Vanishing of the atomic form factor derivatives in non-spherical structural refinement – a key approximation scrutinized in the case of Hirshfeld atom refinement

When calculating derivatives of structure factors, there is one particular term (the derivatives of the atomic form factors) that will always be zero in the case of tabulated spherical atomic form factors. What happens if the form factors are non-spherical? The assumption that this particular term is very close to zero is generally made in non-spherical refinements (for example, implementations of Hirshfeld atom refinement or transferable aspherical atom models), unless the form factors are refinable parameters (for example multipole modelling). To evaluate this general approximation for one specific method, a numerical differentiation was implemented within the NoSpherA2 framework to calculate the derivatives of the structure factors in a Hirshfeld atom refinement directly as accurately as possible, thus bypassing the approximation altogether. Comparing wR 2 factors and atomic parameters, along with their uncertainties from the approximate and numerically differentiating refinements, it turns out that the impact of this approximation on the final crystallographic model is indeed negligible.

Energy levels and transition probabilities of N+, F3+, and Ne4+ ions

Term energies, oscillator strengths, transition probabilities, and transition wavelengths among the low-lying states of (1s2)2s22p2, 2s22p3p, 2s2p3, 2s22p3s, and 2s22p3d 1,3,5L L = S, P, D, F in N+, F3+, and Ne4+ ions were calculated by using the multiconfiguration Rayleigh-Ritz variation method and restricted variation method. The transition oscillator strengths and transition probabilities for the electric dipole transitions are both given in length and velocity gauges. Deviations between these two gauge values are discussed. The calculated atomic parameters are in good agreement with the observed experimental results and other theoretical data. Furthermore, the uncertainty of each electric dipole transition is estimated. Several uncertainties of transition parameters are improved when comparing with values from national institute of standards and technology NIST database. Atomic parameters presented in this paper should be useful for identifying the levels as well as for precise spectral modeling in astrophysical and laboratory plasmas in the future work.

Development of NIST Atomic Databases and Online Tools

Over the last 25 years, the atomic standard reference databases and online tools developed at the National Institute of Standards and Technology (NIST) have provided users around the world with the highest-quality data on various atomic parameters (e.g., level energies, transition wavelengths, and oscillator strengths) and online capabilities for fast and reliable collisional-radiative modeling of diverse plasmas. Here we present an overview of the recent developments regarding NIST numerical and bibliographic atomic databases and outline the prospects and vision of their evolution.

Atomic parameters of Hf XLVIII, Ta XLIX, Os LII, Pt LIV, and Au LV

Ab initio multiconfiguration Dirac-Fock calculations are performed for energy levels and lifetimes of the lowest 115 fine-structure levels generated from the 3s²3p⁶3d⁷, 3s²3p⁵3d⁸, 3s3p⁶3d⁸, 3s²3p⁴3d⁹, and 3s3p⁵3d⁹ configurations of Hf XLVIII, Ta XLIX, Os LII, Pt LIV, and Au LV of fusion interest. Furthermore, radiative rates are calculated for all electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole transitions. Electron correlation is treated through multiconfiguration expansions in the active space approximation. The Breit interaction and the leading quantum electrodynamic corrections, in the form of self-energy and vacuum polarization, are included. Another theoretical attempt, based on the Flexible Atomic Code is presented for the atomic structure to serve as an independent check of the MCDF values and the results show fairly good agreement with the MCDF ones. Comparisons are made with available results in the literature. The uncertainties of our energies and strong transition rates are found to be approximately 0.25% and 2%, respectively. The extended and consistent data presented in this study should be of notable interest in various fusion research.

Plasma-environment effects on K lines of astrophysical interest

Aims. In the context of black-hole accretion disks, we aim to compute the plasma-environment effects on the atomic parameters used to model the decay of K-vacancy states in moderately charged iron ions, namely Fe IX – Fe XVI. Methods. We used the fully relativistic multiconfiguration Dirac–Fock method approximating the plasma electron–nucleus and electron–electron screenings with a time-averaged Debye–Hückel potential. Results. We report modified ionization potentials, K-threshold energies, wavelengths, radiative emission rates, and Auger widths for plasmas characterized by electron temperatures and densities in the ranges 105−107 K and 1018−1022 cm−3. Conclusions. This study confirms that the high-resolution X-ray spectrometers onboard the future XRISM and Athena space missions will be capable of detecting the lowering of the K edges of these ions due to the extreme plasma conditions occurring in accretion disks around compact objects.

How do Uncertainties in Atomic Parameters Influence Theoretical Predictions of X-Ray Production Cross Sections By Proton Impact?

The emission of characteristic X-rays induced by proton impact is a phenomenon known since the first half of the 20th century. Its more widely known application is the analytical technique Particle Induced X-ray Emission (PIXE). Several models have been developed to calculate, first, ionization cross sections and then the subsequent X-ray production cross sections. However, to carry out the comparisons of these predictions with experimental data it is necessary to use atomic parameters databases (fluorescence yields, Coster-Kronig transition probabilities, emission rates) that also have experimental uncertainties. In this work it is demonstrated how these values do not allow to decide which model describes more accurately the cross sections, due to a final “theoretical uncertainty” obtained through the propagation of the original uncertainties.