Atomic lifetime measurements (for example, by beam–foil spectroscopic techniques) of prominent lines and levels in highly charged ions of iron-group elements began decades ago with 3s-3p resonance and intercombination transitions and a few 3p-3d transitions, finding lifetimes in the order of 0.1 ns to dozens of nanoseconds for levels with electric dipole (E1) decay channels. The proximity of the 3p- and 3d-level lifetimes causes well-known problems in multi-exponential decay curve analysis. When, later on, the much longer lifetimes (in the millisecond range) of levels with only E1-forbidden decay channels were addressed in ion traps, the cascade problem initially seemed to be absent, and these long-lived levels were considered to be unique. However, proceeding from Na- and Mg-like ions to Al-like ions and "heavier" isoelectronic sequences, slow cascades appeared that could be traced to specific long-lived 3d levels that also have only E1-forbidden decay channels and thus feature level lifetimes in the same millisecond range, causing the cascade problem to re-appear and to worsen with the increasing number of electrons in the n=3 valence shell. A severe complication arises from the fact that these (often multiple) 3d decays have not been observed directly, so no lifetime measurement has been available to test the computational predictions cleanly. There is at least an astrophysical identification of such a transition in (Al-like) Fe XIV, but this is without time resolution.

Introduction: Radiative transition parameters in Cs XI are essential for analyzing its extreme ultraviolet (EUV) spectrum and modeling high-temperature plasmas in various astrophysical and fusion environments. Cs XI, a Rh I isoelectronic sequence member, exhibits complex spectral features due to strong configuration interactions involving the ground configuration 4d⁹ and excited configurations such as 4d⁸nℓ, 4d⁷nℓ², and 4p⁵4d¹⁰. Previous studies have reported several energy levels and transition arrays, particularly 4d⁹ -4d⁸5p and 4d⁹ - 4d⁸4f; however, the strong mixing effects with the 4p⁵4d¹⁰ configuration were not thoroughly considered. Consequently, a re-examination of Cs XI is necessary to improve the accuracy of transition probabilities and energy levels.

Methods: Comprehensive atomic structure calculations were performed using Cowan’s code suite, incorporating configuration interaction (CI) and valence–valence correlation effects. The LOPT code was used to optimize the known energy levels and to compute Ritz wavelengths with their uncertainties. Theoretical gA-values were determined and compared with previously reported data for consistency and validation.

Results and Discussion: The present analysis confirms all significant energy levels and transitions reported in earlier studies while providing refined gA-values that show improved agreement with observed spectra. The inclusion of configuration mixing with 4p⁵4d¹⁰ substantially enhances the accuracy of transitions involving 4d⁸4f levels. The calculated gA-values and associated uncertainties provide reliable data for plasma diagnostics and modeling of EUV spectra.

Conclusion: This study systematically re-evaluates Cs XI atomic parameters using extended HFR calculations. All known levels of Cs XI were optimized using the LOPT scheme, and thereby evaluated Ritz wavelengths were presented. The inclusion of the 4p⁵4d¹⁰ configuration leads to enhanced accuracy and consistency in theoretical energy levels and gA-values. The refined dataset strengthens the reliability of Cs XI atomic data, which would be a valuable resource for spectroscopic studies and plasma modeling in laboratory and astrophysical applications.

Introduction:
Spectral lines of krypton (Kr V–VII) have been observed in the UV spectrum of the hot DO-
type white dwarf RE 0503–289. About ten spectral lines of Kr V and fourteen lines of Kr VI
have been used to determine the krypton abundance of it (Rauch et al. 2016; doi:
10.1051/0004-6361/201628131). Rauch et al. provided extensive atomic data (Kr IV–VII)
without any uncertainty estimates. However, reliable and evaluated atomic data of these ions
are essential for abundance determination. Recently, we evaluated transition probabilities for
Kr VI. In this work, we intended to perform the same for the Kr V spectrum and its detailed
comparison with the literature data.
Methods:
The theoretical calculations of the Kr V ion have been performed using the Cowan suite of
codes, in which the pseudo-relativistic Hartree–Fock (HFR) method is implemented. Multiple
comparison schemes were employed for transition probability evaluation.
Results and Discussion:
We used different HFR models with a varying number of configurations to compute the
transition probabilities. The transition probability data from these models and the data in the
literature were compared with each other. In general, the agreement between different data
sets was found to be satisfactory. The evaluated radiative transition parameters of Kr V-VI
lines relevant to the spectrum of the white dwarf RE 0503–289 have been tabulated.
Conclusion:
The transition probabilities were obtained from multiple extended HFR calculations for these
ions. The critical evaluation of transition probability data for Kr V-VI has been performed.
The reliable radiative transition parameters have been provided for Kr V–VI spectral lines
observed in the RE 0503–289 spectrum, along with their accuracy estimates.

Optical trapping of alkali atoms such as rubidium (Rb) and cesium (Cs) underpins many modern quantum technologies, including atomic clocks, quantum information processing, and precision spectroscopy. While J-dependent polarizabilities and magic wavelengths of the $5S_{1/2}\rightarrow5P_{1/2,3/2}$ transition in Rb and the $6S_{1/2}\rightarrow6P_{1/2,3/2}$ transition in Cs are well studied, significant gaps remain in understanding hyperfine (F-dependent) polarizabilities and vector contributions. These effects are crucial for hyperfine qubits, where differential light shifts introduce decoherence, and for optical clocks, where vector polarizability can limit accuracy at the $10^{-16}$ level. We employ a relativistic all-order (AO) single–double (SD) method to calculate highly accurate dipole matrix elements and hyperfine-dependent wavefunctions. Both static ($\omega = 0$) and dynamic polarizabilities near the D1 and D2 lines are analyzed to identify magic wavelengths. For Rb $5S_{1/2}(F=1,2)$ and Cs $6S_{1/2}(F=3,4)$ ground states, we present complete sets of scalar, vector, and tensor polarizabilities. The dominant contributions arise from $5P$ and $6P$ states, while core and tail terms are small but non-negligible. Our calculations reveal strong cancellations in tensor components, large resonance-driven variations in dynamic polarizabilities, and precise magic wavelengths for both species. Vector components, particularly in Cs, were found to significantly alter trapping conditions. This work establishes a comprehensive framework for F-dependent polarizability calculations in alkali atoms. By combining relativistic all-order methods with full vector light-shift treatment, we provide benchmark data enabling precision optical trapping, state-insensitive magic wavelengths, and improved control for quantum simulation, metrology, and quantum information applications.

Effects of semi-classical plasma on the doubly excited singlet S states of Ps^- have been investigated. The effective interaction potential in semi-classical plasmas is modelled by a pseudopotential containing two adjustable parameters: screening parameter μ and the de Broglie wavelength of the pair of interacting particles λ. The parameter μ takes care of the collective screening effect, whereas the parameter λ describes the quantum mechanical effect of diffraction at short distances. An extensive highly-correlated Hylleraas-type wavefunction containing 715 square integrable functions with a scaling parameter is employed in the stabilization method to identify the doubly excited states (DESs). The energies and the widths of the DESs are then calculated by fitting the density of the resonant states with the Lorentzian profile. Convergence of the energy and width of each identified state is corroborated by increasing the number of terms in the employed wavefunction. For the plasma-free case, we have been able to identify four DESs lying below the Ps (n=2) excitation threshold. Computed energy and width of those states are in excellent agreement with some reliable results in the literature. An inclusive study is then made on the changes in the energy and width of these states subject to the variation of μ and λ. Our findings reveal that energies of the DESs increase with respect to the increasing λ at a given μ. However, variation of the width with respect to λ at a given μ is distinctive. We hope that our findings of this paper will provide fruitful information to the research communities in plasma physics, atomic physics and astrophysics.

Introduction:
Precise atomic data serve as an indispensable diagnostic probe across a wide range of studies, including atomic physics, astrophysics, cosmology, and industrial plasma physics. Specifically, such data for singly ionised silicon (Si II) in the IR region are crucial for determining the elemental abundances in hot A- and B-type stars, and to probe cooler gas components that do not emit strongly at visible wavelengths. The currently available data of Si II in the NIST Atomic Spectra Database (ASD) lack the desired accuracy and precision; hence, their applications are limited. This work aimed to procure a more accurate and at least ten times more precise spectral data for Si II in the near-IR to mid-IR region using Fourier transform spectroscopy (FTS).

Methods:
To enhance the quality of existing spectral data, we have conducted a comprehensive analysis of 8 high-resolution Si spectrograms, covering a broad IR wavenumber region of 7850–54000 Å (1852–12737 cm⁻¹), recorded on a 1 m FT spectrometer at KPNO, AZ, USA. These spectrograms were meticulously analysed using the XGREMLIN software package to determine various line parameters precisely. A rigorous wavenumber calibration was performed for each spectrogram using well-known low-excitation lines of the buffer gases (Ne I, Ar I-II) and molecular CO.

Results and Discussion:
In this work, we report 37 unique Si II lines in the IR region, whose accurately determined measurements were obtained from different spectrograms recorded under different experimental conditions/sources. A direct comparison of our data with the NIST ASD shows that our measurements offer at least a ten-fold improvement in accuracy.

Conclusion:
The present work on spectral data of Si II in the IR region provides significantly improved precision and reliability for astrophysical and laboratory applications.

The exponential growth of experimental and theoretical data in atomic collision physics demands new strategies beyond traditional tabulations. We present a paradigm shift toward intelligent databases: curated, self-consistent, and predictive data collections powered by machine learning (ML). Our approach combines unsupervised learning for automated data cleaning with deep neural networks (NNs) for interpolation and prediction across broad parameter spaces.

We illustrate this framework with two recent open-source tools: ESPNN [1] and IKEBANA [2]. The code ESPNN uses a DBSCAN-based filtering algorithm to remove outliers from the IAEA stopping power database [3] and trains a deep NN to predict electronic stopping power cross sections for any ion–atomic target pair with a mean absolute percentage error (MAPE) below 6%.
The code IKEBANA, on the other hand, is a machine learning model trained on a recent and comprehensive compilation of experimental K-shell ionization
cross sections [4]. It uses only atomic number and overvoltage as inputs, achieving R² > 0.997 on unseen test data, even for elements with no experimental measurements.

We extend this methodology to new domains: (i) an NN trained on extensive Continuum Distorted Wave (CDW) calculations reproduces ion-impact ionization cross sections with high fidelity; and (ii) a novel transformer-based architecture is under development to predict stopping power in molecular targets, overcoming limitations of atomic additivity rules. These ML-driven databases not only reconcile historical discrepancies but also guide future experiments by identifying regions of high uncertainty or missing data. By transforming passive compilations into active, predictive knowledge engines, intelligent databases represent a powerful tool for both fundamental research and applied simulations in atomic physics.

References:

[1] F. Bivort Haiek et al., J. Appl. Phys. 132, 245103 (2022).
[2] D.M. Mitnik et al., Atoms 13, 80 (2025).
[3] https://www-nds.iaea.org/stopping/
[4] S.P. Limandri et al., At. Data Nucl. Data Tables 166, 101756 (2024).

Accurate computation of collisional rates requires a precise description of the ionic targets involved. However, obtaining an adequate atomic structure often entails significant computational effort. The optimization of target wavefunctions typically relies on configuration interaction (CI) expansions, where additional configurations are included to improve accuracy. The radial orbitals are generated using model potentials that depend on adjustable scaling parameters, whose variation can produce erratic behavior in the results. Consequently, the lack of a systematic procedure for parameter tuning remains a major limitation.

In this work, we implement a Bayesian optimization approach based on Gaussian processes (GPs) to refine the atomic structure of ions. This machine learning technique efficiently minimizes scalar-valued error functions and provides a data-driven framework for systematic optimization. The methodology can be extended from scalar-valued to multi-objective (vector-valued) optimization to simultaneously improve several atomic properties such as energies and oscillator strengths. The scaling parameters of the model potentials are treated as variables within the Bayesian framework, allowing automatic exploration of the parameter space.

The atomic structures of Be and Mg are calculated using the AUTOSTRUCTURE code [1]. The resulting energies and oscillator strengths of the lowest-lying terms show agreement with experimental values within 1% and 10%, respectively, demonstrating the efficiency of the proposed method. The optimized atomic structures obtained are tested by comparing our electron impact excitation results with benchmark results [1, 2, 3]. This approach was proven to provide a robust and general tool for optimizing atomic structure calculations in collisional studies.

References:
[1] Badnell N R 2011 Comput. Phys. Commun. 7 1528
[1] Zatsarinny O et al. 2016 J. Phys. B 49 235701
[2] Ballance C P et al. 2003 Phys. Rev. A 68 062705
[3] Barklem, P. S., Osorio, Y., Fursa, D. V., et al. 2017, A&A, 606, A11

Current state-of-the-art calculations for simple atomic systems routinely include the dominant bound-state QED contributions. To incorporate higher-order effects within relativistic atomic theory, a range of approaches based on the Dirac–Coulomb–Breit Hamiltonian has been developed. Although non-perturbative techniques are widely used, perturbation theory remains highly efficient, particularly in a recursive form that permits access to arbitrarily high orders. In Ref. [1], such a recursive perturbative framework was combined with a finite basis built from Slater determinants of one-electron orbitals generated using the dual kinetic balance approach [2]. This strategy enabled accurate evaluation of interelectronic-interaction effects on the energy levels of lithium-like and boron-like ions [1,3], and its extension to quasi-degenerate configurations allowed for analogous studies for helium-like systems [4,5]. Furthermore, this formalism was applied to compute the impact of interelectronic interactions on nuclear-recoil contributions in these ions [3,6].

Accurate predictions for magnetic-interaction observables such as the g-factor and hyperfine splitting require a consistent treatment of the negative-energy part of the Dirac spectrum. A dedicated method addressing this issue was introduced in Ref. [7], enabling the evaluation of third- and higher-order interelectronic-interaction corrections to the g-factor and hyperfine structure in lithium-like ions [7–9]. Extending the recursive construction to handle multiple perturbations makes it possible to quantify more delicate effects, including many-electron QED contributions [7,9] and nuclear-recoil terms [10-12]. Leading first- and second-order contributions have been obtained rigorously within bound-state QED, and together these results provide the most accurate theoretical values to date for the g-factor of lithium- and boron-like ions.

[1] D. A. Glazov et al., Nucl. Instr. Meth. Phys. Res. B 408, 46 (2017)
[2] V. M. Shabaev et al., Phys. Rev. Lett. 93, 130405 (2004)
[3] A. V. Malyshev et al., Phys. Rev. A 96, 022512 (2017)
[4] A. V. Malyshev et al., Phys. Rev. A 99, 010501(R) (2019)
[5] Y. S. Kozhedub et al., Phys. Rev. A 100, 062506 (2019)
[6] A. V. Malyshev et al., Phys. Rev. A 101, 052506 (2020)
[7] D. A. Glazov et al., Phys. Rev. Lett. 123, 173001 (2019)

Introduction

Recent decades have seen steady interest in the determination of the electronic g-factor of highly charged ions. Comparison of theoretical calculations and experimental measurements provides precise tests of bound-state QED and has already led to the most accurate determination of the electron mass value. High-Z ions provide unique conditions with the strongest electromagnetic fields for electrons, which makes them extremely sensitive to possible variations in fine structure constant and manifestations of dark matter.

This study is devoted to theoretical calculations of the electronic g-factor of boron-like high-Z ions in the 2p3/2 excited state. Consideration of B-like ions, on the one hand, allows us to perform theoretical calculations accurately enough. On the other hand, it is more suitable for experimental studies, due to the complexity of ion production with the innermost shell ionization. From an experimental point of view, it is also important to describe not only the 2p1/2 ground state, but also the 2p3/2 excited state, since they can both be measured in a single setup.

Methods

The total g-factor value includes corrections for the finite nuclear size and nuclear recoil effects, screened QED, and interelectronic interaction. The one-photon exchange and one-loop radiative corrections are evaluated rigorously within the QED formalism. The electron-correlation contributions of the second and higher orders are accounted for within the Breit approximation. Two-loop and higher orders of QED corrections have been estimated employing the non-relativistic estimation.

Results and Discussion

We presented total g-factor values for several high-Z boron-like ions in the 2p3/2 state. Contributions of interelectronic interaction and one-loop QED are presented for different screened potentials. The accuracy of the total values is limited by the two-loop QED contributions.

Conclusions

Obtained results in comparison with experimental data may be applied for determination of fundamental constants, bound-state QED tests, or the search for New Physics.