (NIST ASD or database) recommended values and with experimental and theoretical methods. We obtain the average accuracy in the energy level compared with the NIST database: 0.6%, 1.7%, 0.4%, 0.9% and 0.7% for Se II, Br III, Kr IV, Rb V, and Sr VI, respectively. We calculated properties of electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2) type transitions and investigated its accuracy. We evaluated the accuracy of data, using combination of new methodology, presented in recent works. Majority (77%, 93%, 95%, 97%, and 97% for Se II–Sr VI) of our computed transition properties belongs to D or better accuracy class.

Electron Impact Excitation of Ge-like Te20+–Cd16+ Ions

We study electron impact excitation of dipole allowed transitions in the extreme ultraviolet range—8–55 nm—for the germanium isoelectronic sequence Te20+–Cd16+. The fine structure transitions between the ground state having configuration 4s24p2 and the excited states with configurations 4s4p3 and 4s24p4d are considered for these ions. We employ the relativistic distorted wave method to calculate the excitation cross sections in the incident electron energy range from the excitation threshold to 5000 eV. To obtain the required ionic bound state wavefunctions we have used the multi-configuration Dirac-Fock method with correlations within the n = 5 complexes as well as performed relativistic configuration interaction calculations to include the quantum electrodynamic effects. The accuracy of these wavefunctions is established by comparing our calculated wavelengths and oscillator strengths of the considered transitions with the previously reported measurements and other available theoretical results. We also provide the fitting parameters of the calculated cross sections and the excitation rate coefficients for their direct applications in plasma modeling.

Configuration-interaction calculations on the 3s23pn configuration of neutral phosphorus and two of its ions

We perform valence, core-core, and core-valence nonrelativistic configuration-interaction (CI) calculations on the states belonging to the $3{s}^{2}3{p}^{n}$ configuration with $n=2$, 3, and 4, for ${\mathrm{P}}^{+}(^{3}P,^{1}D, ^{1}S$), $\mathrm{P}{(}^{4}{S}^{\ensuremath{\circ}},^{2}D^{\ensuremath{\circ}}, ^{2}P^{\ensuremath{\circ}}$), and ${\mathrm{P}}^{\ensuremath{-}}(^{3}P,^{1}D, ^{1}S$) species, respectively. Excitation energies, ionization potential, and electron affinities related to these states were calculated using orbital basis sets up to $\ensuremath{\ell}=12$ and corrected with relativistic contributions. We also carry out relativistic CI calculations for the fine structure splitting of the sublevels ${}^{3}{P}_{0,1,2}$ and ${}^{3}{P}_{2,1,0}$ in ${\mathrm{P}}^{+}$ and ${\mathrm{P}}^{\ensuremath{-}}$, respectively, and both ${}^{2}{D}_{3/2,5/2}^{\ensuremath{\circ}}$ and ${}^{2}{P}_{1/2,3/2}^{\ensuremath{\circ}}$ in P, using orbital basis sets up to $\ensuremath{\ell}=3$. Systematic studies on the convergence of both nonrelativistic and relativistic CI calculations for each electronic state show the energy contributions corresponding to each CI excitation level. Our results for the excitation energies, ionization potential, and electron affinity of the ${(3{s}^{2}3{p}^{3})}^{4}{S}^{\ensuremath{\circ}}$ ground state, as well as fine structure splittings, are in very good agreement with the experiment and give reliability to the predicted electron affinities of the ${(3{s}^{2}3{p}^{3})}^{2}{D}^{\ensuremath{\circ}}$ and $^{2}P^{\ensuremath{\circ}}$ excited states of 1135(1) meV and 1040(1) meV, respectively.

Rovibronic spectrum of PbS in 19520–22900 cm−1

The rovibronic spectrum of PbS in the range of 19520−22900 cm−1 are investigated using the laser ablation-laser induced fluorescence method. The spectra in this range are assigned as the transitions of A-X and B-X according to the spectral analyzation. The upper electronic state of the transition in the range of 19520−22900 cm−1 is analyzed and discussed, and it is concluded that the upper state, A, is a mixture of 3Π0+ and 3Σ0+− states, the 3Π0+ state is in domination. The spectrum in the range of 22025−22900 cm−1 is assigned as the B3Π1−X1Σ+ transition. The molecular constants of these two transitions are derived from the observed spectra. The Frank-Condon factors (FCFs) of these two transitions are also calculated using the RKR/LEVEL method. All the results are compared with the reported theoretical and experimental results, showing that the A state is a mixing state which is in consistent with Balasubramanian's relativistic configuration interaction calculation result. And our calculated FCFs are in agreement with our recorded spectra.

Energy levels and transition data of 3p63d8 and 3p53d9 configurations in Fe-like ions (Z = 57,60,62,64,65)

Atomic data of highly charged ions (HCIs) offer an attractive means for plasma diagnostic and stars identification, and the investigations on atomic data are highly desirable. Herein, based on the fully relativistic multi-configuration Dirac–Hartree–Fock (MCDHF) method, we have performed calculations of the fine-structure energy levels, wavelengths, transition rates, oscillator strengths, and line strengths for the lowest 21 states of 3p63d8–3p53d9 electric dipole (E1) transitions configurations in Fe-like ions (Z = 57, 60, 62, 64, 65). The correlation effects of valence–valence (VV) and core–valence (CV) electrons were systematically considered. In addition, we have taken into account transverse-photon (Breit) interaction and quantum electrodynamics (QED) corrections to treat accurately the atomic state wave functions in the final relativistic configuration interaction (RCI) calculations. Our calculated energy levels and transition wavelengths are in excellent agreement with the available experimental and theoretical results. Most importantly, we predicted some new transition parameters that have not yet been reported. These data would further provide critical insights into better analyzing the physical processes of various astrophysical plasmas.

Ab initio multiconfiguration Dirac-Hartree-Fock calculations of the In and Tl electron affinities and their isotope shifts

We report multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction calculations on the Thallium (Tl) electron affinity, as well as on the excited energy levels arising from the ground configuration of Tl$^-$. The results are compared with the available experimental values and further validated by extending the study to its homologous, lighter element, Indium (In), belonging to Group 13 (III.A) of the periodic table. The calculated electron affinities of In and Tl, 383.4 and 322.8 meV, agree with the latest measurements by within 1\%. Three bound states $^3P_{0,1,2}$ are confirmed in the $5s^25p^2$ configuration of In$^-$ while only the ground state $^3P_{0}$ is bound in the $6s^26p^2$ configuration of Tl$^-$. The isotope shifts on the In and Tl electron affinities are also estimated. The E2/M1 intraconfiguration radiative transition rates within $5s^25p^2 \; ^3P_{0,1,2}$ of In$^-$ are used to calculate the radiative lifetimes of the metastable $^3P_{1,2}$ levels.