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.     

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.     

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.     

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.     

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.     

Oscillator strengths and transition probabilities for allowed and forbidden transitions in Fe XIX

An extensive set of oscillator strengths, line strengths, and radiative decay rates for the allowed and forbidden transitions in Fe XIX is presented. They correspond to 1626 fine structure levels of total angular momenta 0≤J≤8 of even and odd parities with 2≤n≤10, 0≤l≤9, 0≤L≤10, and (2S+1)=1, 3, 5. In contrast, the compiled table of the National Institute for Standards and Technology (NIST) lists only 63 observed levels. A total of 289,291 electric dipole allowed transitions are presented. They were obtained in the close coupling approximation using the relativistic Breit-Pauli R-matrix method. The wavefunction expansion included 15 levels of the configurations 2s²2p³, 2s2p⁴, and 2p⁵ of the Fe XX core. The calculated fine structure levels are assigned with spectroscopic identifications using quantum defect analysis. Comparison with the observed energies shows very good agreement, the largest difference being less than 4%. The transitions also compare well with the compiled data by NIST and recent calculations. The forbidden transitions of the electric quadrupole and octupole, and magnetic dipole and quadrupole, type are presented for the 379 levels of the configurations 2s²2p⁴, 2s2p⁵, 2p⁶, 2s²2p³3s, 2s²2p³3p, 2s²2p³3d, 2s²2p³4s, 2s²2p³4p, 2s²2p³4d, 2s²2p³4f, 2s2p⁴3s, 2s2p⁴3p, 2s2p⁴3d, 2s2p⁴4s, 2s2p⁴4p, and 2s²2p²3s² of Fe XIX. They correspond to a total of 66,619 transitions. These results have been obtained from relativistic Breit-Pauli atomic structure calculations using the program SUPERSTRUCTURE. The forbidden transition probabilities show very good agreement with those compiled by NIST.     

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.     

Hartree-Fock values of some atomic integrals useful in simplified LCAO-MO calculations for molecules: I. Atoms B,C, N,O, F

Hartree-Fock values of the kinetic energy, nuclear attraction, and atomic dipole-moment integrals, Condon-Shortley parameters, average energies of configurations, and one-electron (orbital) energies are presented for the configurations 1s² 2s^M 2p^N of boron, carbon, nitrogen, oxygen, fluorine, and their ions. The least-squares polynomial approximations for these integrals in terms of M, N, and Z (the nuclear charge) are also reported. These quantities are useful in Linear Combination of Atomic Orbital-Molecular Orbital (LCAO-MO) calculations.     

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.     

Transition probabilities for 5s-5p, 5p-5d, 4f-5d, and 5d-5f transitions in Ag-like ions with Z = 50-86

The wavelengths, electric dipole transition probabilities, and oscillator strengths are calculated for transitions between low-lying states (5s-5p, 5p-5d, 4f-5d, and 5d-5f) in the silver isoelectronic sequence (50 ? Z ? 86) using relativistic perturbation theory with a zero-approximation model potential. The results are compared with the corresponding data of the relativistic Hartree-Fock theory and the relativistic many-body perturbation theory. The results of these three theoretical approaches are compared with available experimental data for the level lifetimes. Possible reasons for some disagreements are discussed.     

Non-closed-shell many-electron-theory atomic charge wavefunctions: Correlated wavefunctions for 1s2 2sn 2pm electronic states of beryllium through neon and silicon

Atomic wavefunctions are tabulated for L-S coupled terms of 1s² 2sⁿ 2p^m configurations for 4 ≤ Z ≤ 10 and for Z = 14. Results for neutral atoms, positive ions, and negative ions are included. The tables specify the N-electron determinantal basis functions and their coefficients, the one-electron orbital basis functions and their coefficients, the total energy, and the nondynamical correlation energy for each wavefunction. These wavefunctions consist of the restricted Hartree-Fock wavefunction plus the specifically non-closed-shell electron-correlation effects given by the non-closed-shell many-electron theory (NCMET) of Sinano?lu.     

Experimental values of transition probabilities for 2s22p3-2s2p4 transitions along the N I like sequence

Transition probabilities for the 2s²2p³²D/²P-2s2p⁴²P and 2s²2p³²D/²P-2s2p⁴²D transitions in O II, F III, Ne IV and Si VIII ions have been determined. The results are compared with atomic structure calculations. A good overall agreement with data based on the NCMET method is observed which underlines the importance of electron correlations for the investigated decay processes     

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.     

Energy levels for the configurations (3d + 4s)n4p in the first spectra of the iron group,KI-Ga I

Energy levels and Landé g-factors for the configurations 3dⁿ4p + 3d^n?14s4p + 3d^n?24s²4p in the first spectra of the iron group were calculated and compared with experimental values in both general and individual treatments. The calculations, done in intermediate coupling, took into account explicitly the interactions between configurations as well as complete effective interactions of the core and effective d?p interactions. Due to the adoption of a successful starting point based on Hartree-Fock calculations for the Slater parameters, as well as to the insertion of the effective interactions, considerable improvement over previous results was obtained. On fitting 1537 levels with 67 free interaction parameters a mean error of 182 cm^?1 was obtained. Altogether 3652 energy levels were calculated including all the levels for the configurations 3d^n?24s²4p. Some isolated terms with large deviations were found. These are attributed to the interactions with the configurations (3d + 4s)ⁿ5p that were not considered explicitly in this analysis.     

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.     

Atomic data and spectral line intensities for the neon isoelectronic sequence (Si V through Kr XXVII)

The electron impact collision strengths and the spontaneous radiative decay rates are presented for the following ions of the Ne isoelectronic sequence: Si V, Ar IX, Ti XIII, Fe XVII, Ge XXIII and Kr XXVII. Data are given for the 27 levels that belong to four different configurations (2s²2p⁶, 2s²2p⁵3s, 2s²2p⁵3p, and 2s²2p⁵3d). By use of the atomic data calculations of the above-mentioned ions, the atomic data for all the ions with 14 ? Z ? 36 have been interpolated. Energy levels and level populations are presented for all the even-Z ions with 14 ? Z ? 36 (Si V, S VII, Ar IX, Ca XI, Ti XIII, Cr XV, Fe XVII, Ni XIX, Zn XXI, Ge XXIII, Se XXV, and Kr XXVII). The level populations are given for the three electron densities 10¹³, 10¹⁴, and 10¹⁵ cm^?3. Spectral line intensities are also presented for all transitions with intensities within two orders of magnitude of the most intense line in each ion.     

Energy levels in Ag-like (4d4f, 4d5? (? = 0-3)), Pd-like (4d4f [J = 1], 4d5p [J = 1], 4d5f [J = 1]), and Rh-like (4d [J = 5/2, 3/2]) ions with Z ? 86

Relativistic perturbation theory with a model potential is used for the calculation of energy levels of the states 4f_5/2, 4f_7/2, 5s_1/2, 5p_1/2, 5p_3/2, 5d_3/2, 5d_5/2, 5f_5/2, and 5f_7/2 above the 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰ core, with one vacancy , in the same core, in the silver and rhodium isoelectronic sequences with the maximum nuclear charge Z = 86. The method of extrapolation of the model potential parameter is applied to calculate one-electron and one-vacancy wavefunctions. The wavefunctions of Ag- and Rh-like ions were used to calculate the energies of resonance transitions to the ground state ¹S₀ in Pd-like ions. Good agreement between the theoretical and the experimental energies of the resonance transitions in Pd-like ions indicates the reliability of the results obtained.     

Energy levels and radiative rates for transitions in Mg-like iron, cobalt and nickel

Energy levels and radiative rates for electric dipole (E1) transitions among the lowest 141 levels of the (1s²2s²2p⁶) 3?², 3?3?′, and 3?4? configurations of Fe XV, Co XVI, and Ni XVII are calculated through the CIV3 code using extensive configuration-interaction (CI) wavefunctions. The important relativistic effects are included through the Breit-Pauli approximation. In order to keep the calculated energy splittings close to the experimental values, we have made small adjustments to the diagonal elements of the Hamiltonian matrices. The energy levels, including their orderings, are in excellent agreement with the available experimental results for all three ions. However, experimental energies are only available for a few levels. Since mixing among some levels is found to be very strong, it becomes difficult to identify these uniquely. Additionally, some discrepancies with other theoretical work (particularly for Ni XVII) are very large. Therefore, in order to confirm the level ordering as well as to assess the accuracy of energy levels and radiative rates, we have performed two other independent calculations using the GRASP and FAC codes. These codes are fully relativistic, but the CI in the calculations is limited to the basic (minimum) configurations only. This enables us to assess the importance of including elaborate CI for moderately charged ions. Additionally, we report results for electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transitions, and list lifetimes for all levels. Comparisons are made with other available experimental and theoretical results, and the accuracy of the present results is assessed.     

Electron impact collision strengths and oscillator strengths for Ge-, Ga-, Zn-, Cu-, Ni-, and Co-like Au ions

Energy levels, oscillator strengths, and electron impact collision strengths have been calculated for Ge-, Ga-, Zn-, Cu-, Ni-, and Co-like Au ions. For Ni-like Au, these atomic data are obtained among the levels belonging to the configurations of ([Ne])3s²3p⁶3d¹⁰, 3s²3p⁶3d⁹nl, 3s²3p⁵3d¹⁰nl, and 3s 3p⁶3d¹⁰nl (n = 4, 5; l = 0, 1, … , n − 1). For other Au ions, more levels have been obtained with special attention to atomic data up to transitions of 5f → 3d for emission or 3d → 5f for absorption. Configuration interactions are taken into account for all levels included. Collision strengths have been obtained at 20 scattered electron energies (5-40,000 eV) and they are listed at six representative energies of 100, 500, 1000, 5000, 10,000, and 20,000 eV in this work. Effective collision strengths have been obtained by assuming a Maxwellian electron velocity distribution at 10 representative temperatures ranging from 500 to 5000 eV. The present dataset should be adequate for most applications. The energy levels are expected to be accurate to within 0.5%, while oscillator strengths and collision strengths for strong transitions are probably accurate to better than 20%. The complete dataset is available electronically from http://www.astronomy.csdb.cn/EIE/.     

New atomic data for Ti X

A large-scale configuration interaction (CI) calculation using CIV3 is performed for the 303 fine-structure levels of the aluminum-like titanium ion. We have calculated the energy levels, oscillator strengths, and transition probabilities for the electric dipole allowed and intercombination transitions among the levels of ground state 3s²3p (²p^o) and higher energy levels of states 3s3p², 3p³, 3s3p3d, 3p²3d, 3s²4s, 3s3d², 3s²4p, 3s3p4s, 3s3p4p, 3p3d², 3s3p4d, 3s3p4f, 3s²5p, 3p²4p, 3s3d4s, 3s3p5s, 3s3d4p, 3s3p5p, 3s²(4d, 4f, 5s, 5d, 5f, 6s, 6p, 6d, 6f) of Ti X in the LSJ coupling scheme. The calculations include all the major correlation effects. We attempt to correct the inaccuracies in the CI coefficients in the wavefunctions, which would lead to inaccuracies in transition probabilities by applying a “fine-tuning” technique. The relativistic effects are incorporated by adding the mass correction, Darwin, and spin-orbit interaction terms into the non-relativistic Hamiltonian in the Breit-Pauli approximation. The present results are in good agreement with other available calculations and experiments. Several new lines corresponding to 3s3pnl (n = 4, 5 and l = 0, 1), 3s²5p, 3s²(6s, 6p) and other configurations are predicted where no other theoretical or experimental results are available. We expect that our extensive calculations will be useful to experimentalists in identifying the fine-structure levels in their future work.