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The present article discusses some recent advances in methods of critical evaluation of experimental data on wavelengths of spectral lines and theoretical data on transition probabilities and oscillator strengths for atoms and atomic ions. In particular, recently developed new statistical approaches to estimation of uncertainties of weighted means of multiple measurements are described, and a numerical toolbox implementing these new approaches is presented. There are also some new developments in estimation of uncertainties of theoretical transition probabilities. A short review of literature implementing these new procedures is provided, including a description of the methodology. Graphical abstract

The hydrogen molecular ion, H 2 + , is considered in the fixed nuclei approximation. The oscillator strengths relevant to free-bound transitions in H 2 + are presented as asymptotic expansions in an inverse power of the internuclear separation, which is assumed to be large. The asymptotic technique leads to an algebraic representation of the oscillator strengths, contrasting with numerical tables. Graphical abstract

In this study, the energy levels (E), lifetimes (τ), wavelengths (λ), transition probabilities (A), weighted oscillator strengths (gf) and line strengths (S) among the (1s2)2s22p2, 2s22p3s, 2s22p3d, and 2s2p23p configurations of carbon-like ions with Z = 21–30 were determined using the multiconfiguration Dirac–Hartree–Fock (MCDHF) method. We confirmed the reliability of the energy levels by comparing them with the results of other theoretical methods and experimental observations. The present wavelengths for C-like ions were in good agreement with the previous experimental and theoretical results, with most wavelength differences below 0.8%. Based on the relative deviation (dT) and line strengths (S), respectively, we estimated the uncertainty of the computed transition data. Out of the 1300 transitions computed in this work, 1207 (699) have uncertainties fewer than or equal to 7% as determined by dT (S). We hope these data will be utilized to expand the C-like ion database and provide reference information for experimental studies in plasma experiments.

The two-dimensional (2D) hydrogen atom is a fundamental atomic model that is important for various technologies based on 2D materials. Here, the atomic model is revisited to enhance understanding of the hydrogen wavefunctions. Unlike in previous studies, we propose an alternative expression of azimuthal wavefunctions, which are the eigenstates of the square of angular momentum and exhibit rotational symmetry. Remarkably, our expression leads to the rotation and oscillation along the azimuthal direction of the probability densities, which do not appear in the conventional wavefunctions. These behaviors are validated by the numerical results obtained through the 2D finite difference approach. Variation in oscillator strengths due to the rotation of wavefunctions is observed in our proposed 2D hydrogen wavefunctions, whereas those due to the conventional wavefunctions remain constant. More importantly, the proposed wavefunctions’ advantage is illustrating the orbital shapes of the planar hydrogen states, whose orientation is labeled here using Cartesian representation for the first time. This study can be applied to visualize the orbital characteristics of the states in quantum confinement with a radial potential.

We present excitation energies, transition wavelengths, electric dipole (E1) transition rates, oscillator strengths, line strengths, and lifetimes for the 86 lowest states up to and including 1s22s27f in N iii, the 125 lowest states up to and including 1s22s7f in N iv, and the 53 lowest states up to 1s28g in N v using the multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods. The computed results are then compared with data from the Atomic Spectra Database of the National Institute of Standards and Technology (NIST-ASD), experimental results, and other theoretical studies. For all levels in N iii – v, the root mean square energy differences from the NIST values are 130, 103, and 6 cm−1, respectively. Compared to previous multiconfiguration Hartree–Fock and the Breit–Pauli (MCHF-BP) calculations, 89.3%, 98.5%, and 100% of the log(gf) values for N iii – v agree within 5%, respectively.

Excitation energies belonging to the (1 s 2 )2 s 2 2 p 2 , 2 s 2 2 p 3 p , 2 s 2 p 3 , 2 s 2 2 p 3 s , and 2 s 2 2 p 3 d configurations of carbon-like Na VI and Al VIII have been calculated with the multi-configuration Rayleigh–Ritz variation method and restricted variation method, as well as wavelengths, line strengths, oscillator strengths, transition rates for electric dipole transitions among these terms. High-accuracy calculations have been performed using a moderate scale of Slater basis function and accurate treatments of relativity, electron correlation, and quantum electrodynamic (QED) effects. The line strengths, transition oscillator strengths, and transition probabilities for the electric dipole transitions are determined. Deviations of line strengths between the length and velocity gauges are discussed, as well as with the experimentally compiled values from the National Institute for Standards and Technology (NIST) and other theoretical data wherever available. Furthermore, the accuracy of each electric dipole transition is assessed. The present results are accurate enough for identification of emission lines involving these terms and are also useful for precise spectral modeling and diagnosing in astrophysical and laboratory plasmas.

Background The 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. Result Fourier 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. Conclusion In 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.

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.

An expression of unexpected simplicity is derived for the shift in optical transition energies of solute molecules in nonpolar solvents. The expression reveals a new spectroscopic rule that says: The higher the excited state of the solute, the larger the solvatochromic red shift. A puzzle formulated >50 years ago by Bayliss is solved. Bayliss, based on arguments from classical physics, assumed that the shift scales with the oscillator strength of the solute transition, but noted strong quantitative deviations from this rule in experiments. As the present expression shows, the shift does not depend on the oscillator strength of the transition, but reflects the change in dispersive solute-solvent interactions between the ground and excited states of the solute, that are determined by the anisotropy of intramolecular electron correlation. The theory is applied to explain the solvatochromic shifts of the two lowest electronic excitations of bacteriochlorophyll a and bacteriopheophytin a.