The Kβ/Kα intensity ratios are critical parameters that quantitatively characterize atomic shell transition dynamics and radiative branching probabilities. In this study, we systematically evaluated the capability of machine learning (ML) algorithms to predict these ratios, as well as their advantages over traditional theoretical models (such as Scofield and semi-empirical calculations). A large dataset comprising 2124 experimental measurements compiled from the literature, covering elements with atomic numbers (Z) from 11 to 96, was structured to include more than ten variables, such as atomic number, sample form, excitation source, detector type, and energy resolution. Missing observations were imputed using the multivariate imputation by chained equations (MICE) method in the R programming language. Categorical variables were one-hot encoded, and the data were split into an 80% training set and a 20% test set. Seven heterogeneous individual models (RF, XGBoost, Cubist, SVR, GPR, BRNN, and GLMNET) were constructed, along with seven different stacking combinations derived from them. Following 10×10-fold cross-validation, the highest accuracy was achieved by the stacked model using a BRNN meta-learner (RMSE = 0.009; R2 = 0.973). This model reduced the test error of the Scofield theory by nearly 48% and performed significantly better according to the Diebold-Mariano test (p < 0.001). SHAP analysis revealed that atomic number is the primary determinant, while sample purity and excitation source have secondary yet physically consistent effects. Furthermore, an online R/Shiny-based calculator enhances the practical applicability of the method by enabling users to input their experimental parameters and receive instantaneous Kβ/Kα predictions. These results demonstrate that at the current stage of theoretical and experimental development, data-driven approaches provide significant advantages in both accuracy and interpretability over classical theories for complex atomic parameters such as the Kβ/Κα intensity ratio. Overall, this work constitutes a significant step toward reducing deviations in high-Z elements, improving detector calibration, and establishing new atomic databases.

The early spectra of the kilonova AT2017gfo following the binary neutron star merger GW170817 exhibit numerous features shaped by r-process nucleosynthesis products. Although a few species were tentatively detected, no third-peak elements were unambiguously identified, as the amount of atomic data required for radiative transfer modeling is immense. Although comprehensive atomic data, including atomic opacities, is now available for many elements, wavelength-calibrated data remain limited to a few selected ions. To examine the atomic opacities of all singly and doubly ionized lanthanides, from La (Z = 57) to Yb (Z = 70), we perform atomic structure calculations using the FAC code. Our calculations incorporate an innovative optimization of the local central potential and the number of configurations considered, alongside a calibration technique aimed at enhancing agreement between theoretical and experimental atomic energy levels. We assess the accuracy of the computed data, including energy levels and electric dipole (E1) transition strengths, as well as their impact on kilonova opacities. We find that strong transitions [log(gf) > -1] are in good agreement with both experiments and semiempirical calculations. For ions with substantial experimental data, the computed opacities exhibit good agreement with prior calculations. By calibrating low-lying energy levels with experimental data, we have identified 66 722 transitions with experimentally calibrated wavelength information, rendering future lanthanide line identifications through radiative transfer modeling feasible. In total, our calculations encompass 28 ions, yielding 146 849 energy levels below the ionization threshold and 29 337 507 transitions among these levels.

This work presents a comprehensive analytical investigation of Coster-Kronig transition probabilities f12, f13, f23, F1, and F123 for elements with atomic numbers 28 <= Z <= 98. Experimental data from our previous studies were systematically compiled and employed to construct smooth empirical trends by polynomial interpolation so as to represent the variation of these transitions across the different elements. In parallel, new theoretical values were calculated for selected elements using the Multiconfiguration Dirac-Fock (MCDF) method, incorporating relativistic effects. When compared with available theoretical and experimental data the results show good agreement, especially for medium and heavy elements. These new results provide reliable reference data for modeling L-shell vacancy decay processes and support a range of applications in atomic physics, X-ray spectroscopy, and radiation interaction studies.

In this study, we use the relativistic multiconfiguration Dirac-Fock method (MCFD) to compute the probabilities of radiative and radiationless vacancy transfer from K- to L-1-,L- L2-, and( L3_) subshells in S-16, Ar-18, Ti-22, Cu-29, Zn-30, Ge-32, As-33, Se-34, Kr-36, Zr-40, Cd-48, Sn-50, Te-52, Hg-80, Bi-83, and( 86)Rn atoms. Semi-theoretical calculations for elements within the atomic range of 18 < Z < 96 (Ar-18 to( 96)Cm) were also conducted, leveraging available data on radiative and radiationless transitions from the scientific literature. The theoretical calculation results aligned well with the values calculated semi-theoretically and with other published works. However, some notable differences were identified.

X-ray spectra linewidths have been measured in Nb, Mo, and Rh. From the obtained experimental values, the K , L 2 , and L 3 level widths were estimated and compared with the recommended and semi-empirical values, as well as our theoretical results.

This work presents a comprehensive analytical investigation of Coster–Kronig transition probabilities , , , , and for elements with atomic numbers . Experimental data from our previous studies were systematically compiled and employed to construct smooth empirical trends by polynomial interpolation so as to represent the variation of these transitions across the different elements. In parallel, new theoretical values were calculated for selected elements using the Multiconfiguration Dirac–Fock (MCDF) method, incorporating relativistic effects. When compared with available theoretical and experimental data the results show good agreement, especially for medium and heavy elements. These new results provide reliable reference data for modeling L-shell vacancy decay processes and support a range of applications in atomic physics, X-ray spectroscopy, and radiation interaction studies.

K alpha 1,2, L alpha 1,2, and L beta 1 X-ray spectra linewidths have been measured in elements Nb, Mo, and Rh, using a high-resolution double-crystal X-ray spectrometer. From the obtained experimental values, Gamma K, Gamma L2, and Gamma L3 level widths were estimated and compared with the recommended and semi-empirical ones, and our theoretical results. The overall tendency of the corrected full width at half maximum of the K alpha 1 and K alpha 2 lines as a function of Z agrees with the data in the literature.

The significance of theoretical, experimental, and analytical methods in calculating the intensity ratios of L-shell transitions for diverse elements lies in their widespread applications across various domains, including physical chemistry and medical research. In the present paper, empirical values for intensity ratios were computed through polynomial interpolations using experimental databases within the scope of atomic number 39 <= Z <= 92 for IL beta and IL gamma IL alpha, and extending to the range of 39 <= Z <= 94 for ILl IL alpha. Additionally, new theoretical calculations were IL alpha conducted using the Multiconfiguration Dirac-Fock Method for specific elements. The obtained results were compared with standard theoretical, experimental, and empirical values, showing a reasonable agreement with them.

We measure the energy-differential cross sections for collisional excitation of the soft x-ray electric-dipole K alpha (x + y + w) emission from He-like oxygen (O VII), using an electron beam ion trap. Values near their excitation thresholds were extracted from the observed emissivity by rapidly cycling the energy of the exciting electron beam. This allows us to subtract time-dependent contributions of the forbidden z-line emission to the multiplet. We develop a time-dependent collisional-radiative model to further demonstrate the method and predict all spectral features. We then compare the extracted x + y + w cross sections with calculations based on distorted-wave and R-matrix methods from the literature and our own predictions using the FLEXIBLE ATOMIC CODE. All R-matrix results are validated by our measurements of direct and resonant excitation, supporting the use of such state-of-the-art codes for astrophysical and plasma physics diagnostics.

In this study, a comprehensive dataset of X-ray emission intensity ratios has been compiled, including IL beta/IL alpha, IL gamma/IL alpha, ILl/IL alpha, IL gamma/IL beta, ILl/IL gamma, ILl/IL beta, IL gamma 5/IL alpha, IL gamma 44 '/IL alpha, IL eta/IL alpha, and IL gamma 1/IL alpha, extracted from literature spanning the years 1971 to 2023, and encompassing 83 research papers. Over this timeframe, a total of 2600 values were collected, comprising some 678 values for IL beta/IL alpha, 696 values for IL gamma/IL alpha, 617 values for ILl/IL alpha, along with 132, 132, 89, 60, 70, 71, and 55 data points for IL gamma/IL beta, ILl/IL gamma, ILl/IL beta, IL gamma 5/IL alpha, IL gamma 44 '/IL alpha, IL eta/IL alpha, and IL gamma 1/IL alpha, respectively. The reported values are presented with precision up to three to four decimal places, accompanied by their associated uncertainties. Additionally, the tables include calculated weighted averages (ILi/ILj)W, uncertainty values (epsilon ISD, epsilon ESD), combined standard deviations (zISD, zESD), and average z-scores (zISD, zESD) for these intensity ratios. The data encompasses elements ranging from 39Y to 94Pu when excited by photon bombardment. The assessment of how these experimental data values are distributed according to atomic number indicates extensive coverage across most elements. However, a few isolated instances were identified where either no data or fewer than two data values were available.

The main purpose of this paper is to collect from various sources over 3300 experimental values of K-shell fluorescence cross sections (σKβ1,3,σKβ2,4,σKα1,σKα2,σKβ1,σKβ2,σKβ′1,σKβ′2,σKα,σKβ and σKtot) of elements with atomic number in the range 16≤Z≤92by photo-ionization in multiple excitation energy ranging from 5.46 to 661.6 keV, which are presented in a form of 11 tables. The experimental values reported in 96 papers by numerous researches were published between 1985 and 2023. Therefore, by considering in the same tables a calculation of weighted average fluorescence cross section (σKj)W, with (j=β1,3,β2,4,α1,α2,β1,β2,β′1,β′2,α,βandtot) for each element; a full study of these data is carried out. However, dividing the measured values (σKj)Expby the weighted average (σKj)W, a new weighted means ratio SW=(σKj)Exp/(σKj)Ware also studied.

In the present work, we offer a collection of documented values for vacancy transfer probabilities (ηXY, X=K,Li; Y=L,M,N,Li,Mj,Np,Op; i=1,2,3;j=1,2,3,4,5;p=1,4,5) sourced from published technical literature spanning 1993 to 2023 for elements in the atomic range 16≤Z≤92. We found 1200 experimental vacancy transfer probability values from 68 scientific papers, during the specified period. These have been compiled and summarized in tables, encompassing various parameters and elements. This data is also comprehensively analysed, including tables that display weighted average vacancy transfer probability (ηXY)W values along with the combined standard deviation and the average z-score. We also recommend a new collection of empirical values for the atomic parameters ηKL(T),ηKL2(R), ηKL3(R),andηKM(R) of vacancy transfer probabilities. This compilation offers an overview of the present state of atomic data for vacancy transfer probabilities. It is a valuable resource to guide future experimental and theoretical studies in this area.

An investigation of Cu Kα X-ray emission spectra, together with their satellite lines, using both experimental techniques and theoretical calculations, provides accurate values for the natural linewidths and other parameters of the emission lines.

In this study, semi-empirical L-1 subshells fluorescence yields (omega(L1)) were calculated from the available experimental data covering the period from 1955 to 2022 for elements with 28 <= Z <= 96 for L-1 subshell, and 23 <= Z <= 96 for L-2 and L-3 subshells. First, we critically examine these data and obtain weighted average values (omega(L1) (W), omega(L2) (W), and omega(L3) (W)) using a formula based on experimental (omega(EXP)) values and measurement errors. New recommended values omega(WR) are obtained by calculating the ratio S = omega(EXP)/omega(W) and removing out-of-range values (less than 0.8 or greater than 1.2). Semi-empirical values were derived for the three subshells using two interpolations: the analytical function [omega(WR)/(1 - omega(WR))](1/4) and the fitting ratio S = omega(EXP)/omega(WR), both as function of the atomic number Z. Furthermore, new theoretical calculations based on the Multiconfiguration Dirac-Fock Method have been performed for some elements and are presented in this work. Finally, our semi-empirically and theorical calculated L-i subshell fluorescence yields were compared with other theoretical, experimental, and empirical values from the literature.

The main objective of this study is to obtain three-dimensional empirical K-shell x-ray fluorescence cross-section ( sigma K alpha,sigma K beta and sigma Ktot) values for a wide range of elements 16 <= Z <= 92 for photons with energies from 5.46 keV to 123.6 keV, using more than 3300 experimental data values published between 1985 and 2023 by numerous researchers. These data values are fitted using an interpolation method including a three-dimensional function against atomic number Z and excitation energy E, resulting in a three-dimensional plot to estimate empirically a three-dimensional set of K alpha,K beta and Ktot x-ray fluorescence cross sections. The results of this empirical calculation are compared, for selected elements, with other empirical and experimental values reported in the literature, and a reasonable agreement is observed.

Even though the electromagnetic counterpart AT2017gfo to the binary neutron star merger GW170817 is powered by the radioactive decay of r-process nuclei, only few tentative identifications of light r-process elements have been made so far. One of the major limitations for the identification of heavy nuclei is incomplete or missing atomic data. While substantial progress has been made on lanthanide atomic data over the last few years, for actinides there has been less emphasis, with the first complete set of opacity data only recently published. We perform atomic structure calculations of neodymium (Z=60) as well as the corresponding actinide uranium (Z=92). Using two different codes (FAC and HFR) for the calculation of the atomic data, we investigate the accuracy of the calculated data (energy levels and electric dipole transitions) and their effect on kilonova opacities. For the FAC calculations, we optimise the local central potential and the number of included configurations and use a dedicated calibration technique to improve the agreement between theoretical and available experimental atomic energy levels (AELs). For ions with vast amounts of experimental data available, the presented opacities agree quite well with previous estimations. On the other hand, the optimisation and calibration method cannot be used for ions with only few available AELs. For these cases, where no experimental nor benchmarked calculations are available, a large spread in the opacities estimated from the atomic data obtained with the various atomic structure codes is observed.We find that the opacity of uranium is almost double the neodymium opacity.

In multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations, there is a strong coupling between the localization of the orbital set and the configuration state function (CSF) expansion used to determine it. Furthermore, it is well known that an orbital set resulting from calculations, including CSFs describing core–core correlation and other effects, which aims to lower the weighted energies of a number of targeted states as much as possible, may be inadequate for building CSFs that account for correlation effects that are energetically unimportant but decisive for computed properties, e.g., hyperfine structures or transition rates. This inadequacy can be traced in irregular or oscillating convergence patterns of the computed properties as functions of the increasing orbital set. In order to alleviate the above problems, we propose a procedure in which the orbital set is obtained by merging several separately optimized, and mutually non-orthogonal, orbital sets. This computational strategy preserves the advantages of capturing electron correlation on the total energy through the variational MCDHF method and allows to target efficiently the correlation effects on the considered property. The orbital sets that are merged are successively orthogonalized against each other to retain orthonormality. The merged orbital set is used to build CSFs that efficiently lower the energy and also adequately account for the correlation effects that are important for the property. We apply the procedure to compute the hyperfine structure constants for the 1s22s2S1/2 and 1s22p2P1/2,3/2o states in 7Li and show that it leads to considerably improved convergence patterns with respect to the increasing orbital set compared to standard calculations based on a single orbital set, energy-optimized in the variational procedure. The perspectives of the new procedure are discussed in a broader context in the summary.

The knowledge of atomic fundamental parameters, such as the fluorescence yields with low uncertainties, is of decisive importance in elemental quantification involving X-ray fluorescence analysis techniques. However, especially for the low-Z elements, the available literature data are either of poor quality, of unknown or very large uncertainty, or both. For this reason, the K-shell fluorescence yield of carbon was determined in the PTB laboratory at the synchrotron radiation facility BESSY II. In addition, theoretical calculations of the same parameter were performed using the multiconfiguration Dirac-Fock method, including relativistic and quantum electrodynamics (QED) corrections. Both values obtained in this work are compared to the corresponding available literature data.