Theoretical energy level spectra and transition data for 4p4d, 4p4f and 4p4d configurations of W ion

The ab initio quasirelativistic Hartree-Fock method developed specifically for the calculation of spectral parameters of heavy atoms and highly charged ions was applied to determine atomic data for tungsten ions. The correlation effects were included by adopting the configuration interaction method. The Breit-Pauli approximation for quasirelativistic Hartree-Fock radial orbitals was employed to take into account relativistic effects. The energy level spectra, radiative lifetimes, Lande factors g were calculated for the 4p⁶4d, 4p⁶4f and 4p⁵4d² configurations of W³⁷⁺ ion. The atomic data, namely, the transition wavelengths, spontaneous emission rates and oscillator strengths for the electric dipole, electric quadrupole and magnetic dipole transitions among and within the levels of these configurations are tabulated.     

The energy levels and radiative transition probabilities for electric quadrupole and magnetic dipole transitions among the levels of the ground configuration, [Kr]4d4f, of W

Large-scale multiconfiguration Hartree-Fock and Dirac-Fock calculations have been performed for the ground configuration, [Kr]4d¹⁰4f⁴, energy levels of the W²⁴⁺ ion. The relativistic corrections were taken into account in the quasirelativistic Breit-Pauli and fully relativistic Breit (taking into account QED effects) approximations. The role of correlation, relativistic, and QED corrections is discussed. Line strengths, oscillator strengths, and transition probabilities in the Coulomb and Babushkin gauges are presented for the electric quadrupole (E2) transitions among these levels. The magnetic dipole transitions are also investigated. Dependence of the E2 transition probabilities on the gauge condition of the electromagnetic field potential is studied as well.     

Energies and E1, M1, E2, and M2 transition rates for states of the 2s2p, 2s2p,and 2p configurations in nitrogen-like ions between F III and Kr XXX

Based on relativistic wavefunctions from multiconfiguration Dirac–Hartree–Fock and configuration interaction calculations, E1, M1, E2, and M2 transition rates, weighted oscillator strengths, and lifetimes are evaluated for the states of the (1s²)2s²2p³,2s2p⁴, and 2p⁵ configurations in all nitrogen-like ions between F  III and Kr  XXX. The wavefunction expansions include valence, core–valence, and core–core correlation effects through single–double multireference expansions to increasing sets of active orbitals. The computed energies agree very well with experimental values, with differences of only 300–600 cm⁻¹ for the majority of the levels and ions in the sequence. Computed transitions rates are in close agreement with available data from MCHF-BP calculations by Tachiev and Froese Fischer [G.I. Tachiev, C. Froese Fischer, A&A 385 (2002) 716].     

Energy levels and radiative transition rates for Ge XXXI,As XXXII,and Se XXXIII

Fine-structure energies of the 67 levels belonging to the 1s², 1s 2l$l$, 1s3l$l$, 1s4l$l$, 1s5l$l$, and 1s6l$l$ configurations of Ge XXXI, As XXXII, and Se XXXIII have been calculated using the General-Purpose Relativistic Atomic Structure Package. In addition, radiative rates, oscillator strengths, transition wavelengths, and line strengths have been calculated for all electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transitions among these levels. Lifetimes are also presented for all excited levels of these three ions. 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, oscillator strengths, and transition probabilities where no other theoretical or experimental results are available, which will form the basis for future experimental work.     

Oscillator strengths and transition probabilities from the Breit–Pauli R-matrix method: Ne IV

The atomic parameters–oscillator strengths, line strengths, radiative decay rates (A$A$), and lifetimes–for fine structure transitions of electric dipole (E1) type for the astrophysically abundant ion Ne IV are presented. The results include 868 fine structure levels with n≤$n\le$ 10, l≤$l\le$ 9, and 1/2≤J≤$\le J\le$ 19/2 of even and odd parities, and the corresponding 83,767 E1 transitions. The calculations were carried out using the relativistic Breit–Pauli R-matrix method in the close coupling approximation. The transitions have been identified spectroscopically using an algorithm based on quantum defect analysis and other criteria. The calculated energies agree with the 103 observed and identified energies to within 3% or better for most of the levels. Some larger differences are also noted. The A$A$-values show good to fair agreement with the very limited number of available transitions in the table compiled by NIST, but show very good agreement with the latest published multi-configuration Hartree–Fock calculations. The present transitions should be useful for diagnostics as well as for precise and complete spectral modeling in the soft X-ray to infra-red regions of astrophysical and laboratory plasmas.     

Energy levels,lifetimes, and transition probabilities for Mn XII and Ge XIX

Energy levels, transition probabilities, oscillator strengths, line strengths, and lifetimes have been calculated for silicon-like manganese and germanium, Mn XII and Ge XIX. The configurations 3s²3p², 3s3p³, 3s²3p3d, 3s3p²3d, and 3p⁴ were used in the calculations and 88 fine-structure levels were obtained. The fully relativistic GRASP code has been adopted, and results are reported for all electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole transitions among levels of Mn XII and Ge XIX. Comparisons have been made with available theoretical and experimental results.     

Electric-dipole allowed and intercombination transitions among the 3d, 3d4s and 3d4p levels of Fe IV

Oscillator strengths and transition rates for the electric-dipole (E1) allowed and intercombination transitions among 3d⁵, 3d⁴4s and 3d⁴4p levels of Fe IV are calculated using the CIV3 code of Hibbert and coworkers. Using the Hartree-Fock functions up to 3d orbitals we have also optimized 4s, 4p, 4d, 4f, 5s, 5p and 5d orbitals of which 4s and 4p are taken to be spectroscopic and the remaining orbitals represent corrections to the spectroscopic orbitals or the correlation effects. The J-dependent levels of 108 LS states are included in the calculation and the relativistic effects are accounted for via the Breit-Pauli operator. Configurations are chosen in two steps: (a) two promotions were allowed from the 3p, 3d, 4s and 4p subshells, using all the orbitals; and (b) selective promotions from the 3s subshell are included, but only to the 3s and 4s orbitals. The ab initio fine-structure levels are then fine tuned to reproduce observed energy levels as closely as possible, and the resulting wavefunctions are used to calculate oscillator strengths and transition rates for all possible E1 transitions. For many of these transitions, the present results show good agreement between the length and velocity forms while for some transitions, some large disagreements are found with other available results. The complete list of weighted oscillator strengths, transition rates, and line strengths for transitions among the fine structure levels of the three lowest configurations are presented in ascending order of wavelength.     

Weighted f-values, A-values, and line strengths for the E1 transitions among 3d, 3d4s, and 3d4p levels of Fe III

Weighted oscillator strengths, weighted radiative rates, and line strengths for all the E1 transitions between 285 fine-structure levels belonging to the 3d⁶, 3d⁵4s, and 3d⁵4p configurations of Fe III are presented, in ascending order of wavelength. Calculations have been undertaken using the general configuration interaction (CI) code CIV3. The large configuration set is constructed by allowing single and double replacements from any of 3d⁶, 3d⁵4s, 3d⁵4p, and 3d⁵4d configurations to nl orbitals with n?5,l?3 as well as 6p. Additional selective promotions from 3s and 3p subshells are also included in the CI expansions to incorporate the important correlation effects in the n=3 shell. Results of some strong transitions between levels of 3d⁶, 3d⁵4s, and 3d⁵4p configurations are also presented and compared with other available calculations. It is found that large disagreements occur in many transitions among the existing calculations.     

Energy levels and radiative rates for transitions in Ga XXIV

Energy levels, transition probabilities, oscillator strengths, line strengths, and lifetimes have been calculated for Oxygen-like Gallium, Ga XXIV. The configurations 2s²2p⁴, 2s2p⁵, 2p⁶, 2s2p⁴3?, 2s²2p³3?, and 2p⁵3? were used in calculations and 226 fine-structure levels were obtained. The fully relativistic GRASP code has been adopted, and results are reported for all electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions among the lowest 226 levels of Ga XXIV, belonging to the n≤3 configurations. Comparisons have been made with earlier available theoretical and experimental results.     

Breit–Pauli atomic structure calculations for Fe XI

Energy levels, oscillator strengths, and transition probabilities are calculated for the lowest-lying 165 energy levels of Fe XI using configuration-interaction wavefunctions. The calculations include all the major correlation effects. Relativistic effects are included in the Breit–Pauli approximation by adding mass-correction, Darwin, and spin–orbit interaction terms to the non-relativistic Hamiltonian. For comparison with the calculated ab initio energy levels, we have also calculated the energy levels by using the fully relativistic multiconfiguration Dirac–Fock method. The calculated results are in close agreement with the National Institute of Standards and Technology compilation and other available results. New results are predicted for many of the levels belonging to the 3s3p⁴3d and 3s3p³3d² configurations, which are very important in astrophysics, relevant, for example, to the recent observations by the Hinode spacecraft. We expect that our extensive calculations will be useful to experimentalists in identifying the fine structure levels in their future work.     

Electric quadrupole transition probabilities and line strengths of Ti

Electric quadrupole transition probabilities and line strengths have been calculated using the weakest bound electron potential model for sodium-like titanium, considering many transition arrays. We employed numerical Coulomb approximation and non-relativistic Hartree–Fock wavefunctions for the expectation values of radii in determination of parameters of the model. The necessary energy values have been taken from experimental data in the literature. The calculated electric quadrupole line strengths have been compared with available data in the literature and good agreement has been obtained. Moreover, some electric quadrupole transition probability and line strength values not existing in the literature for some highly excited levels have been obtained using this method.     

Energy levels,wavelengths, and transition rates of multipole transitions (E1, E2, M1, M2) in Au and Au ions

The fully relativistic configuration interaction method of the FAC code is used to calculate atomic data for multipole transitions in Mg-like Au (Au⁶⁷⁺) and Al-like Au (Au⁶⁶⁺) ions. Generated atomic data are important in the modeling of M-shell spectra for heavy Au ions and Au plasma diagnostics. Energy levels, oscillator strengths and transition rates are calculated for electric-dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) for transitions between excited and ground states 3l−nl^′$3l-n{l}^{\prime }$, such that n=4,5,6,7$n=4,5,6,7$. The local central potential is derived using the Dirac–Fock–Slater method. Correlation effects to all orders are considered by the configuration interaction expansion. All relativistic effects are included in the calculations. Calculated energy levels are compared against published values that were calculated using the multi-reference many body perturbation theory, which includes higher order QED effects. Favorable agreement was observed, with less than 0.15% difference.     

Energy levels,oscillator strengths,radiative decay rates,and fine-structure collision strengths for the Zn-like ions Nb XII and Mo XIII

Energy levels, line strengths, oscillator strengths, radiative decay rates, and fine-structure collision strengths are presented for the Zn-like ions Nb XII and Mo XIII. The atomic data are calculated with the AUTOSTRUCTURE code, where relativistic corrections are introduced according to the Breit–Pauli distorted wave approach. We present the calculations of atomic data for 110 fine-structure levels generated from fifteen configurations (1s²2s²2p⁶3s²3p⁶3d¹⁰)4s², 4s4p, 4p², 4s4d, 4s4f, 4s5s, 4p4d, 4s5p, 4s5d, 4p4f, 4p5s, 4d², 4d4f, 4f², and 3d⁹4s²4p. Fine-structure collision strengths for transitions from the ground and the first four excited levels are presented at six electron energies (20, 50, 80, 110, 150, and 180 Ryd). Our atomic structure data are compared with the available experimental and theoretical results.     

Relativistic many-body calculations of multipole (E1, M1, E2, M2, E3, and M3) transition wavelengths and rates between 3l4l′ excited and ground states in nickel-like ions

Wavelengths, transition rates, and line strengths are calculated for the 76 possible multipole (E1, M1, E2, M2, E3, and M3) transitions between the excited 3s²3p⁶3d⁹4l, 3s²3p⁵3d¹⁰4l, and 3s3p⁶3d¹⁰4l and the ground 3s²3p⁶3d¹⁰ states in Ni-like ions with the nuclear charges ranging from Z = 30 to 100. The relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate energies and transition rates for multipole transitions in hole-particle systems. This method is based on relativistic many-body perturbation theory, agrees with MCDF calculations in lowest-order, includes all second-order correlation corrections, and includes corrections from negative energy states. The calculations start from a 1s²2s²2p⁶3s²3p⁶3d¹⁰ Dirac-Fock potential. First-order perturbation theory is used to obtain intermediate-coupling coefficients, and the second-order RMBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order E1, M1, E2, M2, E3, and M3 matrix elements. The resulting transition energies and transition rates are compared with experimental values and with results from other recent calculations. As a result, we present wavelengths and transition rates data for the selected transitions that include the 76 possible multipole (E1, M1, E2, M2, E3, and M3) transitions between the excited 3s²3p⁶3d⁹4l, 3s²3p⁵3d¹⁰4l, and 3s3p⁶3d¹⁰4l states and the ground 3s²3p⁶3d¹⁰ state in Ni-like ions. Trends of the line strengths for the 76 multipole transitions and oscillator strengths for the 13 E1 transitions as function of Z are illustrated graphically. The Z-dependence of the energy splitting for all triplet terms of the 3s²3p⁶3d⁹4l, 3s²3p⁵3d¹⁰4l, and 3s3p⁶3d¹⁰4l configurations are shown in the range of Z = 30-100.     

Energies, wavelengths, and transition probabilities for Ge-like Kr, Mo, Sn, and Xe ions

Energy levels, wavelengths, transition probabilities, and oscillator strengths have been calculated for Ge-like Kr, Mo, Sn, and Xe ions among the fine-structure levels of terms belonging to the ([Ar] 3d¹⁰)4s²4p², ([Ar] 3d¹⁰)4s 4p³, ([Ar] 3d¹⁰)4s²4p 4d, and ([Ar] 3d¹⁰)4p⁴ configurations. The fully relativistic multiconfiguration Dirac-Fock method, taking both correlations within the n=4 complex and the quantum electrodynamic effects into account, have been used in the calculations. The results are compared with the available experimental and other theoretical results.     

Fine-structure calculations of energy levels,oscillator strengths,and transition probabilities for sulfur-like iron,Fe XI

Energy levels, oscillator strengths, and transition probabilities for transitions among the 14 LS states belonging to configurations of sulfur-like iron, Fe XI, have been calculated. These states are represented by configuration interaction wavefunctions and have configurations 3s²3p⁴, 3s3p⁵, 3s²3p³3d, 3s²3p³4s, 3s²3p³4p, and 3s²3p³4d, which give rise to 123 fine-structure energy levels. Extensive configuration interaction calculations using the CIV3 code have been performed. To assess the importance of relativistic effects, the intermediate coupling scheme by means of the Breit–Pauli Hamiltonian terms, such as the one-body mass correction and Darwin term, and spin–orbit, spin–other-orbit, and spin–spin corrections, are incorporated within the code. These incorporations adjusted the energy levels, therefore the calculated values are close to the available experimental data. Comparisons between the present calculated energy levels as well as oscillator strengths and both experimental and theoretical data have been performed. Our results show good agreement with earlier works, and they might be useful in thermonuclear fusion research and astrophysical applications.     

Transition probabilities and oscillator strengths of E1 transitions in Fe XII and Fe XIV

Non-orthogonal orbitals in the multiconfiguration Hartree-Fock approach are used to calculate line strengths, oscillator strengths and transition probabilities for E1 transitions among the fine-structure levels of the 3s²3p³, 3s3p⁴, 3s²3p²3d, 3s3p³3d, 3p⁵ and 3s²3p3d² configurations in Fe XII and 3s²3p, 3s3p², 3s²3d, 3p³, 3s3p3d, 3p²3d, 3s3d², 3p3d², 3s²4s, 3s²4p, 3s3p4s and 3s²4d configurations in Fe XIV. The lifetimes of excited levels belonging to these configurations of Fe XII and Fe XIV are also presented. An accurate representation of the levels has been obtained using spectroscopic and correlation radial functions. The wavefunctions exhibit large correlations and significant dependence of one-electron valence orbitals due to both the total and intermediate terms. The relativistic corrections are included through the one-body and two-body operators in the Breit-Pauli Hamiltonian. Progressively larger calculations are performed to check for important electron correlation contributions and for convergence of results. The atomic wavefunctions give excitation energies which are in close agreement with experiment. The present oscillator strengths and transition probabilities compare very well with previous large scale calculations.     

Energy levels,oscillator strengths,and radiative rates for Si-like Zn XVII,Ga XVIII,Ge XIX,and As XX

The energy levels, oscillator strengths, line strengths, and transition probabilities for transitions among the terms belonging to the 3s²3p², 3s3p³, 3s²3p3d, 3s²3p4s, 3s²3p4p and 3s²3p4d configurations of silicon-like ions (Zn XVII, Ga XVIII, Ge XIX, and As XX) have been calculated using the configuration-interaction code CIV3. The calculations have been carried out in the intermediate coupling scheme using the Breit–Pauli Hamiltonian. The present calculations have been compared with the available experimental data and other theoretical calculations. Most of our calculations of energy levels and oscillator strengths (in length form) show good agreement with both experimental and theoretical data. Lifetimes of the excited levels have also been calculated.