Relativistic Configuration Interaction Calculations Research Articles

CALCULATIONS WITH SPECTROSCOPIC ACCURACY: ENERGIES AND TRANSITION RATES IN THE NITROGEN ISOELECTRONIC SEQUENCE FROM Ar XII TO Zn XXIV

ABSTRACT Combined relativistic configuration interaction and many-body perturbation calculations are performed for the 359 fine-structure levels of the 2s 2 2p 3, 2 s2p 4, 2p 5, 2s 2 2p 2 3l, 2 s2p 3 3l, 2p 4 3l, and 2s 2 2p 2 4l configurations in N-like ions from Ar xii to Zn xxiv. Complete and consistent data sets of energies, wavelengths, radiative rates, oscillator strengths, and line strengths for all possible electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transitions among the 359 levels are given for each ion. The present work significantly increases the amount of accurate data for ions in the nitrogen-like sequence, and the accuracy of the energy levels is high enough to enable the identification and interpretation of observed spectra involving the n = 3, 4 levels, for which experimental values are largely scarce. Meanwhile, the results should be of great help for modeling and diagnosing astrophysical and fusion plasmas.

Experimental and theoretical study of the electronic states and spectra of NaAs

Gas-phase emission spectra of the hitherto unknown free radical NaAs were measured in the NIR region with a Fourier-transform spectrometer. The emissions were observed from a fast-flow system in which arsenic vapor in argon carrier gas was passed through a microwave discharge and mixed with sodium vapor in an observation tube. Seven transitions from all five Ω components of the low-lying A3Π and a1Δ excited states (A12, A21, A30+, A40−, a2) to the X10+ and/or X21 components of the X3Σ− ground state have been observed and analysed. With the help of parallel relativistic configuration interaction calculations all observed spectral features could be assigned and analyzed.

Relativistic configuration interaction calculations of multi-pole transitions rates and spectra of Ar I and Ar II

Relativistic configuration interaction calculations of multi-pole transitions rates and spectra of Ar I and Ar II

Relativistic configuration-interaction calculations for atoms with one valence electron based on altering hydrogenlike or Dirac-Fock spin orbitals

Relativistic configuration-interaction calculations using hydrogenlike or Dirac-Fock spin orbitals of the transition from the ground state to some $n{p}_{1/2}$, $n{p}_{3/2}$ low-lying excited states for the alkali metals are presented. In these calculations each virtual spin orbital corresponds to a unique noninteger atomic number determined iteratively using the virtual-particle model. The virtual-particle model based on ``condensed-space'' idea is here adopted to many electron systems consisting of a single valence electron and the core. The transition energy and the oscillator strength values were computed for sodium, potassium, rubidium, cesium, and francium. Both hydrogenlike and Dirac-Fock basis functions have been used in the computations for comparison.

Accurate multiconfiguration calculations of energy levels, lifetimes, and transition rates for the silicon isoelectronic sequence

Multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations and relativistic configuration interaction (RCI) calculations are performed for states of the 3s2 3p2 , 3s3p3 and 3s2 3p3d configurations in the Si-like ions Ti IX – Ge XIX, Sr XXV, Zr XXVII and Mo XXIX. Valence and core-valence electron correlation effects are accounted for through large configuration state function expansions. Calculated energy levels are compared with data from other calculations and with experimental data from the reference databases. Lifetime and transition rates along with uncertainty estimations are given for all ions. Energies from the calculations are in excellent agreement with observations and computed wavelength are almost of spectroscopic accuracy, aiding line identification in spectra.

Finite-field calculation of static polarizabilities and hyperpolarizabilities ofIn+and Sr

The dipole polarizabilities, dipole hyperpolarizabilities, quadrupole moments, and quadrupole polarizabilities of the $5{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S$ and $5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}^{o}$ states of ${\mathrm{In}}^{+}$ and Sr are calculated by using the finite-field method. The electron correlation effect and the basis set convergence are investigated in the relativistic coupled-cluster and configuration interaction calculations in order to obtain polarizabilities of high accuracy. Comparative study of the fully and scalar relativistic calculations reveals the effect of the spin-orbit coupling on the dipole polarizabilities of ${\mathrm{In}}^{+}$ and Sr. The blackbody-radiation shifts of the clock transition $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5fp\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ due to the dipole polarizabilities, quadrupole polarizabilities, and dipole hyperpolarizabilities are evaluated to be 0.017, $8.33\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$, and $1.93\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ Hz for ${\mathrm{In}}^{+}$ and 2.09 and $5.82\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$, and $1.69\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ Hz for Sr. The blackbody-radiation shifts from the quadrupole polarizabilities and dipole hyperpolarizabilities are significantly less than that from the dipole polarizabilities and therefore can be safely omitted for the quoted ${10}^{\ensuremath{-}18}$ uncertainty of the optical frequency standard of ${\mathrm{In}}^{+}$ and Sr.

Experimental and theoretical study of the electronic states and spectra of SbNa

Gas-phase emission spectra of the hitherto unknown free radical SbNa were measured in the NIR region with a Fourier-transform spectrometer. The emissions were observed from a fast-flow system in which antimony vapor in argon or neon carrier gas was passed through a microwave discharge and mixed with sodium vapor in an observation tube. Seven transitions from five low-lying excited states A12, A21, A30+, A40−, and B2 to the X10+ and/or X21 components of the X3Σ− ground state have been observed and analyzed.In parallel to the experiments, relativistic configuration interaction calculations of potential energy curves, vibrational constants, bond lengths, transition moments and radiative lifetimes were carried out to aid in the analysis of the experimental data.

Extended calculations of level and transition properties in the nitrogen isoelectronic sequence: Cr XVIII, Fe XX, Ni XXII, and Zn XXIV

Extensive multiconfiguration Dirac-Hartree-Fock (MCDHF) calculations and relativistic configuration interaction (RCI) calculations are performed for 272 states of the 2s 2 2p 3 ,2 s2p 4 ,2 p 5 ,2 s 2 2p 2 3l ,2 s2p 3 3l, and 2p 4 3l (l = 0, 1, 2) configurations in the nitrogen-like ions Cr XVIII, Fe XX, Ni XXII, and Zn XXIV. Valence, core-valence, and core-core electron correlation effects are accounted for through large configuration state function expansions. Calculated energy levels are compared with data from other calculations and with experimental data from the NIST database. Lande gJ-factors; hyperfine structures; isotope shifts; and radiative electric dipole (E1), electric quadrupole (E2), and magnetic dipole (M1) transition rates are given for all ions. The accuracy of the calculated energy levels �

Transition probabilities of the low-lying levels of Kr XXIV

Energy levels, radiative rates, and wavelengths are calculated for all levels of 3s23p, 3s3p2, 3s23d, 3p3, 3s3p3d, 3p23d and 3s3d2 configurations of Al-like krypton ion (Kr XXIV). Multiconfigurational Dirac–Hartree–Fock (MCDHF) method is adopted for calculating energy levels and radiative rates. 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.

Relativistic configuration-interaction calculation of the1s2s22S1/2state of Li-like ions

The magnetic and electric dipole radiations due to double electron jump from $1s2{s}^{2}$ ${}^{2}{S}_{1/2}$ state of Li isoelectronic sequence are evaluated for 20 ions with $8\ensuremath{\le}Z\ensuremath{\le}92$ using fully relativistic multiconfiguration Dirac Fock wave functions in the active space approximation with the inclusion of finite nuclear size, Breit interaction, self-energy, and vacuum polarization. The contributions from correlation and higher-order corrections to the x-ray energies and rates are discussed in detail. The effects of relaxed and frozen spin orbitals of the initial and final states on the correlation sensitive radiative rates are analyzed. The Auger electron emission rates calculated from a scaling procedure on the available relativistic radial matrix elements for a single vacancy in the $K$ shell have been used to evaluate the fluorescence yields. The numerical results for the x-ray and Auger transitions have been compared with other available theoretical and experimental values. The calculated electric dipole results are supplemented with error estimates wherever possible.

Relativistic many-body calculations on wavelengths and transition probabilities for forbidden transitions within the ground configurations in Co- through K-like ions of hafnium, tantalum, tungsten and gold

Wavelengths and transition probabilities have been computed for forbidden lines within the 3dk(k = 1-9) ground configurations in ions of hafnium, tantalum, tungsten and gold, employing the second-order relativistic many-body perturbation theory (RMBPT). For comparison, the relativistic configuration-interaction (RCI) calculations have also been performed. Comparing to the previously published theoretical wavelengths and the present RCI ones, the present RMBPT results are in much better agreement with the experimental values measured recently by using the electron beam ion trap facility, reproducing these observed wavelengths to within 0.2% for all transitions only with one exception. In addition, it removes dramatically the systematic underestimation/overestimation for shorter/longer wavelengths existing in the present RCI and other calculations.

Energy level structure of the ground configuration in the Er3+ free ion

Energy levels of the ground configuration [Xe]4f11 in the Er3+ ion are reported from relativistic configuration interaction calculations. Calculations are performed using the relativistic atomic structure package GRASP2K, which implements the multiconfiguration Dirac–Hartree–Fock method. The Breit transverse interaction and leading QED effects are included as perturbations. The final energies of 41 levels are compared with results from experiment and semi-empirical methods.

Relativistic configuration-interaction calculation of Kα transition energies in beryllium-like argon

Relativistic configuration-interaction calculations have been performed for energy levels of the low-lying and core-excited states of beryllium-like argon, Ar14+. These calculations include the one-loop quantum electrodynamics (QED) effects as obtained by two different methods: the screening-potential approach and the model QED operator approach. The calculations are supplemented by a systematic estimation of the uncertainties of the theoretical predictions.

Experimental and theoretical study of visible transitions in promethium-like tungsten

Visible transitions of promethium-like tungsten (W13+) were studied using the Shanghai high temperature superconducting electron beam ion trap. The M1 transition between the ground state (4f135s2 2F) fine structure levels was measured to be at 549.95 ± 0.06 nm. Seven other lines from W13+ were also found and five of them were classified as belonging to transitions within the first excited configuration (4f125s25p). These lines were assigned with the help of relativistic configuration interaction calculations and collisional-radiative model predictions of the relative line intensities.

Magnetic dipole and electric quadrupole hyperfine constants for V II 3d4, 3d3 4s and 3d2 4s2J = 1–5 states

Relativistic configuration interaction (RCI) calculations have been done for hyperfine constants and Lande g-values for 69 even parity V II states. Our results are in good agreement with the few recent experimental magnetic dipole results. We suggest that several Lande g-values need to be re-measured. Our electric quadrupole constants seem to be the first ones available. Analysis and methodology improvements include the introduction of an approximate sum rule for hyperfine constants, and a way of producing a more diagonal reference basis function set. The importance of mixing of 3dn−1 4s basis members with near degenerate 3dn or 3dn−2 4s2 is emphasized.

Experimental and theoretical study of the electronic states and spectra of BiLi

Gas phase emission spectra of the hitherto unknown free radical BiLi were measured in the NIR range with a Fourier-transform spectrometer. The emissions were observed from a fast-flow system in which bismuth vapor in argon carrier gas was passed through a microwave discharge and mixed with lithium vapor in an observation tube. Two systems of blue-degraded bands observed in the range 6900–9800cm−1 are assigned to the transitions A3Π(A20+)→X3Σ−(X10+, X21). The Δv=0, +1, and −1 sequences of both systems were measured at high spectral resolution. Rotational and vibrational analyses of 12 bands have yielded the spectroscopic parameters of the X10+, X21, and A20+ states including a hfs splitting parameter of the X21 state.In order to aid in the analysis of the experimental data, a series of relativistic configuration interaction calculations has been carried out to obtain spectroscopic parameters and potential curves for the low-lying states of BiLi and also electric dipole transition moments connecting them.

Relativistic configuration interaction calculation on the ground and excited states of iridium monoxide.

We present the fully relativistic multi-reference configuration interaction calculations of the ground and low-lying excited electronic states of IrO for individual spin-orbit component. The lowest-lying state is calculated for Ω = 1/2, 3/2, 5/2, and 7/2 in order to clarify the ground state of IrO. Our calculation suggests that the ground state is of Ω = 1/2, which is highly mixed with (4)Σ(-) and (2)Π states in Λ - S notation. The two low-lying states 5/2 and 7/2 are nearly degenerate with the ground state and locate only 234 and 260 cm(-1) above, respectively. The equilibrium bond length 1.712 Å and the harmonic vibrational frequency 903 cm(-1) of the 5/2 state are close to the experimental measurement of 1.724 Å and 909 cm(-1), which suggests that the 5/2 state should be the low-lying state that contributes to the experimental spectra. Moreover, the electronic states that give rise to the observed transition bands are assigned for Ω = 5/2 and 7/2 in terms of the obtained excited energies and oscillator strengths.

A theoretical study on trivalent europium: from the free ion to the water complex.

The energy levels within the (7)F and (5)D manifolds of trivalent europium were computed for the free ion and in the crystal field of 6-9 water molecules. Fully relativistic Kramers pairs configuration interaction (KRCI) calculations were performed with different correlation spaces for the free ion, and with the complete open-shell configuration interaction (COSCI) method including the 4f electrons in the active space for the water clusters. The best agreement with experimental data was found with the KRCI method or when including the spin-other-orbit effect in the COSCI calculations. For the free ion, the (7)F6 multiplet is found only 162 cm(-1) higher compared to experiment, while the (5)D(0-3) multiplets are approximately 3100 cm(-1) too high. In the crystal field of six water molecules, the multiplets with J > 0 split by 48-123 cm(-1). The energy separation (7)F0-(5)D0 of the unsplit multiplets is computed within 255 cm(-1)/247 cm(-1) compared to the experimental data for the free ion/in water. It has been found that the effect of higher coordination number or lower symmetry is small, increasing the transition energies by only about 40 cm(-1) by lowering the (7)F(J) states by the same amount. The hypersensitive transition (5)D0-(7)F2 is computed at 17079 cm(-1) with the KRCI method as compared to the experimental value of 16267 cm(-1).

Accurate multiconfiguration Dirac–Hartree–Fock calculations of transition probabilities for magnesium-like ions

Results from multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) calculations are presented for the n=3 to n′=3 transitions in the Mg isoelectronic sequence. The calculated values for the lowest 35 levels including core–valence correlation are found to be similar and to compare very well with other theoretical and experimental values. The Breit interaction and leading quantum electrodynamic effects are included as perturbations. The calculations can provide useful data for the experimental study of determining the fine structure levels in future work.

Relativistic configuration-interaction calculation ofKαtransition energies in berylliumlike iron

We perform relativistic configuration-interaction calculations of the energy levels of the low-lying and core-excited states of beryllium-like iron, Fe$^{22+}$. The results include the QED contributions calculated by two different methods, the model QED operator approach and the screening-potential approach. The uncertainties of theoretical energies are estimated systematically. The predicted wavelengths of the K\alpha transitions in beryllium-like iron improve previous theoretical results and compare favorably with the experimental data.