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.     

Relativistic multi-configuration calculations of Kα and Kβ X-ray transitions for highly ionized Mo ions

A relativistic multi-configuration Dirac-Fock technique has been used for computing the transition wavelengths, transition probabilities, absorption oscillator strengths, and line strengths for the Kα and Kβ line transitions of He-like to Ne-like molybdenum ions. The contributions from the Breit interaction, quantum electrodynamic corrections, and nuclear mass corrections to the initial and final levels have been taken into account. Transitions from the ground state to the n = 2 and 3 states of He-like and Li-like molybdenum have been calculated using two sets of configuration-interaction wavefunctions. One set of wavefunctions was generated using the fully relativistic GRASPVU code and the other was obtained using GRASP², the calculated transition wavelength, transition probabilities, and absorption strengths obtained by these two independent methods are in very good agreement and there is good agreement between these results and recent theoretical and experimental results. These data provide reference values for the level lifetimes, charge state distributions, and average charge of molybdenum plasmas.     

Theoretical energy level spectra and transition data for 4p4d, 4p4d4f,and 4p4d configurations of W

The ab initio   quasirelativistic Hartree–Fock method developed specifically for the calculation of spectral parameters of heavy atoms and highly charged ions is used to derive transition data for a multicharged tungsten ion. The configuration interaction method is applied to include electron correlation effects. The relativistic effects are taken into account in the Breit–Pauli approximation for quasirelativistic Hartree–Fock radial orbitals. The energy level spectra, radiative lifetimes and Lande g$g$-factors are calculated for the 4p⁶4d², 4p⁶4d4f, and 4p⁵4d³ configurations of the ion W³⁶⁺. The transition wavelengths, spontaneous transition probabilities, oscillator strengths, and line strengths for the electric dipole, electric quadrupole, electric octupole, and magnetic dipole transitions among the levels of these configurations are tabulated.     

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.     

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.     

Wavelengths and transition probabilities in heavy Ge-like ions (70 ? Z ? 92)

Wavelengths and transition probabilities have been calculated for the 4s²4p²-4s4p³ and 4s²4p²-4s²4p4d allowed transitions and for the forbidden (M1 and E2) transitions occurring within the ground configuration (4s²4p²) in the heavy Ge-like ions with Z = 70-92. The fully relativistic multiconfiguration Dirac-Fock method taking into account both the correlations within the n = 4 complex and the QED effects has been used for the calculations. The present results are compared to and agree well with recent electron-beam ion-trap measurements in tungsten, osmium, gold, bismuth, thorium, and uranium.     

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.     

Breit-Pauli energy levels belonging to 2p, 2s2p, 2p, 2p3? configurations and all E1 transitions among these levels in Mg V

We present accurate oscillator strengths, line strengths and radiative rates for 1073 E1 transitions among the 86 levels belonging to 2s²2p⁴, 2s2p⁵, 2p⁶, and 2s²2p³(⁴S^o, ²D^o, ²P^o)3? configurations in Mg V. We have used 1s and 2s Hartree-Fock orbitals, re-optimized 2p on 2p³(²D^o)3s ³D^o and optimized 3s,3p,3d orbitals on real states. Sixteen additional orbitals up to 8d are optimized either as a correction to n = 3 physical orbitals or as a correlation orbital. A very large set of configurations including up to three electron promotions are used to account for all important correlation effects. All of the main five terms in the Breit-Pauli operator (except the orbit-orbit interaction) are included in order to account for the relativistic effects. Small adjustments to the diagonal elements of the Hamiltonian matrix are made to bring the calculated energies within a few cm⁻¹ of the corresponding NIST recommended data wherever available. The calculated oscillator strengths, line strengths, and radiative rates for almost all of the E1 transitions show excellent agreement with the corresponding MCDF results of Fischer. The recent results of Bhatia et al. are found to be consistently higher by 20-45%. The accuracy of the present calculation is considered to be better than the NIST accuracy ratings for various transitions.     

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.     

Energy levels,wavelengths, and transition probabilities of Cu-like ions

Wavelengths, oscillator strengths, and transition probabilities for the electric dipole transitions between low-lying states (n = 4, 5, 6) of Cu-like ions are presented. The data are calculated from relativistic Hartree-Fock wavefunctions.     

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.     

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.     

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.     

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.     

Relativistic energy contributions to the N = 2 triplet levels in helium-like ions

The 1s2s³S?1s2p³P_J (J = 0, 1, 2) transitions in helium-like ions can be used to test QED, but only if the other contributions to the transition energy, and especially the relativistic contributions are known to high accuracy.This work tests the relativistic calculations by comparing the theoretical ${}^3\text{P}{}_{\mathrm{J}}$ splittings (which are nearly ndependent of QED) with each other and with experiment. An estimate of the largest uncalculated relativistic term, of relative order α⁴Z⁴, is also made.It is found that the calculations of Hata and Grant are not very accurate, and that the small discrepancy between Drake and experiment vanishes if the α⁴Z⁴ relativistic term is included.     

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.     

Relativistic energy levels, lifetimes, and transition probabilities for the sodium-like to argon-like sequences

Energy levels, lifetimes, and transition probabilities for transitions between computed levels are reported for the Na-like (Z = 11, … , 26) to Ar-like (Z = 18, … , 30) sequences. Several methods have been used—non-orthogonal spline CI, multiconfiguration Hartree-Fock (MCHF), and also multiconfiguration Dirac-Hartree-Fock (MCDHF). The first two methods included relativistic effects through the Breit-Pauli Hamiltonian, omitting only the orbit-orbit interaction. Both allowed (E1) and some forbidden (M1, E2, M2, E3) transitions are reported.     

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.     

Energy levels,radiative rates,and lifetimes for transitions in W LVIII

Energy levels and radiative rates are reported for transitions in Cl-like W LVIII. Configuration interaction (CI) has been included among 44 configurations (generating 4978 levels) over a wide energy range up to 363 Ryd, and the general-purpose relativistic atomic structure package (grasp) adopted for the calculations. Since no other results of comparable complexity are available, calculations have also been performed with the flexible atomic code (fac), which help in assessing the accuracy of our results. Energies are listed for the lowest 400 levels (with energies up to ∼98 Ryd), which mainly belong to the 3s²3p⁵, 3s3p⁶, 3s²3p⁴3d, 3s²3p³3d², 3s3p⁴3d², 3s²3p²3d³, and 3p⁶3d configurations, and radiative rates are provided for four types of transitions, i.e. E1, E2, M1, and M2. Our energy levels are assessed to be accurate to better than 0.5%, whereas radiative rates (and lifetimes) should be accurate to better than 20% for a majority of the strong transitions.     

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.