Multiconfiguration Dirac Hartree Fock Research Articles

Theoretical energies, transition rates, lifetimes, hyperfine interaction constants and Land[formula omitted] gJ-factors for the Se XXVII spectrum of fusion interest

An extensive set of level energies, wavelengths, line strengths, oscillator strengths, lifetimes, hyperfine structures, Lande´ gJ-factors, electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) radiative transition rates among the lowest 318 states arising from the 2s22p4, 2s2p5, 2p6, 2s22p33l (l = 0, 1, 2), 2s2p43l (l = 0, 1, 2), 2p53l (l = 0, 1, 2), and 2s22p34l (l = 0, 1, 2, 3) configurations has been obtained for Se XXVII. These new data, calculated within the frameworks of the multi-configuration Dirac–Hartree–Fock method and the second-order many-body perturbation theory, fill in the gap existing in the atomic data needed for the diagnostic processes of tokamak plasmas. Using two methods allowed us to make an intercomparison and to estimate the uncertainties on the obtained data. The results arising in the two sets of calculations are quite close, suggesting that there is a high degree of convergence achieved in our work. i.e., our two sets of energies agree to better than 0.02%, and the lifetimes mostly agree to within 2%. Comparison is also made with the limited number of experimental data and previous computations to assess the accuracy of our calculations.

Extended calculations of energies, transition rates, and lifetimes for F-like Kr XXVIII

The excitation energies, lifetimes, wavelengths and E1, E2, M1 and M2 transition rates for the lowest 389 levels of the 2l7, 2l63l′, 2l64l′, and 2l65l′ configurations from second-order many-body perturbation theory (MBPT) calculations, and the results for the lowest 200 states of the 2l7, 2l63l′, and 2l64l′ configurations from multi-configuration Dirac-Hartree-Fock (MCDHF) calculations in F-like Kr XXVIII are presented in this work. The relative differences between our two sets of level energies are mostly within 0.005% for the lowest 200 levels. Comparisons are made with experimental and other available theoretical results to assess the reliability and accuracy of the present calculations. We believe them to be the most complete and accurate results for Kr XXVIII at present.

Hyperfine induced transition probabilities from states in Sm-like ions

The hyperfine induced transition probabilities for highly charged Sm-like ions are calculated within the framework of the multiconfiguration Dirac–Hartree–Fock method. Electron correlation, the Breit interaction and quantum electrodynamical effects are taken into account. For ions ranging from Z = 79 to is the first excited state, and the hyperfine induced transition (HIT) is a dominant decay channel. For the state, the HIT rates of Sm-like ions with are reported as well as the magnetic dipole (M1) , the electric quadrupole (E2) , and the magnetic quadrupole (M2) transition probabilities. It is found that M1 transition from the state is the most important decay channel in this range on .

Multi-configuration Dirac–Hartree–Fock (MCDHF) calculations for Ni XXV

We present accurate 165 fine-structure energy levels related to the configurations 1s22s2, 1s22p2, 1s2nƖn′l′ (n = 2, n′ = 2, 3, 4, 5, Ɩ = s,p Ɩ′ = s, p, d, f, g) of Ni XXV which may be useful ion for astrophysical and fusion plasma. For the calculations of energy levels and radiative rates, we have used the multiconfiguration Dirac-Hartree-Fock (MCDHF) method employed in GRASP2K code. The calculations are carried out in the active space approximation with the inclusion of the Breit interaction, the finite nuclear size effect, and quantum electrodynamic corrections. The transition wavelengths, transition probabilities, line strengths, and absorption oscillator strengths are reported for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), magnetic quadrupole (M2) transitions from the ground state. We have compared our calculated results with available theoretical and experimental data and good agreement is achieved. We predict new energy levels, oscillator strengths, line strengths and transition probabilities, where no other experimental or theoretical results are available. The present complete set of results should be of great help in line identification and the interpretation of spectra, as well as in the modelling and diagnostics of astrophysical and fusion plasmas.

The energy levels and transition properties of In-like ions

The energy levels and transition properties of In-like ions are investigated by using the multi-configuration Dirac–Hartree–Fock method. The results for the energy levels, transition probabilities, wavelengths, line strengths and lifetimes of In-like Cs VII—Pm XIII are reported. Relativistic effects and electron correlation are included. Our calculations agree well with the experimental and other theoretical values. The new data of energy levels and transition parameters are predicted. The level crossing happens between the configurations 5s 24f and 5s 25p with increasing nuclear charge. The transition frequencies are within the range of usual lasers because of the level crossing. In-like ions may be developed into atomic clock.

Theoretical investigation on forbidden transition properties of fine-structure splitting in 2D state for K-like ions with **Project supported by the National Natural Science Foundation of China (Grant Nos. 91436103, 91536102, and 91336211), the Research Programme of National University of Defense Technology, China (Grant No. JC15-0203), and the Strategic Priority Research Programme of the Chinese Academy of Sciences (Grant No. XDB21030300).

Excitation energies, magnetic dipole, and electric quadrupole transition probabilities of the transition in the potassium-like (K-like) sequence with are investigated by using the multi-configuration Dirac–Hartree–Fock (MCDHF) method. The contributions of the electron correlations, Breit interaction, and the leading-order quantum electrodynamic (QED) effects on the transition properties are analyzed. The present results are interested in the laboratory tokamak and the astronomical observations. Furthermore, the feasibility of these ions for the highly charged ion (HCI) clocks is discussed. Considering the wavelength of lasers and manipulation process of the atomic clocks, Cu10+ and Zn11+ are recommended as promising candidates with achievable quality factors at the 1015 level.

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.

Atomic data of intermediate autoionzing Rydberg series nf[K]J (n = 4, 5), nd[K]J (n = 5, 6), np[K]J (n = 6, 7) and ns[K]J (n = 7, 8) of neutral argon atom in the multiconfiguration Dirac-Hartree-Fock framework

We report the results of an accurate computation of the energy levels, oscillator strengths \(f_{ij}\), the radiative transition rates \(A_{ij}\), the Lande g-factor, the magnetic dipole and the electric quadrupole hyperfine constants of the intermediate Rydberg series \(n{\rm f}[K]_{J}\) \( (n = 4, 5)\), \( n{\rm d}[K]_{J}\) \( (n = 5, 6)\), \(n{\rm p}[K]_{J}\) \((n = 6, 7)\) and \(n{\rm s}[K]_{J}\) \((n = 7, 8)\) relative to the ground state 3p6 1S0 for neutral argon atom spectra based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) approach. In this approach, the quantum electrodynamics (QED) effects with transverse photon Breit interaction and vacuum photon polarization self-energy corrections are included. Moreover, the perturbation due to the core-polarization and electron correlation effects are taken into account. We also reported the oscillator strengths and transition rates in Coulomb and Babushkin gauges for the 3p5(2P)3d-3p5(2P)4f, 3p5(2P)3d-3p5(2P)5f, 3p5(2P)4d-3p5(2P)4f, 3p5(2P)4d-3p5(2P)5f, 3p5(2P)5d-3p5(2P)4f, 3p5(2P)5d-3p5(2P)5f, 3p5(2P)6d-3p5(2P)4f and 3p5(2P)6d-3p5(2P)5f transition arrays as well as the 3p5(2P)5d-3p5(2P)6p, 3p5(2P)7s-3p5(2P)6p, 3p5(2P)7s-3p5(2P)7p and 3p5(2P)8s-3p5(2P)7p transition arrays. Insofar as experimental or theoretical values by other authors exist, comparison is made with those values; it turns out that, for most of the levels, a rather satisfying agreement with these experimental and theoretical results is obtained, thus confirming the reliability of our data.

Large-scale calculations of atomic level and transition properties in the aluminum isoelectronic sequence from Ti X through Kr XXIV, Xe XLII, and W LXII

Large-scale self-consistent multiconfiguration Dirac–Hartree–Fock subsequent relativistic configuration interaction (RCI) calculations are reported for 360 states belonging to the 30 configurations 3s2{3l,4l,5l}, 3p2{3d,4l}, 3s{3p2,3d2}, 3s{3p3d,3p4l,3p5s,3d4l′}, 3p3d2, 3p3 and 3d3 with l=0,1,…,n−1 and l′=0,1,2 in 17 systems of the aluminum-like isoelectronic sequence: Ti X through Kr XXIV, Xe XLII, and W LXII. Effects from electron correlation are taken into account by means of large expansions in terms of a basis of configuration state functions (CSF) and calculated energy levels are compared with existing theoretical calculations and the NIST Atomic Spectra database. Radiative E1, E2, M1 and M2 transition rates and associated lifetimes of energy levels are presented in online tables. The uncertainties of the calculated energies are very small, on average between 0.02% and 0.05%, which aid new line identifications in laboratory and astronomical spectra and also make it possible to find and rule out misidentifications. The uncertainties of the E1 transition probabilities, based on the agreement between values in the length and velocity gauges, are estimated to be of the order 0.5% for the strong transitions and 25% for the weaker intercombination transitions. The M1 transition values are not sensitive to electron correlation and are believed to be accurate to well within 1%.

Atomic properties and transition parameters of highly charged Sb-like isoelectronic ions

The atomic properties and transition parameters of Sb-like Cs4+, Ba5+, La6+, Ce7+, Pr8+, Nd9+, Pm10+, and Sm11+ ions were first calculated using the GRASP2K package. This method is based on the multi-configuration Dirac–Hartree–Fock (MCDHF) method. In this calculation, the contributions of Breit and QED corrections were taken into consideration. By comparison, our results were in good agreement with the NIST values for Cs4+ and Ba5+, which revealed that our calculations are dependable. Meanwhile, it also showed that these ions have high sensitivity to the fine-structure constant α and long-lived metastable states. In particular, Pm10+ and Sm11+ had very long-lived metastable states with transitions within the optical transition. These ions are useful for the research of ultra-accurate atomic clocks and fundamental physics.

Energies and Spectral Lines for the States of 4s 24p 2, 4s4p 3, and 4s 24p4d Configurations in Ge-Like Te, Xe, and Ba Ions

The energy levels, wavelengths, transition rates, and line strengths have been calculated for the 4s 24p 2–4s4p 3 and 4s 24p 2–4s 24p4d allowed transitions occurring within the ground configuration (4s 24p 2) in the heavy Ge-like Te, Xe, and Ba ions. The fully relativistic multiconfiguration Dirac–Hartree–Fock method taking into account both correlations within the n = 5 complex and the QED effects has been used in the calculations. The calculation results are found to agree well with the data obtained on the TFR tokamak and by recent EBIT measurements in Xe. The isoelectronic sequence of the Ge-like ions is important in nuclear fusion research as their spectra may provide diagnostic information on magnetically confined plasmas.

Multiconfiguration Dirac-Hartree-Fock Calculations with Spectroscopic Accuracy: Applications to Astrophysics

Atomic data, such as wavelengths, spectroscopic labels, broadening parameters and transition rates, are necessary for many applications, especially in plasma diagnostics, and for interpreting the spectra of distant astrophysical objects. The experiment with its limited resources is unlikely to ever be able to provide a complete dataset on any atomic system. Instead, the bulk of the data must be calculated. Based on fundamental principles and well-justified approximations, theoretical atomic physics derives and implements algorithms and computational procedures that yield the desired data. We review progress and recent developments in fully-relativistic multiconfiguration Dirac–Hartree–Fock methods and show how large-scale calculations can give transition energies of spectroscopic accuracy, i.e., with an accuracy comparable to the one obtained from observations, as well as transition rates with estimated uncertainties of a few percent for a broad range of ions. Finally, we discuss further developments and challenges.

Extended Calculations of Spectroscopic Data: Energy Levels, Lifetimes, and Transition Rates for O-like Ions from Cr xvii to Zn xxiii

Abstract Employing two state-of-the-art methods, multiconfiguration Dirac–Hartree–Fock and second-order many-body perturbation theory, the excitation energies and lifetimes for the lowest 200 states of the , , , , , , , , and configurations, and multipole (electric dipole (E1), magnetic dipole (M1), and electric quadrupole (E2)) transition rates, line strengths, and oscillator strengths among these states are calculated for each O-like ion, from Cr xvii to Zn xxiii. Our two data sets are compared with the National Institute of Standards and Technology and CHIANTI compiled values, and previous calculations. The data are accurate enough for identification and deblending of new emission lines from the Sun and other astrophysical sources. The amount of high-accuracy data is significantly increased for the n = 3 states of several O-like ions of astrophysical interest, where experimental data are very scarce.

Multiconfiguration Dirac-Hartree-Fock energy levels, oscillator strengths, transition probabilities, hyperfine constants and Landé g-factor of intermediate Rydberg series in neutral argon atom

We computed the energy levels, oscillator strengths $f_{ij}$ , the radiative transition rates $A_{ij}$ , the Lande g -factor, the magnetic dipole moment and the electric quadrupole hyperfine constants of the intermediate Rydberg series $n{\rm s}$ $[k]_{J}$ ( $ 4 \le n \le 6$ ), $n{\rm d}$ $ [k]_{J}$ ( $3 \le n \le 4$ ), $n{\rm p}$ $[k]_{J}$ ( $4 \le n \le 5$ ) relative to the ground state 3p6 1S0 for neutral argon atom spectra. The values are obtained in the framework of the multiconfiguration Dirac-Hartree-Fock (MCDHF) approach. In this approach, Breit interaction, leading quantum electrodynamics (QED) effects and self-energy correction are taken into account. Moreover, these spectroscopic parameters have been calculated for many levels belonging to the configuration 3p54s, 3p55s, 3p56s, 3p53d, 3p54d, 3p54p, 3p55p as well as for transitions between levels 3p54s-3p54p, 3p54p-3p53d, 3p54p-3p55s, 3p55s-3p55p and 3p55p-3p56s. The large majority of the lines from the 4p-5s and 4p-3d, 5s-5p and 5p-6s transition arrays have been observed and the calculations are consistent with the J -file-sum rule. The obtained theoretical values are compared with previous experimental and theoretical data available in the literature. An overall satisfactory agreement is noticed allowing assessing the reliability of our data.

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.

Core Effects on Transition Energies for 3dk Configurations in Tungsten Ions

Allenergylevelsofthe3dk,k=1,2,...,8,9,configurationsfortungstenions,computedusing the GRASP2K fully relativistic code based on the variational multiconfiguration Dirac–Hartree–Fock method, are reported. Included in the calculations are valence correlation where all 3s,3p,3d orbitals are considered to be valence orbitals, as well as core–valence and core–core effects from the 2s,2p subshells. Results are compared with other recent theory and with levels obtained from the wavelengths of lines observed in the experimental spectra. It is shown that the core correlation effects considerably reduce the disagreement with levels linked directly to observed wavelengths, but may differ significantly from the NIST levels, where an unknown shift of the levels could not be determined from experimental wavelengths. For low values of k, levels were in good agreement with relativistic many-body perturbation levels, but for 2 < k < 8, the present results were in better agreement with observation.

Isotope shift calculations of Li-like neutron-rich and neutron-deficient Mg isotopes

The isotope shifts of the [Formula: see text]–[Formula: see text] transitions for the Li-like neutron-rich and neutron-deficient [Formula: see text] isotopes are calculated using the multi-configuration Dirac–Hartree–Fock (MCDHF) method and the relativistic configuration interaction approach. The results provided herein can be employed for the consistency check with the nuclear root-mean-square (rms) nuclear charge radii of the short-lived magnesium isotopes from the experimental isotope shifts using the corresponding transitions. The methods used here could also be applied to other few-electron Li-like systems and the analogous isotope shift results could be obtained.

Theoretical calculations on isotope shifts of Mg I by using relativistic multiconfiguration Dirac-Hartree-Fock method

The isotope shift parameters for the atomic transitions 1S0-1P1 and 1S0-3P1 of Mg are calculated by the relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) method, including the normal mass shift (NMS) coefficients, the specific mass shift (SMS) coefficients and the field shift (FS) factors. The detailed calculations of the isotope shifts for the three stable isotopes 24Mg, 25Mg and 26Mg are also carried out, in which the GRASP2K package is used together with another modified relativistic isotope shift computation code package RIS3. The two-parameter Fermi model is used here to describe the nuclear charge distribution in order to calculate the field shift by the first-order perturbation. A restricted double excitation mode is used in our calculations, one electron is excited from the two electrons in the 3s shell (3s2), another electron is excited from the eight electrons in the 2s or 2p shells (2s22p6), and the two electrons in the 1s shell (1s2) are not excited. The active configurations are expanded from the occupied orbitals to some active sets layer by layer, each correlation layer is numbered by the principal quantum numbers n (n= 3, 4, 5, …) and contains the corresponding orbitals s, p, d, …. The active configurations with the mixing coefficients in the added layer can be optimized by the MCDHF calculations. In this work, the atomic state functions are optimized simultaneously by the self-consistent field method and the relativistic configuration interaction approach in which the Breit interaction is taken into account perturbatively as well. The maximum principal quantum number n equals 10 and the largest orbital quantum number lmax is g. In our calculations, the NMS coefficients are -576.8 and -359.9 GHz·u, the SMS coefficients are 133.9 and -479.6 GHz·u, and the FS factors are -62.7 and -78.0 MHz·fm-2 for the 1S0-1P1 and 1S0-3P1 transitions of Mg, respectively. The difference between our isotope shift calculations and the previous experimental measurements is in a range from 6 MHz to 20 MHz with the relative error range from 0.6% to 1.3%, which shows that our results are in good agreement with experimental values. Our calculations are also coincident with other theoretical results. The isotope shift parameters provided here can be applied to the quick calculations of isotope shifts for the short-lived Mg isotopes, including 20-23Mg and 27-40Mg, and can be referred to for the corresponding isotope shift experiments. The methods used here canbe applied to calculating the isotope shifts and the atomic spectroscopic structures for other Mg-like ions with twelve extranuclear electrons.

Fine-structure energy levels and radiative rates in Al-like molybdenum

Based on relativistic wavefunctions from multiconfigurational Dirac–Hartree–Fock and configuration interaction calculations, energy levels, radiative rates, and wavelengths are evaluated for all levels of 3s23p, 3s3p2, 3s23d, 3p3, 3s3p3d, 3p23d, and 3s3d2 configurations of Al-like molybdenum ion (Mo XXX). Transition probabilities are reported for E1 and M2 transitions from the ground level. The valence–valence and core–valence correlation effects are accounted for in a systematic way. Breit interactions and quantum electrodynamics effects are estimated in subsequent relativistic configuration interaction calculations. Comparisons are made with the available data in the literature and good agreement has been found, which confirms the reliability of our results.