Special Issue "Spectra of Ionized Atoms: From Laboratory to Space"

A special issue of Atoms (ISSN 2218-2004). This special issue belongs to the section "Atomic, Molecular and Nuclear Spectroscopy and Collisions".

Deadline for manuscript submissions: closed (30 July 2017)

Special Issue Editor

Guest Editor
Dr. Joseph Reader

National Institute of Standards and Technology, Gaithersburg, MD, USA
Website | E-Mail
Interests: spectra of highly ionized atoms; hyperfine structure; ionization energies; critical compilations of atomic spectra

Special Issue Information

Dear Colleagues,

The spectra of ionized atoms continue to play an important role in understanding a wide variety of plasmas. The relatively new discipline of Laser-Induced Breakdown Spectroscopy (LIBS) is being used on Earth to produce lower ionization stages of atoms for diagnostics of solid samples, and also in space to determine contents of rocks on Mars and Venus. Spectra of lower stages of ionization are also found in space in nebulae, interstellar clouds, chemically peculiar stars, and in the sun. There is a continuing need for the wavelengths, energy levels, and oscillator strengths. For higher ionization stages, data are needed for spectra found in the hot plasmas of tokamaks and other machines aimed at developing new energy sources. Since much of the data for these hot plasmas must come from ab initio calculations, laboratory experiments can serve to evaluate the accuracy of the calculations. Experiments with electron beam ion traps (EBITs) can remove all but a few remaining electrons and thus form a basis for evaluating calculations of ions having only a few electrons. This Special Issue of Atoms will highlight the need for continuing research on the spectra of all types of ionized atoms.

Dr. Joseph Reader
Guest Editor

Manuscript Submission Information

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Keywords

  • spectra
  • ionized atoms
  • wavelengths
  • energy levels
  • oscillator strengths
  • ionization energies

Published Papers (16 papers)

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Research

Jump to: Review

Open AccessFeature PaperArticle Identification and Plasma Diagnostics Study of Extreme Ultraviolet Transitions in Highly Charged Yttrium
Atoms 2017, 5(3), 30; doi:10.3390/atoms5030030
Received: 17 July 2017 / Revised: 8 September 2017 / Accepted: 12 September 2017 / Published: 18 September 2017
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Abstract
Extreme ultraviolet spectra of the L-shell ions of highly charged yttrium (Y26+–Y36+) were observed in the electron beam ion trap of the National Institute of Standards and Technology using a flat-field grazing-incidence spectrometer in the wavelength range
[...] Read more.
Extreme ultraviolet spectra of the L-shell ions of highly charged yttrium (Y 26 + –Y 36 + ) were observed in the electron beam ion trap of the National Institute of Standards and Technology using a flat-field grazing-incidence spectrometer in the wavelength range of 4 nm-20 nm. The electron beam energy was systematically varied from 2.3 keV–6.0 keV to selectively produce different ionization stages. Fifty-nine spectral lines corresponding to Δ n = 0 transitions within the n = 2 and n = 3 shells have been identified using detailed collisional-radiative (CR) modeling of the non-Maxwellian plasma. The uncertainties of the wavelength determinations ranged between 0.0004 nm and 0.0020 nm. Li-like resonance lines, 2s 2 p 1 / 2 and 2s–2 p 3 / 2 , and the Na-like D lines, 3s 3 p 1 / 2 and 3s 3 p 3 / 2 , have been measured and compared with previous measurements and calculations. Forbidden magnetic dipole (M1) transitions were identified and analyzed for their potential applicability in plasma diagnostics using large-scale CR calculations including approximately 1.5 million transitions. Several line ratios were found to show strong dependence on electron density and, hence, may be implemented in the diagnostics of hot plasmas, in particular in fusion devices. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessFeature PaperArticle Wavelengths of the Self-Photopumped Nickel-Like 4f 1P1→4d 1P1 X-ray Laser Transitions
Atoms 2017, 5(3), 25; doi:10.3390/atoms5030025
Received: 31 January 2017 / Revised: 6 June 2017 / Accepted: 27 June 2017 / Published: 13 July 2017
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Abstract
The energies for the lower 3d3/24d3/2 [J = 1] and upper 3d3/24f5/2 [J = 1] working levels in the self-photopumped X-ray laser are analyzed along the Ni-like sequence. We have found some irregularities in these energy levels
[...] Read more.
The energies for the lower 3d3/24d3/2 [J = 1] and upper 3d3/24f5/2 [J = 1] working levels in the self-photopumped X-ray laser are analyzed along the Ni-like sequence. We have found some irregularities in these energy levels in the range Z = 42–49. The causes of the irregularities are studied. The list of elements that lase on the self-photopumped transition can be extended much further than originally known. We calculate the wavelengths of this transition in Ni-like sequence to Z = 79 using the relativistic perturbation theory with a zero approximation model potential. We estimate the wavelength accuracy for Z > 50 as Δλ/λ ≤ 0.005. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessArticle Spectrum of Singly Charged Uranium (U II) : Theoretical Interpretation of Energy Levels, Partition Function and Classified Ultraviolet Lines
Atoms 2017, 5(3), 24; doi:10.3390/atoms5030024
Received: 23 March 2017 / Revised: 8 June 2017 / Accepted: 16 June 2017 / Published: 26 June 2017
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Abstract
In an attempt to improve U II analysis, the lowest configurations of both parities have been interpreted by means of the Racah-Slater parametric method, using Cowan codes. In the odd parity, including the ground state, 253 levels of the interacting configurations 5f
[...] Read more.
In an attempt to improve U II analysis, the lowest configurations of both parities have been interpreted by means of the Racah-Slater parametric method, using Cowan codes. In the odd parity, including the ground state, 253 levels of the interacting configurations 5 f 3 7 s 2 + 5 f 3 6 d 7 s + 5 f 3 6 d 2 + 5 f 4 7 p + 5 f 5 are interpreted by 24 free parameters and 64 constrained ones, with a root mean square (rms) deviation of 60 cm 1 . In the even parity, the four known configurations 5 f 4 7 s , 5 f 4 6 d , 5 f 2 6 d 2 7 s , 5 f 2 6 d 7 s 2 and the unknown 5 f 2 6 d 3 form a basis for interpreting 125 levels with a rms deviation of 84 cm 1 . Due to perturbations, the theoretical description of the higher configurations 5 f 3 7 s 7 p + 5 f 3 6 d 7 p remains unsatisfactory. The known and predicted levels of U II are used for a determination of the partition function. The parametric study led us to a re-investigation of high resolution ultraviolet spectrum of uranium recorded at the Meudon Observatory in the late eighties, of which the analysis was unachieved. In the course of the present study, a number of 451 lines of U II has been classified in the region 2344 –2955 Å. One new level has been established as 5 f 3 6 d 7 p ( 4 I ) 6 K ( J = 5.5 ) at 39113.98 ± 0.1 cm 1 . Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessArticle The Third Spectrum of Indium: In III
Atoms 2017, 5(2), 23; doi:10.3390/atoms5020023
Received: 1 February 2017 / Revised: 1 June 2017 / Accepted: 5 June 2017 / Published: 13 June 2017
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Abstract
The present investigation reports on the extended study of the third spectrum of indium (In III). This spectrum was previously analyzed in many articles, but, nevertheless, this study represents a significant extension of the previous analyses. The main new contribution is connected to
[...] Read more.
The present investigation reports on the extended study of the third spectrum of indium (In III). This spectrum was previously analyzed in many articles, but, nevertheless, this study represents a significant extension of the previous analyses. The main new contribution is connected to the observation of transitions involving core-excited configurations. Previous data are critically evaluated and in some cases are corrected. The spectra were recorded on 3-m as well as on 10.7-m normal incidence spectrographs using a triggered spark source. Theoretical calculations were made with Cowan’s code. The analysis results in the identifications of 70 spectral lines and determination of 24 new energy levels. In addition, the manuscript represents a compilation of all presently available data on In III. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessFeature PaperArticle Configuration Interaction Effects in Unresolved 5p65dN+1−5p55dN+2+5p65dN5f1 Transition Arrays in Ions Z = 79–92
Atoms 2017, 5(2), 20; doi:10.3390/atoms5020020
Received: 12 April 2017 / Revised: 10 May 2017 / Accepted: 12 May 2017 / Published: 21 May 2017
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Abstract
Configuration interaction (CI) effects can greatly influence the way in which extreme ultraviolet (EUV) and soft X-ray (SXR) spectra of heavier ions are dominated by emission from unresolved transition arrays (UTAs), the most intense of which originate from Δn = 0, 4p6
[...] Read more.
Configuration interaction (CI) effects can greatly influence the way in which extreme ultraviolet (EUV) and soft X-ray (SXR) spectra of heavier ions are dominated by emission from unresolved transition arrays (UTAs), the most intense of which originate from Δn = 0, 4p64dN+14p54dN+2+4p64dN4f1 transitions. Changing the principle quantum number n, from 4 to 5, changes the origin of the UTA from Δn = 0, 4p64dN+14p54dN+2+4p64dN4f1 to Δn = 0, 5p65dN+15p55dN+2+5p65dN5f1 transitions. This causes unexpected and significant changes in the impact of configuration interaction from that observed in the heavily studied n = 4 – n = 4 arrays. In this study, the properties of n = 5n = 5 arrays have been investigated theoretically with the aid of Hartree-Fock with configuration interaction (HFCI) calculations. In addition to predicting the wavelengths and spectral details of the anticipated features, the calculations show that the effects of configuration interaction are quite different for the two different families of Δn = 0 transitions, a conclusion which is reinforced by comparison with experimental results. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessFeature PaperArticle Resonance Transitions in the Spectra of the Ag6+–Ag8+ Ions
Atoms 2017, 5(1), 11; doi:10.3390/atoms5010011
Received: 16 January 2017 / Revised: 14 February 2017 / Accepted: 21 February 2017 / Published: 4 March 2017
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Abstract
The spectrum of silver, excited in a vacuum spark, was recorded in the region 150–350 Å on a 3-m grazing incidence spectrograph. The resonance 4dk–(4dk−15p + 4dk−14f + 4p54dk+1) was studied in the
[...] Read more.
The spectrum of silver, excited in a vacuum spark, was recorded in the region 150–350 Å on a 3-m grazing incidence spectrograph. The resonance 4dk–(4dk−15p + 4dk−14f + 4p54dk+1) was studied in the Ag6+–Ag8+ spectra (Ag VII–Ag IX) with k = 5–3, respectively. Several hundred lines were identified with the aid of the Cowan code and orthogonal operator technique calculations. The energy levels were found and the transition probabilities were calculated. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessFeature PaperArticle The Role of the Hyperfine Structure for the Determination of Improved Level Energies of Ta II, Pr II and La II
Atoms 2017, 5(1), 10; doi:10.3390/atoms5010010
Received: 19 January 2017 / Revised: 14 February 2017 / Accepted: 21 February 2017 / Published: 28 February 2017
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Abstract
For the determination of improved energy levels of ionic spectra of elements with large values of nuclear magnetic dipole moment (and eventually large values of nuclear quadrupole moments), it is necessary to determine the center of gravity of spectral lines from resolved hyperfine
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For the determination of improved energy levels of ionic spectra of elements with large values of nuclear magnetic dipole moment (and eventually large values of nuclear quadrupole moments), it is necessary to determine the center of gravity of spectral lines from resolved hyperfine structure patterns appearing in highly resolved spectra. This is demonstrated on spectral lines of Ta II, Pr II and La II. Blend situations (different transitions with accidentally nearly the same wave number difference between the combining levels) must also be considered. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessFeature PaperArticle The Cu II Spectrum
Atoms 2017, 5(1), 9; doi:10.3390/atoms5010009
Received: 16 December 2016 / Revised: 7 February 2017 / Accepted: 8 February 2017 / Published: 24 February 2017
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Abstract
New wavelength measurements in the vacuum ultraviolet (VUV), ultraviolet and visible spectral regions have been combined with available literature data to refine and extend the description of the spectrum of singly ionized copper (Cu II). In the VUV region, we measured 401 lines
[...] Read more.
New wavelength measurements in the vacuum ultraviolet (VUV), ultraviolet and visible spectral regions have been combined with available literature data to refine and extend the description of the spectrum of singly ionized copper (Cu II). In the VUV region, we measured 401 lines using a concave grating spectrograph and photographic plates. In the UV and visible regions, we measured 276 lines using a Fourier-transform spectrometer. These new measurements were combined with previously unpublished data from the thesis of Ross, with accurate VUV grating measurements of Kaufman and Ward, and with less accurate older measurements of Shenstone to construct a comprehensive list of ≈2440 observed lines, from which we derived a revised set of 379 optimized energy levels, complemented with 89 additional levels obtained using series formulas. Among the 379 experimental levels, 29 are new. Intensities of all lines observed in different experiments have been reduced to the same uniform scale by using newly calculated transition probabilities (A-values). We combined our calculations with published measured and calculated A-values to provide a set of 555 critically evaluated transition probabilities with estimated uncertainties, 162 of which are less than 20%. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessFeature PaperArticle Calculation of Rates of 4p–4d Transitions in Ar II
Atoms 2017, 5(1), 8; doi:10.3390/atoms5010008
Received: 29 December 2016 / Revised: 27 January 2017 / Accepted: 9 February 2017 / Published: 21 February 2017
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Abstract
Recent experimental work by Belmonte et al. (2014) has given rates for some 4p–4d transitions that are significantly at variance with the previous experimental work of Rudko and Tang (1967) recommended in the NIST tabulations. To date, there are no theoretical rates with
[...] Read more.
Recent experimental work by Belmonte et al. (2014) has given rates for some 4p–4d transitions that are significantly at variance with the previous experimental work of Rudko and Tang (1967) recommended in the NIST tabulations. To date, there are no theoretical rates with which to compare. In this work, we provide such theoretical data. We have undertaken a substantial and systematic configuration interaction calculation, with an extrapolation process applied to ab initio mixing coefficients, which gives energy differences in agreement with experiment. The length and velocity forms give values that are within 10%–15% of each other. Our results are in sufficiently close agreement with those of Belmonte et al. that we can confidently recommend that their results are much more accurate than the early results of Rudko and Tang, and should be adopted in place of the latter. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
Open AccessArticle Core Effects on Transition Energies for 3dk Configurations in Tungsten Ions
Atoms 2017, 5(1), 7; doi:10.3390/atoms5010007
Received: 20 December 2016 / Accepted: 26 January 2017 / Published: 8 February 2017
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Abstract
Allenergylevelsofthe3dk,k=1,2,...,8,9,configurationsfortungstenions,computedusing the GRASP2K fully relativistic code based on the variational multiconfiguration Dirac–Hartree–Fock method, are reported. Included in the calculations are valence correlation where all 3s,3p,3d orbitals are considered to be valence orbitals, as well as core–valence and core–core effects from the 2s,2p subshells.
[...] Read more.
Allenergylevelsofthe3dk,k=1,2,...,8,9,configurationsfortungstenions,computedusing the GRASP2K fully relativistic code based on the variational multiconfiguration Dirac–Hartree–Fock method, are reported. Included in the calculations are valence correlation where all 3s,3p,3d orbitals are considered to be valence orbitals, as well as core–valence and core–core effects from the 2s,2p subshells. Results are compared with other recent theory and with levels obtained from the wavelengths of lines observed in the experimental spectra. It is shown that the core correlation effects considerably reduce the disagreement with levels linked directly to observed wavelengths, but may differ significantly from the NIST levels, where an unknown shift of the levels could not be determined from experimental wavelengths. For low values of k, levels were in good agreement with relativistic many-body perturbation levels, but for 2 < k < 8, the present results were in better agreement with observation. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessArticle JJ2LSJ Transformation and Unique Labeling for Energy Levels
Atoms 2017, 5(1), 6; doi:10.3390/atoms5010006
Received: 21 December 2016 / Accepted: 19 January 2017 / Published: 27 January 2017
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Abstract
The JJ2LSJ program, which is important not only for the GRASP2K package but for the atom theory in general, is presented. The program performs the transformation of atomic state functions(ASFs) from a jj-coupled CSF basis into an LSJ-coupled CSF basis. In addition, the
[...] Read more.
The JJ2LSJ program, which is important not only for the GRASP2K package but for the atom theory in general, is presented. The program performs the transformation of atomic state functions(ASFs) from a jj-coupled CSF basis into an LSJ-coupled CSF basis. In addition, the program implements a procedure that assigns a unique label to all energy levels. Examples of how to use the JJ2LSJ program are given. Several cases are presented where there is a unique labeling problem. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
Open AccessFeature PaperArticle Hyperfine Structure and Isotope Shifts in Dy II
Atoms 2017, 5(1), 5; doi:10.3390/atoms5010005
Received: 8 December 2016 / Revised: 10 January 2017 / Accepted: 13 January 2017 / Published: 20 January 2017
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Abstract
Using fast-ion-beam laser-fluorescence spectroscopy (FIBLAS), we have measured the hyperfine structure (hfs) of 14 levels and an additional four transitions in Dy II and the isotope shifts (IS) of 12 transitions in the wavelength range of 422–460 nm. These are the first precision
[...] Read more.
Using fast-ion-beam laser-fluorescence spectroscopy (FIBLAS), we have measured the hyperfine structure (hfs) of 14 levels and an additional four transitions in Dy II and the isotope shifts (IS) of 12 transitions in the wavelength range of 422–460 nm. These are the first precision measurements of this kind in Dy II. Along with hfs and IS, new undocumented transitions were discovered within 3 GHz of the targeted transitions. These atomic data are essential for astrophysical studies of chemical abundances, allowing correction for saturation and the effects of blended lines. Lanthanide abundances are important in diffusion modeling of stellar interiors, and in the mechanisms and history of nucleosynthesis in the universe. Hfs and IS also play an important role in the classification of energy levels, and provide a benchmark for theoretical atomic structure calculations. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessFeature PaperArticle Combining Multiconfiguration and Perturbation Methods: Perturbative Estimates of Core–Core Electron Correlation Contributions to Excitation Energies in Mg-Like Iron
Atoms 2017, 5(1), 3; doi:10.3390/atoms5010003
Received: 25 November 2016 / Revised: 22 December 2016 / Accepted: 6 January 2017 / Published: 12 January 2017
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Abstract
Large configuration interaction (CI) calculations can be performed if part of the interaction is treated perturbatively. To evaluate the combined CI and perturbative method, we compute excitation energies for the 3l3l, 3l4l and 3
[...] Read more.
Large configuration interaction (CI) calculations can be performed if part of the interaction is treated perturbatively. To evaluate the combined CI and perturbative method, we compute excitation energies for the 3 l 3 l , 3 l 4 l and 3 s 5 l states in Mg-like iron. Starting from a CI calculation including valence and core–valence correlation effects, it is found that the perturbative inclusion of core–core electron correlation halves the mean relative differences between calculated and observed excitation energies. The effect of the core–core electron correlation is largest for the more excited states. The final relative differences between calculated and observed excitation energies is 0.023%, which is small enough for the calculated energies to be of direct use in line identifications in astrophysical and laboratory spectra. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
Open AccessFeature PaperArticle Spectrum and Energy Levels of Four-Times Ionized Yttrium (Y V)
Atoms 2016, 4(4), 31; doi:10.3390/atoms4040031
Received: 18 November 2016 / Accepted: 6 December 2016 / Published: 21 December 2016
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Abstract
The analysis of the spectrum of four-times-ionized yttrium, Y V, was extended to provide a large number of new spectrum lines and energy levels. The new analysis is based on spectrograms made with sliding-spark discharges on 10.7 m normal- and grazing-incidence spectrographs. The
[...] Read more.
The analysis of the spectrum of four-times-ionized yttrium, Y V, was extended to provide a large number of new spectrum lines and energy levels. The new analysis is based on spectrograms made with sliding-spark discharges on 10.7 m normal- and grazing-incidence spectrographs. The measurements cover the region 184–2549 Å. The results revise levels for this spectrum by Zahid-Ali et al. (1975) and by Ateqad et al. (1984). Five hundred and seventy lines were classified as transitions between 23 odd-parity and 90 even-parity levels. The 4s24p5, 4s4p6, 4s24p44d, 5s, 5p, 5d, 6s configurations are now complete. Results for the 4s24p46d and 7s configurations are tentative. Ritz-type wavelengths were determined from the optimized energy levels, with uncertainties as low as ±0.0004 Å. The observed configurations were interpreted with Hartree-Fock calculations and least-squares fits of the energy parameters to the observed levels. Oscillator strengths for all classified lines were calculated with the fitted parameters. The results are compared with values for the level energies, percentage compositions, and transition probabilities from recent ab initio theoretical calculations. The ionization energy was revised to 607,760 ± 300 cm−1 (75.353 ± 0.037 eV). Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Review

Jump to: Research

Open AccessFeature PaperReview Multiconfiguration Dirac-Hartree-Fock Calculations with Spectroscopic Accuracy: Applications to Astrophysics
Atoms 2017, 5(2), 16; doi:10.3390/atoms5020016
Received: 31 January 2017 / Revised: 5 April 2017 / Accepted: 7 April 2017 / Published: 14 April 2017
Cited by 1 | PDF Full-text (353 KB) | HTML Full-text | XML Full-text
Abstract
Atomic data, such as wavelengths, spectroscopic labels, broadening parameters and transition rates, are necessary for many applications, especially in plasma diagnostics, and for interpreting the spectra of distant astrophysical objects. The experiment with its limited resources is unlikely to ever be able to
[...] Read more.
Atomic data, such as wavelengths, spectroscopic labels, broadening parameters and transition rates, are necessary for many applications, especially in plasma diagnostics, and for interpreting the spectra of distant astrophysical objects. The experiment with its limited resources is unlikely to ever be able to provide a complete dataset on any atomic system. Instead, the bulk of the data must be calculated. Based on fundamental principles and well-justified approximations, theoretical atomic physics derives and implements algorithms and computational procedures that yield the desired data. We review progress and recent developments in fully-relativistic multiconfiguration Dirac–Hartree–Fock methods and show how large-scale calculations can give transition energies of spectroscopic accuracy, i.e., with an accuracy comparable to the one obtained from observations, as well as transition rates with estimated uncertainties of a few percent for a broad range of ions. Finally, we discuss further developments and challenges. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Open AccessFeature PaperReview Spectral Analysis of Moderately Charged Rare-Gas Atoms
Atoms 2017, 5(1), 12; doi:10.3390/atoms5010012
Received: 27 December 2016 / Revised: 16 February 2017 / Accepted: 21 February 2017 / Published: 7 March 2017
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Abstract
This article presents a review concerning the spectral analysis of several ions of neon, argon, krypton and xenon, with impact on laser studies and astrophysics that were mainly carried out in our collaborative groups between Argentina and Brazil during many years. The spectra
[...] Read more.
This article presents a review concerning the spectral analysis of several ions of neon, argon, krypton and xenon, with impact on laser studies and astrophysics that were mainly carried out in our collaborative groups between Argentina and Brazil during many years. The spectra were recorded from the vacuum ultraviolet to infrared regions using pulsed discharges. Semi-empirical approaches with relativistic Hartree–Fock and Dirac-Fock calculations were also included in these investigations. The spectral analysis produced new classified lines and energy levels. Lifetimes and oscillator strengths were also calculated. Full article
(This article belongs to the Special Issue Spectra of Ionized Atoms: From Laboratory to Space)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

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