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Fine-structure calculations of energy levels, oscillator strengths, and transition probabilities for sulfur-like iron, Fe XI
Abstract
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 onebody
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.
Supplementary resource (1)
... Bhatia et al. [11] presented the results of energy levels, oscillator strengths, radiative decay rates, and collision strengths for the configurations 3s 2 3p 4 , 3s3p 5 , 3s 2 3p 3 3d, and 3p 6 of S-like Fe using the SUPERSTRUCTURE (SS) program. Abou El-Maaref et al. [12] reported calculated energy levels, oscillator strengths, and transition probabilities for transitions among the 14 LS states belonging to the 3s 2 3p 4 , 3s3p 5 , 3s 2 3p 3 3d, 3s 2 3p 3 4s, 3s 2 3p 3 4p, and 3s 2 3p 3 4d configurations of S-like Fe. Ishikawa et al. [13] calculated term energies of the 46 excited states arising from the 3s 2 3p 4 , 3s3p 5 , and 3s 2 3p 3 3d configurations in ions of the sulfur isoelectronic sequence (Z = 26-32) using the relativistic multi-reference many-body perturbation theory (RMBPT). ...
... It can be found that the BI effects are more important with increasing atomic number (i.e, for the 3s 2 3p 4 ͑ 2 3 P͒ 3 P 1 level, the contributions of the BI to the energies are about 0.36%, 0.65%, and 0.92% for Nb XXVI, Rh XXX, and In XXXIV, respectively. To assess the accuracy of present results, in Table 3 the present energy levels of Fe XI are compared with the energies from SS calculations by Del Zanna et al. [18], CIV3 calculations by Abou El-Maaref et al. [12], MCHF calculations by Fischer et al. [17], and SS calculations by Bhatia et al. [11,20]. Also listed in this table are the experimentally compiled values of Del Zanna et al. [18] and the recommended values taken from the NIST database [19]. ...
... Relative differences between the present MCDF and other theoretical and experimental energies of the 42 fine structure levels in Fe XI are plotted in Fig. 1. It can be found that the agreement between the present MCDF and CIV3 energies calculated by Abou El-Maaref et al. [12] is better than 1.5%, with four exceptions for 3s 2 P͒ 3 P 0 and 3s 2 3p 4 ͑ 2 1 D͒ 1 D 2 levels, respectively, their level energies agree with the present MCDF ones to better than 0.4% and 0.5%, respectively. Moreover, it is worth mentioning that there are some significant differences from the SS energies calculated by Bhatia et al. [11,20], where their values are somewhat lower for the low-lying levels and higher for the higher levels than those of Del Zanna et al. [18], Abou El-Maaref et al. [12], Froese Fischer et al. [17], NIST [19], and our calculations. ...
Energies, wavelengths, lifetimes, oscillator strengths, electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) transition rates among the 42 fine structure levels belonging to the 3s²3p⁴, 3s²3p³3d, and 3s3p⁵ configurations for S-like Fe and S-like ions with 41 ≤ Z ≤ 49 are calculated using the fully relativistic multiconfiguration Dirac-Fock (MCDF) method. In the calculations, contributions from correlations within the n = 6 complex, Breit interaction, and quantum electrodynamics effects are included. Detailed comparisons are made between the present results and the available experimental and other theoretical data. We found that our calculated energy levels generally agree within ≤0.5% with the experimentally compiled results, and the transition rates agree within ≤12% with other theoretical results for a majority of the transitions. These accurate theoretical data should be beneficial in fusion plasma research and astrophysical applications.
... The Fischer et al. 2006;Del Zanna et al. 2010;El-Maaref et al. 2014) reproduce excitation energies to a high degree. ...
We present a consistent set of calculated energies and E1, M1, E2, M2 radiative transition data for the main n = 3 levels from the $3s^23p^4$, $3p^6$, $3s3{p}^{4}3d$, $3{s}^{2}3{p}^{2}3{d}^{2}$, $3s3{p}^{5}$, $3{s}^{2}3{p}^{3}3d$, and $3s3{p}^{3}3{d}^{2}$ configurations for S-like ions from Cr ix to Cu xiv. The fully relativistic multiconfiguration Dirac–Hartree–Fock method implemented in the GRASP2K code is used to perform the present calculations. The excitation energies of the lowest 47 levels from the $3{s}^{2}3{p}^{4}$, $3s3{p}^{5}$, and $3{s}^{2}3{p}^{3}3d$ configurations, producing the strongest lines, are found to be in good agreement, reaching spectroscopic accuracy, with the latest experimental values for Fe xi evaluated by Del Zanna. Our energies can reliably be used to identify in astrophysical and laboratory spectra the $3{s}^{2}3{p}^{3}3d$ levels in other S-like ions, which are mostly unknown. On the contrary, significant discrepancies with the 3s3p 43d levels were found, emphasizing the need for more detailed experimental studies. A few new tentative identifications are suggested. The benchmarks we present indicate that our consistent set of radiative data is accurate and can be used for spectral line modeling.
... Fawcett [11] has calculated wavelengths and oscillator strengths of the 3s 2 3p 4 -3s3p 5 , 3s 2 3p 4 -3s 2 3p 3 3d, and 3s 2 3p 4 -3s 2 3p 3 4s transitions, and energy levels for the S I isoelectronic sequence between S I and Ni XIII using the Hartree-Fock-Relativistic program (HFR). Furthermore, a great deal of efforts in the past 10 years regarding the excited levels in sulfurlike ions have been presented, for example, the energy levels and oscillator strengths of sulfurlike Cl II [12,13], Ti VII [14], and Fe XI [15] have been calculated using CIV3 code. Wavelengths and transition probabilities of the 3s 2 3p 4 -3s3p 5 , 3s 2 3p 4 -3s 2 3p 3 3d and 3s 2 3p 4 -3s 2 3p 3 4s transitions for the sulfur sequence, and energy levels for the 3s 2 3p 4 , 3s3p 5 , 3s 2 3p 3 3d and 3s 2 3p 3 4s configurations of Ca V, Se VI and Ti VII have been calculated using the relativistic Hartree-Fock (HFR) method [16]. ...
Fine-structure calculations of energies and transition parameters have been performed using the configuration interaction technique (CI) as implemented in CIV3 code for sulfurlike manganese, Mn X. The calculations are executed in an intermediate coupling scheme using the Breit-Pauli Hamiltonian. As well as, energy levels and oscillator strengths are calculated using LANL code, where the calculations by LANL have been used to estimate the accuracy of the present CI calculations. The calculated energy levels, oscillator strengths, and lifetimes are in reasonable agreement with the published experimental and theoretical values. Electron impact excitation rates of the transitions emit soft X-ray and extreme ultraviolet (EUV) wavelengths have been evaluated. The level population densities are calculated using the collisional radiative model (CRM), as well. The collisional excitation rates and collision strengths have been calculated in the electron temperature range ≤ the ionization potential, ∼1–250 eV.
... Using the above theoretical schemes, the atomic physics group was able to extensively investigate the possibility of X-ray laser emission in several isoelectronic systems , see for example Figs. 8 and 9. The studies include helium isoelectronic sequence [77], beryllium isoelectronic sequence [69,78], boron isoelectronic sequence [79][80][81] , carbon isoelectronic sequence [82], sodium isoelectronic sequence [83][84][85], magnesium isoelectronic sequence [86][87][88] , aluminum isoelectronic sequence [89], silicon isoelectronic sequence [90][91][92] , sulfur isoelectronic sequence [93], potassium isoelectronic sequence [94], scandium isoelectronic sequence [95], and nickel isoelectronic sequence [96]. Most of the heavy members of the isoelectronic sequences studied radiate in the XUV and Soft X- Ray spectral regions (k between 50 and 1000 A ˚ ). ...
In this review article, important developments in the field of atomic physics are highlighted and linked to research works the author was involved in himself as a leader of the Cairo University – Atomic Physics Group. Starting from the late 1960s – when the author first engaged in research – an overview is provided of the milestones in the fascinating landscape of atomic physics.
Multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations of energy levels, oscillator strengths and transition rates of open K-shell transitions in beryllium-like tungsten ion, W[Formula: see text], are performed using the fully relativistic GRASP2018 code. For only principal quantum number [Formula: see text], energy levels of 1[Formula: see text] 2[Formula: see text], 1[Formula: see text]2[Formula: see text], 1[Formula: see text]2[Formula: see text], 1[Formula: see text]2p, 1[Formula: see text] and 1[Formula: see text] at different angular momenta and parity ([Formula: see text] are presented. Excitations of up to four electrons from the ground level, 1[Formula: see text] 2[Formula: see text], to excited levels are allowed. Correlations up to 5l orbitals are included in the configuration state function (CSF), [Formula: see text], p, d, f and g. The fine-structure calculations of E1, E2, M1 and M2 oscillator strengths and radiative rates between intercombination transitions in W[Formula: see text] ions are evaluated. The accuracy of these results is estimated using different ways, such as the comparison with previously published results and calculating the uncertainty of the transition data. The uncertainty of the transition probabilities showed low values for most of transitions.
For 3p63d4l where l=s,p,d,f states in Ni+8, we evaluated both oscillator strengths and energy levels to investigate the probability of laser wavelengths production in the soft X-ray and XUV regions. The calculations are executed using CIV3 and LANL codes. By comparing the values of our results with other published experimental and theoretical data, a good match is achieved in addition to unpublished values of oscillator strengths and energy levels have been obtained. Using calculated oscillator strengths, the gain coefficients, and reduced populations have been calculated for Ni+8 at different plasma temperatures, such as T=1/4 the ionization potential energy (IP) of the Ni+8; and the same thing for T=1/2IP and T=3/4IP. Promised values of positive laser gain are shown to obtain laser wavelengths in XUV and soft X-ray regions from current computed atomic data. Extreme ultraviolet radiation XUV is electromagnetic radiation in the part of the electromagnetic spectrum spanning wavelengths from 124 nm down to 10 nm.
Total solar eclipses, as the recent one seen across North America, are rare opportunities for optical spectroscopy of the corona. In view of the dearth of accurate rest-frame wavelength data, we measured 11 of the strongest optical coronal lines belonging to Fe X-XIV thereby proving the existence of the Fe XII line at 290.385(8) nm. Four lines, such as the green coronal line at 530.28113(13) nm, were measured with unprecedented precision, allowing in principle for absolute velocity determinations of plasmas with uncertainties of 0.08 km s−1. These results furthermore stringently benchmark the theory of complex open-3p-shell ions.
Energy levels, Oscillator strengths, and transition probabilities for sulfur-like scandium are calculated using CIV3 code. The calculations have been executed in an intermediate coupling scheme using Breit–Pauli Hamiltonian. The present calculations have been compared with the experimental data and other theoretical calculations. LANL code has been used to confirm the accuracy of the present calculations, where the calculations using CIV3 code agree well with the corresponding values by LANL code. The calculated energy levels and oscillator strengths are in reasonable agreement with the published experimental data and theoretical values. We have calculated lifetimes of some excited levels, as well.
This report summarizes laboratory measurements of atomic wavelengths, energy
levels, hyperfine and isotope structure, energy level lifetimes, and oscillator
strengths. Theoretical calculations of lifetimes and oscillator strengths are
also included. The bibliography is limited to species of astrophysical
interest. Compilations of atomic data and internet databases are also included.
Papers are listed in the bibliography in alphabetical order, with a reference
number in the text. Comprehensive lists of references for atomic spectra can be
found in the NIST Atomic Spectra Bibliographic Databases
http://physics.nist.gov/asbib.
The fine structure splittings in the (3s23p4)3P and (3s3p5)3Po terms of the S-like ions are calculated by using the multiconfiguration Dirac-Fock (MCDF) method. The subtraction of the spurious nonrelativistic contributions substantially improves the agreement of the theoretical results with experiment.
The Silences of the Archives, the Reknown of the Story.
The Martin Guerre affair has been told many times since Jean de Coras and Guillaume Lesueur published their stories in 1561. It is in many ways a perfect intrigue with uncanny resemblance, persuasive deception and a surprizing end when the two Martin stood face to face, memory to memory, before captivated judges and a guilty feeling Bertrande de Rols. The historian wanted to go beyond the known story in order to discover the world of the heroes. This research led to disappointments and surprizes as documents were discovered concerning the environment of Artigat’s inhabitants and bearing directly on the main characters thanks to notarial contracts. Along the way, study of the works of Coras and Lesueur took a new direction. Coming back to the affair a quarter century later did not result in finding new documents (some are perhaps still buried in Spanish archives), but by going back over her tracks, the historian could only be struck by the silences of the archives that refuse to reveal their secrets and, at the same time, by the possible openings they suggest, by the intuition that almost invisible threads link here and there characters and events.
Transition probabilities have been calculated by means of the relativistic Hartree-Fock (HFR) method for the 3s23p4-3s3p5, 3s23p4- 3s23p33d and 3s23p4- 3s23p34s transitions of the sulfur sequence for the elements calcium through titanium. The HFR ab initio technique has been combined with a least-square optimization process in order to fit calculated eigenvalues of the Hamiltonian with the available experimental energy levels.
Wavelengths and oscillator strengths are calculated for 3s23p4-3s3p5, 3s23p4-3s23p33d, and 3s23p4-3s23p34s transitions, and energy levels for the 3s23p33d configuration, of ions in the S I isoelectronic sequence between S I and Ni XIII. Measured wavelengths are also listed for 3s23p4-3s23p33d transitions. Enhanced accuracy is obtained through the optimization of Slater parameters previously calculated ab initio with a Hartree-Fock-Relativistic program package which uses the Blume-Watson method for spin-orbit interactions. Dominant configuration interactions are taken into account. A Multiconfiguration-Dirac-Fock program is applied to check the accuracy of the ab initio calculations. The tabulated data highlight contemporary problems in atomic physics and are of interest in studies of the solar spectrum.
Theoretical level values have been calculated for the energy levels of the 3s23p4 ground-state configuration of all sulfur-like ions of atomic number Z = 16–92. Transition probabilities have been obtained for the magnetic dipole (M1) and electric quadrupole (E2) transitions within this configuration. The calculations were by means of a multiconfiguration-Dirac-Fock technique which included perturbatively the Breit interaction and the Lamb shift for the K-, L-, and M-shell electrons. Results are presented which use experimental and semiempirical fits to level energies for ions with atomic numbers up to Z = 42. Above Z = 42, purely theoretical results are given. It is shown that the agreement between our theoretical results and the semiempirical values of the level energies improves rapidly as Z increases, with all values in excellent agreement by Z = 42.
This is a revision of the compilation of energy levels of iron for all ionization stages made in 1975 by Reader and Sugar. New material has since been proived for all but two of these ions. The present compilation includes electron configurations, energy levels, term designations, calculated leading percentages for most ions, experimental g-values, and ionization energies.
We have calculated configuration-interaction wave functions in intermediate coupling for the states 2s22p6, 2s22p53l (l = 0, 1, 2), and 2s22p63l (l = 0, 1, 2) of neon-like ions Ne I through Kr XXVII, incorporating variationally optimized orbitals and a modified Breit-Pauli Hamiltonian into the code CIV3. The percentage LS compositions of the LSJ levels are presented, together with their energies, oscillator strengths, and probabilities of transition between them. The lifetimes of the 2s22p53l levels are also presented.
Electron impact collision strengths and spontaneous radiative decay rates are calculated for Fe XVII. The data pertain to the 73 levels of the configurations, 2s22p6, 2s22p53s, 2s22p53p 2s22p53d, 2s2p63s, 2s2p63p, 2s2p63d, 2s22p54s, 2s22p54p, 2s22p54d, 2s2p64s, 2s2p64p, and 2s2p64d. Collision strengths are calculated at 11 incident electron energies: 58.5, 65.0, 70.0, 76.0, 85.0, 127.5, 170.0, 212.5, 255.0, 340.0, and 425.0Ry. This work is an improvement over our earlier work on Fe XVII in two respects: (1) configurations involving 4s, 4p, and 4d electrons have been added and (2) a broader range of incident electron energies is used in the computation of collision strengths and excitation rate coefficients. Relative spectral line intensities are calculated for astrophysically important transitions. These are obtained by computing the excitation rate coefficients (cm3s-1), i.e., the collision strengths integrated over a Maxwellian electron distribution, and then solving the equations of detailed balance for the populations of the 73 energy levels, assuming a collisional excitation model and an electron temperature of 4×106K. This temperature is typical for Fe XVII when formed in equilibrium by collisional ionization and recombination. Using the excitation rate coefficients and the radiative decay rates, level populations are computed for five electron densities and are given in this paper.
The method of superposition of configurations is used to obtain accurate
ab initio energy levels for the `2p hole' states of
Cl?II.
The wavefunctions are generated using the superposition-of-configurations
code CIV3. Relativistic effects are introduced by means of the
Breit-Pauli
approximation. Excellent agreement with recently published experimental data
is observed and values are reported for levels which have not been determined
experimentally.
Not Available
On leave of absence during 1976-6 at: Observatoire de Paris, Section
d'Astrophysique, 92190 Meudon, France.
Energy levels, oscillator strengths and transition probabilities for transitions among the fine-structure levels of the terms belonging to the 3s23p2, 3s3p3, 3s23p3d, 3p4, 3s23p4s, 3s23p4p, 3s23p4d and 3s23p4f configurations of Ca VII are calculated using extensive configuration-interaction (CI) wavefunctions obtained with the CIV3 (configuration interaction version 3) computer code of Hibbert. The relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian which consists of the non-relativistic term plus the one-body mass correction, Darwin term, and spin–orbit, spin–other–orbit, and spin–spin operators. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made, so that the energy splittings are as close as possible to the experimental values. The energy splitting of 70 fine-structure levels, oscillator strengths and transition probabilities for electric-dipole-allowed and intercombination transitions and, also the lifetimes of fine-structure levels are presented and compared with available experimental and other theoretical results. Our calculated fine-structure energies, including their ordering, show excellent agreement (better than 0.5%) with the available experimental results. In this calculation, we also predict new data for several levels where no other theoretical and experimental results are available.
Collision strengths for electron impact excitation of fine-structure levels in sulfur-like Fe XI are calculated in a semirelativistic R-matrix approach. The 38 fine-structure levels arising from the 20 LS states 3s23p43P,1D,1S; 3s3p53Po,1Po; 3s23p3(4So)3d3Do, 3s23p3(2Po)3d1,3Po,1,3Do,1,3Fo, 3s23p3(2Do)3d1,3So,1,3Po,1,3Do,1,3Fo are included in our calculation. The target levels are represented by configuration interaction wave functions. The relativistic effects are considered in the Breit-Pauli approximation by including one-body mass correction, Darwin term, and spin-orbit terms in the scattering equations. Collision strengths for transitions from the 3s23p43P2,1,0 levels to the fine-structure levels of the 3s23p33d configuration are compared with the distorted-wave results of Bhatia & Doschek at 8.0, 16.0, 24.0 ryd. There are some significant discrepancies between the two calculations, mostly caused by the difference in target wave functions. The collision strengths are integrated over a Maxwellian distribution of electron energies to obtain effective collision strengths over the temperature range from 5 × 105 to 5 × 106 K.
The general availability of electronic computers has resulted in a variety of developments in calculations of the electronic structure of atoms. The starting point is generally the Hartree-Fock approximation, which inadequately accounts for the motion of the electrons. A treatment of electron correlation has been the aim of most of the recent work in this field, and the methods which have been proposed are reviewed. The accuracy to which energies (or at least energy differences) can be evaluated, and calculations of electron affinities and term ratios are considered. The evaluation of oscillator strengths (transition probabilities) and hyperfine structure are also covered. Available atomic structure programs based on the correlation methods are discussed.
With the increasing accuracy of experimental data obtained from high resolution techniques, it becomes necessary to introduce relativistic effects into the study of atomic structure. A general method of evaluating relativistic effects in atomic structure problems is described. Each operator is expressed as a product of irreducible tensors whose matrix elements are calculated using Racah algebra techniques. The question at what stage the Breit interaction should be included in the Hamiltonian is discussed.
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.
Energy levels and oscillator strengths (transition probabilities) have been calculated for transitions among 46 fine-structure levels of the (1s$^2$) 2s$^2$2p$^2$, 2s2p$^3$, 2p$^4$, 2s$^2$2p3s, 2s$^2$2p3p and 2s$^2$2p3d configurations of C-like K XIV, Sc XVI, Ti XVII, V XVIII, Cr XIX and Mn XX using the GRASP code. Configuration interaction and relativistic effects have been included while generating the wavefunctions. Calculated values of energy levels agree within 3% with the experimentally compiled results, and the length and velocity forms of oscillator strengths agree within 20% for a majority of allowed transitions.
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