Oscillator Strengths Of Lines Research Articles

Benford’s law in atomic spectra and opacity databases

The intriguing law of anomalous numbers, also named Benford’s law, states that the significant digits of data follow a logarithmic distribution favoring the smallest values. In this work, we test the compliance with this law of the atomic databases developed at the National Institute of Standards and Technology (NIST) focusing on line energies, oscillator strengths, Einstein coefficients and radiative opacities. The considered databases are the Atomic Spectra Database (ASD) and the NIST-LANL (Los Alamos National Laboratory) Lanthanide/Actinide Opacity Database. The present study is not limited to the first digit and the case of multipole lines is also considered. The fact that the law is verified with a high accuracy means that the occurrence of digits reflects the constraints induced, in a given angular-momentum coupling, by the selection rules for atomic processes. As a consequence, Benford’s law may be of great interest to detect inconsistencies in atomic databases.

Curves of growth for transiting exocomets: Application to Fe II lines in the β Pictoris system

Using transit spectroscopy, exocomets are routinely observed in the young planetary system of β Pic. However, despite more than 35 yr of observations, we still have very little information on the physical properties and almost no information on the abundances of the gaseous clouds surrounding the comets’ nuclei, the difficulty being the conversion of the observed absorption profiles into column density measurements. Here, we present a new method to interpret the exocomet absorptions observed in β Pic spectrum and link them to the physical properties of the transiting cometary tails (e.g. size, temperature, and column density). We show that the absorption depth of a comet in a set of lines arising from similar excitation levels of a given chemical species follows a simple curve as a function of g·f, where f is the line oscillator strength and g its lower level multiplicity. This curve is the analogue of the curve of growth for interstellar absorption lines, where equivalent widths are replaced by absorption depths. To fit this exocomet curve of growth, we introduced a model where the cometary absorption is produced by a homogeneous cloud, covering only a limited fraction of the stellar disc. This model is defined by two parameters: α, characterising the size of the cloud relative to the star, and β, related to the optical depth of the absorbing gas. This model was tested on two comets observed with the Hubble Space Telescope in December 1997 and October 2018, in a set of lines of ionised iron (Fe II) at 2750 Å. The measured absorption depths are found to satisfactory match the two-parameter curve of growth model, indicating that both comets cover roughly 40% of the stellar disc (α = 0.4) and have optical thicknesses close to unity in those lines (β ~ 1). Then, we show that if we consider a set of lines arising from a wider range of energy levels, the absorbing species seems to be populated at thermodynamical equilibrium, causing the cometary absorption to follow a curve of growth as a function of g f ⋅ e−El/kBT (where T is the temperature of the absorbing medium). For the comet observed on December 6, 1997, we derive a temperature of T = 10 500 ± 500 K and a total Fe II column density of NFeII = (1.11 ± 0.09) × 1015 cm−2. By considering the departure from the Boltzmann distribution of the highest excited energy levels (El ~ 25 000 cm−1), we also estimate an electronic density of ne ≈ (3 ± 1) × 107 cm−3.

Computation of hyperfine multiplet oscillator strengths in Tantalum atom

BackgroundThe electronic transitions between two fine levels depend on the transition probability. The transition probability depends on spectral line strength and oscillator strength. The oscillator strength depends on the number of oscillators and their energies. In this research, we will find the oscillator strengths of hyperfine multiplets of the Tantalum atom. The oscillator strength of hyperfine multiplet investigation aims to enhance our understanding of Tantalum's spectral characteristics. This work provides valuable information in the spectroscopy of material, atomic/molecular, and astrophysics.ResultFourier transform spectra from ultraviolet to far infrared regions have been obtained from TUGRAZ. Fourier transform spectra give the most reliable position of the wavelength of hyperfine multiplets. The Fourier transform spectra of Tantalum contain thousands of Tantalum I and II spectral lines. Each spectral line can be characterized by its upper and lower levels and corresponding angular momenta and hyperfine constants. These properties of the spectral lines were collected from the literature. Hyperfine multiplets for each fine structure were calculated, and they revealed their spectroscopic behavior with high precision.ConclusionIn this study, Tantalum's hyperfine multiplet oscillator strength was calculated using advanced computational techniques to address its atomic structure. The fine structure “gf” values were obtained from literature, and intensities of the multiplets were determined. They combined with the gf values to calculate the oscillator strengths of the hyperfine multiplets.

Absorption Line Oscillator Strengths for the C 2Π(0)-A 2Σ+(0) Band of Nitric Oxide

We have determined absorption oscillator strengths for rotational transitions of the C 2Π(0)-A 2Σ+(0) band of NO, which has been detected in the upper atmosphere of Venus. The molecular quantum defect orbital method has been used in the calculation of the electronic transition moment and the Rydberg–valence interaction between the C 2Π(v = 0) and the B 2Π (v = 7) states has been considered. Considerable deviations from normal intensity distribution of the rotational lines have been found at J ≤ 5.5. As far as we know, the present line f-values are reported here for the first time. These data may be useful in the interpretation of the observations obtained by the Visible and Infrared Thermal Imaging Spectrometer instrument on the Venus Express spacecraft.

Transition Energies and Line Oscillator Strengths of the C 2Π(0)-X 2Π(0–6) Absorption Bands of Nitric Oxide. A Theoretical Study

Theoretical absorption oscillator strengths and wavelengths for rotational transitions of the C 2Π(v′ = 0)-X 2Π(v″) bands with v″ = 0–6 of nitric oxide are reported. The Molecular Quantum Defect Orbital method has been used in the calculations and the known interaction between the C 2Π(v = 0) Rydberg and the B 2Π (v = 7) valence states has been dealt with through an appropriate rovibronic energy matrix. We hope that the reported data may be useful in the analysis of the observed ultraviolet nightglow emission from nitric oxide in the upper atmospheres of Earth, Venus, and Mars.

Radiative Properties of Rb-Isoelectronic Technetium (Tc VII), Ruthenium (Ru VIII) and Rhodium (Rh IX) Ions for Astrophysical Applications

In this work, we present high-accuracy spectroscopic properties, such as line strengths, transition probabilities and oscillator strengths for allowed transitions among nD3/2,5/2,n′S1/2 and n′P1/2,3/2(n=4,n′=5,6) states of Rb-isoelectronic Tc (Tc VII), Ru (Ru VIII) and Rh (Rh IX) ions for their applications in the analysis of astrophysical phenomena occurring inside celestial bodies containing Tc, Ru and Rh ions. Due to the scarcity of computational data of atomic properties of these transitions, as well as considerable discrepancies within the literature about these ions, the precise determination of these properties is necessary. For this purpose, we have implemented relativistic many-body perturbation theory (RMBPT) for evaluation of the wave functions of the considered states. For better accuracy, we have accounted for electron interactions through random phase approximation, Brückner orbitals and structural radiations of wave functions in our RMBPT method for further precise evaluation of electric dipole amplitudes. Combining these values of the observed wavelengths, the above transition properties and radiative lifetimes, a number of excited states of Tc VII, Ru VIII and Rh IX ions have been calculated. For further validation of our work, we have compared our results with the data already available in the literature.

Judd-Ofelt Analysis of High Erbium Content Yttrium-Aluminum and Yttrium-Scandium-Aluminum Garnet Ceramics

The Er1.5Y1.5Al5O12 (Er:YAG) and (Er1.43Y1.43Sc0.14)(Sc0.24Al1.76)Al3O12 (Er:YSAG) ceramics have been characterized using the Judd-Ofelt (JO) theory. The line strengths and oscillator strengths of several transitions from the ground state 4I15/2 to excited state manifolds have been evaluated from transmittance spectra measured at room temperature (300 K). The JO parameters have been calculated, and the values of the radiative decays rate and the radiative lifetimes for the 4I13/2 excited state, and the luminescence cross-section of 4I15/2 → 4I13/2 in Er-doped ceramic samples have been established. We have traced the influence of Sc3+ inclusion on spectroscopic properties and crystal quality and estimate prospects of application in laser systems.

Relativistic coupled-cluster calculations of the energies, Landé g factors, radiative transition properties including line strengths, oscillator strengths, and transition rates for Th3+

Energies, Landé g factors, line strengths, transition probabilities, and oscillator strengths for electric dipole (E1), electric quadrupole (E2), and magnetic dipole (M1) transitions arising from the nS1/2 (n=7-10), nP1/2,3/2 (n=7-9), nD3/2,5/2 (n=6-9), nF5/2,7/2 (n=5-8), and nG7/2,9/2 (n=5,6) energy levels in Th3+, are calculated using the singles and doubles approximation of the relativistic coupled-cluster (CCSD) method. The data are compared with available experimental and theoretical results, showing a good agreement. To the best of our knowledge, many results are reported for the first time. This work reports a high-precision atomic property calculation of Th3+ and is of great significance for future spectral analysis and precision experiments targeting various applications.

OUP accepted manuscript

We present precise radiative data of line strengths, transition probabilities and oscillator strengths for the allowed transitions among the $nS_{1/2}$, $nP_{1/2,3/2}$, $n'D_{3/2,5/2}$ and $n'F_{5/2,7/2}$ states with $n=4$ to $6$ and $n'=4,5$ of the Cu-isoelectronic As, Se and Br ions. Due to unavailability of precise observations of these spectroscopic data, their accurate estimations are of great interest and useful in analyzing various astrophysical phenomena undergoing inside the heavenly bodies that contain As, Se and Br elements. An all-order perturbative many-body method in the relativistic theory framework has been employed to determine the atomic wave functions, which are further used to estimate the above quantities with the uncertainties. We found significant differences between some of our results and results that are available earlier.

Accurate line strengths, transition rates and lifetimes of 2s2p2(4P)3s in N II

Abstract The accurate line strengths, transition rates, oscillator strengths, and lifetimes from the inner-shell 2s2p2(4P)3s states 5P and 3P of N II are reported within the framework of the multiconfiguration Dirac-Hartree-Fock (MCDHF) method. The effects of core-core, core-valence, and valence correlations; the Breit interaction; and QED effect are taken into account. Through investigating the influences of electron correlation effects on the quintet states, it is found that the core correlation effect has certain compensation effect in accurately optimizing the line strengths, transition rates and lifetimes of quintet states; the branching fractions of 2s2p3 5S$^\circ _{2}$–2s2p2(4P)3s 5P1, 2, 3 tend to 1, which is inferred as a peculiar intrinsic property that can be useful for plasma diagnostics; unlike 3P0, 1, 2 and 5P1, 3, the calculations of lifetime of 5P2 show some J-dependence, and the velocity form calculations for this J=2-dependence are much more sensitive to electron correlations of 1s22s2p2(4P)3l (l = p, d) than those in the length gauge, which will be helpful to deal with the calculations of lifetime with J=2-dependence in the carbon like isoelectronic series.

Transition spectral parameters of In-like Ba, La, and Ce ions

The spectral parameters (energy levels, wavelengths, transition probabilities, line strengths, and oscillator strengths) of resonance lines for Ba VIII, La IX, and Ce X have been obtained using the multiconfiguration Dirac–Hartree–Fock method, with contributions of quantum electrodynamics and Breit interaction corrections taken into consideration. The calculated results of energy levels and wavelengths are in good agreement with experimental values and other calculations. The number of energy levels and wavelengths considered is larger than that of any other experiment or other calculations. The transition probabilities, line strengths, and oscillator strengths are also calculated where no other theoretical results and experimental values are available.

Radiative transition properties including line strengths, oscillator strengths, and transition rates for Ra II

In this paper, we calculate the energy and radiative transition properties of singly charged Ra using the singles and doubles approximated relativistic coupled-cluster method. The excitation energies of the (7 - 12)S1/2, (7 - 12)P1/2,3/2, (6 - 10)D3/2,5/2 states in Ra+ are reported. The results are compared with available experimental results, showing a good agreement. Accurate values along with their uncertainties of the electric-dipole (E1), electric-quadrupole (E2), and several important magnetic-dipole (M1) matrix elements for transitions in singly charged Ra are determined by the relativistic coupled-cluster method at different approximations. Using these computed E1, E2, and M1 matrix elements, we also provide the related radiative transition properties of Ra+, including line strengths, oscillator strengths, and transition rates. Furthermore, we also investigate the role of electron correlation in these properties. To the best of our knowledge, many results are reported for the first time. Present work reports a high-precision atomic property calculation of Ra+ and is beneficial for present and future experiments using Ra+ targeting various applications such as atomic clocks and studies of parity non-conservation.

Line Oscillator Strengths for the c4′ 1Σu +(4)–X1Σg +(0–7) Absorption Bands of N2

Abstract Theoretical absorption oscillator strengths for rotational lines of the c 4 ′ 1 Σ u + ( 4 ) – X 1 Σ g + (0–7) bands of N2, which are relevant to analyze the spectra of the atmospheres of the Earth, Titan, and Mars, are reported. The known interaction between the c 4 ′ 1 Σ u + ( 4 ) and c 3 1 Π u + ( 4 ) Rydberg states and the b ′ 1 Σ u + ( 13 ) valence state has been dealt with through an appropriate rovibronic energy matrix. Deviations in the intensity distribution of the rotational lines from considerations based on Hönl–London factors have been found for each of the studied bands. Emission branching ratios for the above bands and lifetimes of the rotational levels of the v = 4 level of the c 4 ′ 1 Σ u + state are also reported.

Model potential study of Rydberg one-electron spectrum of thallium

Semi-empirical model potential calculations of excitation energies, fine structure splittings, oscillator strengths and line strengths ratios were computed for high Rydberg transitions in principal, sharp and diffuse series of thallium one-electron spectrum with allowance for core–valence electron correlations in core polarization picture. Relativistic effects are fully included through solving Dirac equations and core–valence electron correlation is represented in core polarization picture by appropriate term in model potential optimized to reproduce ionization energies of the system for lowest states of given |nlj〉 symmetry. The dipole-moment operator of transition is modified in accordance. Systematic trends are investigated in line strength ratios and oscillator strengths along the spectral series, the latter showing hydrogen-like behavior for large n* effective quantum number of upper states of transition. The influence of core–valence correlation (core polarization) on line strength ratios and oscillator strengths along the spectral series is studied in detail demonstrating its importance even for transitions to highly excited Rydberg states with n=20. The strong effect of cancellation of positive and negative contributions to transition matrix element was observed for oscillator strengths and line strength ratios in principal series of thallium spectrum.

Atomic Data Needs in Astrophysics: The Galactic Center “Scandium Mystery”

Investigating the Galactic center offers unique insights into the buildup and history of our Galaxy and is a stepping stone to understand galaxies in a larger context. It is reasonable to expect that the stars found in the Galactic center might have a different composition compared to stars found in the local neighborhood around the Sun. It is therefore quite exciting when recently there were reports of unusual neutral scandium, yttrium, and vanadium abundances found in the Galactic center stars, compared to local neighborhood stars. To explain the scandium abundances in the Galactic center, we turn to recent laboratory measurements and theoretical calculations done on the atomic oscillator strengths of neutral scandium lines in the near infrared. We combine these with measurements of the hyper fine splitting of neutral scandium. We show how these results can be used to explain the reported unusual scandium abundances and conclude that in this respect, the environment of the Galactic center is not that different from the environment in the local neighborhood around the sun.

Extended calculations of energy levels, radiative properties, and lifetimes for nitrogen-like Zr XXXIV

Highly accurate calculations are performed for the lowest 272 fine-structure levels arising from the 2s22p3, 2s2p4, 2p5, 2s22p23l, 2s2p33l, and 2p43l configurations in N-like Zr XXXIV using two state-of-the-art methods, second-order many-body perturbation theory and multiconfiguration Dirac–Fock. Complete and consistent atomic data, including excitation energies, wavelengths, E1, E2, M1, M2 line strengths, oscillator strengths, transition rates, and lifetimes for these 272 levels, are provided. Comparisons are made between the present two data sets, as well as with other available results. The present data are accurate enough for identification and deblending of emission lines involving the n=3 levels and are also useful for modeling and diagnosing fusion plasmas. These data can be considered as a benchmark for other calculations.

Extended calculations of energy levels, radiative properties, and lifetimes for oxygen-like Mo XXXV

Employing two state-of-the-art methods, second-order many-body perturbation theory and multiconfiguration Dirac–Fock, highly accurate calculations are performed for the lowest 318 fine-structure levels arising from the 2s22p4, 2s2p5, 2p6, 2s22p33l, 2s2p43l, 2p53l, and 2s22p34l configurations in O-like Mo XXXV. Complete and consistent atomic data, including excitation energies, lifetimes, wavelengths, and E1, E2, M1 line strengths, oscillator strengths, and transition rates among these 318 levels are provided. Comparisons are made between the present two data sets, as well as with other available experimental and theoretical values. The present data are accurate enough for identification and deblending of emission lines involving the n=3,4 levels and are also useful for modeling and diagnosing fusion plasmas. These data can be considered as a benchmark for other calculations.

Study of energies and oscillator strengths of Fe XXI including plasma shielding effects

We present a theoretical study of plasma shielding effects on the energies and oscillator strengths among the levels of the 2s22p2, 2s2p3, and 2p4 configurations of Fe XXI under dense plasma conditions using two kinds of ion sphere potentials combined with the multi-configuration Dirac–Fock model. The relativistic effects, electronic correlation effects, and higher order corrections from the Breit interaction, quantum electrodynamics and the finite nuclear size in the above atomic system are included in the calculations to make the results more precise. The plasma-free values obtained in this work are compared with those from other theories and experiments. Satisfactory agreement is found between them. Systematic trends are observed for all the properties under study with respect to increased temperature and electron density. Our results show that the energy shift of most of the levels becomes more sensitive to the plasma electron density when the plasma electron temperature is lower, while the oscillator strengths of the transition lines vary very little at the range of plasma conditions considered. The present results should be useful for diagnostics as well as for precise spectral modeling in fusion plasmas.

Strong and selective isotope effect in the vacuum ultraviolet photodissociation branching ratios of carbon monoxide

Rare isotope (13C, 17O and 18O) substitutions can substantially change absorption line positions, oscillator strengths and photodissociation rates of carbon monoxide (CO) in the vacuum ultraviolet (VUV) region, which has been well accounted for in recent photochemical models for understanding the large isotopic fractionation effects that are apparent in carbon and oxygen in the solar system and molecular clouds. Here, we demonstrate a strong isotope effect associated with the VUV photodissociation of CO by measuring the branching ratios of 12C16O and 13C16O in the Rydberg 4p(2), 5p(0) and 5s(0) complex region. The measurements show that the quantum yields of electronically excited C atoms in the photodissociation of 13C16O are dramatically different from those of 12C16O, revealing strong isotope effect. This isotope effect strongly depends on specific quantum states of CO being excited, which implies that such effect must be considered in the photochemical models on a state by state basis.

The Belgian Repository of fundamental Atomic data and Stellar Spectra (BRASS)

AbstractThe Belgian Repository of fundamental Atomic data and Stellar Spectra (BRASS) aims to provide one of the largest systematic and homogeneous quality assessment to date of literature atomic data required for stellar spectroscopy. By comparing state-of-the-art synthetic spectrum calculations with extremely high-quality observed benchmark spectra, we have critically evaluated fundamental atomic data, such as line wavelengths and oscillator strengths, for thousands of astrophysically-relevant transitions found in the literature and across several major atomic data repositories. These proceedings provide a short overview of the BRASS project to date, highlighting our recent efforts to investigate and quality-assess the atomic literature data pertaining to over a thousand atomic transitions present in FGK-type stellar spectra. BRASS provides all quality assessed data, theoretical spectra, and observed spectra in a new interactive database under development at brass.sdf.org.