Atoms

20 pages, 819 KB

Open AccessEditor’s ChoiceArticle

Multiplatform Computing of Transition Probabilities in Os V

by Patrick Palmeri, Saturnin Enzonga Yoca, Exaucé Bokamba Motoumba, Alix Niels, Maxime Brasseur and Pascal Quinet

Atoms 2026, 14(3), 22; https://doi.org/10.3390/atoms14030022 - 11 Mar 2026

Viewed by 525

Abstract

Osmium is an element of the Periodic Table with an atomic number Z equal to 76. In Tokamaks with divertors made of tungsten (

Z = 74

), it is produced in the neutron-induced transmutation of the latter. Therefore one can expect that [...] Read more.

Osmium is an element of the Periodic Table with an atomic number Z equal to 76. In Tokamaks with divertors made of tungsten (

Z = 74

), it is produced in the neutron-induced transmutation of the latter. Therefore one can expect that their sputtering may generate ionic impurities of all possible charge states in the fusion plasma. As a consequence, these could contribute to radiation losses in these controlled nuclear devices. The knowledge of radiative rates in all the spectra of osmium is thus important in this field. In this framework, a multiplatform approach has been used to determine the Os V radiative properties and estimate their accuracy. The transition probabilities have been computed for the 2677 electric dipole (E1) transitions falling in the spectral range from 400 Å to 12,000 Å. Three independent atomic structure models have been considered; one based on the fully relativistic ab initio multiconfiguration Dirac–Hartree–Fock (MCDHF) method and two based on the semi-empirical pseudo-relativistic Hartree–Fock (HFR) method. Full article

(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)

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28 pages, 491 KB

Open AccessEditor’s ChoiceArticle

Extension of an Efficient Approach for Spin-Angular Integrations in Atomic Structure Calculations

by Gediminas Gaigalas

Atoms 2026, 14(3), 21; https://doi.org/10.3390/atoms14030021 - 9 Mar 2026

Cited by 2 | Viewed by 754

Abstract

In this study, an extension of the general method [G. Gaigalas, Z. Rudzikas, C. Froese Fischer, J. Phys. B, At. Mol. Phys. (1997). DOI: 10.1088/0953-4075/30/17/006] is described for finding algebraic expressions of the spin-angular parts of the reduced matrix elements of any one- [...] Read more.

In this study, an extension of the general method [G. Gaigalas, Z. Rudzikas, C. Froese Fischer, J. Phys. B, At. Mol. Phys. (1997). DOI: 10.1088/0953-4075/30/17/006] is described for finding algebraic expressions of the spin-angular parts of the reduced matrix elements of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration. This extension is related, at first, to a change in the definition of tensor structure, where a non-scalar space with respect to l and s for any two-particle operator acts on four different shells. This leads to more efficient expressions for recoupling matrices and amplitudes, which are presented in the paper. In addition, the paper presents new expressions for some of the recoupling matrices, in which 6j- and 9j-coefficients are summed up algebraically. All this leads to a significantly simpler and faster calculation of the spin-angular parts of any non-scalar two-particle operator. Full article

(This article belongs to the Special Issue Future Directions in Atomic Physics Inspired by the Pioneering Work of Charlotte Froese Fischer and Ian Philip Grant)

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12 pages, 324 KB

Open AccessEditor’s ChoiceArticle

jj to LSJ Transformation for Configuration State Functions with an Arbitrary Number of Open Shells

by Gediminas Gaigalas

Atoms 2026, 14(3), 20; https://doi.org/10.3390/atoms14030020 - 9 Mar 2026

Cited by 1 | Viewed by 953

Abstract

This paper presents a methodology that allows for calculated energy levels and other atomic characteristics in relativistic atomic theory, i.e., using the

j j

-coupling scheme, to be identified in terms of

L S J

-coupling characteristics. The paper begins with outlining the [...] Read more.

This paper presents a methodology that allows for calculated energy levels and other atomic characteristics in relativistic atomic theory, i.e., using the

j j

-coupling scheme, to be identified in terms of

L S J

-coupling characteristics. The paper begins with outlining the general principles for effectively addressing this problem. Furthermore, it provides a general expression that enables such identification when the atomic state function consists of any number of configuration state functions, each with any number of open shells, and explains how this expression was obtained. The methodology developed in this paper has been successfully implemented in the General Relativistic Atomic Structure Package and can be applied to other similar packages. Full article

(This article belongs to the Special Issue Future Directions in Atomic Physics Inspired by the Pioneering Work of Charlotte Froese Fischer and Ian Philip Grant)

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44 pages, 1063 KB

Open AccessEditor’s ChoiceArticle

Numerical Computation of Critical Binding Parameters of Screened Coulomb Potentials

by Grant B. Bunker

Atoms 2026, 14(3), 18; https://doi.org/10.3390/atoms14030018 - 5 Mar 2026

Cited by 1 | Viewed by 1516

Abstract

For nearly a century, screened Coulomb potentials have been of recognized importance in diverse areas of physics and chemistry. A key feature of interest in these potentials is the phenomenon of critical screening. This paper has three main purposes: to present an extensive, [...] Read more.

For nearly a century, screened Coulomb potentials have been of recognized importance in diverse areas of physics and chemistry. A key feature of interest in these potentials is the phenomenon of critical screening. This paper has three main purposes: to present an extensive, open-access, high accuracy (60 digit) benchmark reference dataset of critical screening parameters, with validation; to confirm excellent past work in the field (to 30 digits), and to correct an historical oversight in its literature; and to present the essentials of our new approach, the “Phase Method” (PM), for computing them. Using the PM, we calculate critical screening parameters, accurate to 60 decimal digits, for the Yukawa/Debye, Hulthén, Pseudo-Hulthén, and Exponential Cosine Screened Coulomb (ECSC)) potentials. The practical feasibility of such calculations on inexpensive hardware opens up new possibilities in research and education. We highlight an apparently overlooked 1989 paper of Demiralp on critical screening parameters of the Yukawa potential, which accurately calculated them to 30 decimal digits. Our main results are computations of the critical screening parameters

μ_{c} = 1 / D_{c}

for screening lengths

D \leq 1000

au and angular momenta

l = 0, \dots, 20

. The claimed accuracy of our results is supported by several independent lines of evidence: comparison with the most accurate (30 digit) values available in the print literature for the Yukawa, Hulthén, and ECSC potentials; comparison to 60 decimal digits accuracy with exactly known eigenvalues and critical binding parameters of the Pseudo-Hulthén potential; consistency tests between computed critical parameters, for various l-values for the Pseudo-Hulthén Potential, and known exact relations between eigenvalues; and application of a novel consistency test between results with different potential parameters, that exploits an exact scaling symmetry of this entire class of potentials. Similar calculations were done for ECSC and Yukawa potentials for screening lengths up to

D \leq 10^{5}

and

l \leq 12

, to 30 digit accuracy, which show interesting (and to our knowledge, not previously reported) periodic structure in

D_{c} (n, l)

for the ECSC potential that is not observed for the Yukawa potential. The asymptotic scaling behavior of critical parameters for the Yukawa and Hulthén potentials is explained quantitatively by simple semiclassical calculations, as is the scaling of circular states for those and other potentials. Full article

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20 pages, 361 KB

Open AccessEditor’s ChoiceArticle

Study of the Hyperfine Structure of Sr II, Ba I and Ba II: An MCDHF Approach for Modeling the Low-Lying Levels

by Lorenzo Nezosi, Lucas Maison, Patrick Palmeri, Per Jönsson and Michel Godefroid

Atoms 2026, 14(3), 17; https://doi.org/10.3390/atoms14030017 - 5 Mar 2026

Viewed by 927

Abstract

Using the Multiconfiguration Dirac–Hartree–Fock method as implemented in the General Relativistic Atomic Structure Package, the magnetic dipole and electric quadrupole hyperfine structure constants were determined for the ground and first excited levels of ^135,137Ba II isotopes, as well as for ¹³⁷Ba [...] Read more.

Using the Multiconfiguration Dirac–Hartree–Fock method as implemented in the General Relativistic Atomic Structure Package, the magnetic dipole and electric quadrupole hyperfine structure constants were determined for the ground and first excited levels of ^135,137Ba II isotopes, as well as for ¹³⁷Ba I and ⁸⁷Sr II, to assess the robustness of the developed model. This study builds upon and extends previous investigations by examining the levels involved in resonance lines, with the aim of resolving persistent discrepancies in the hyperfine structure of ¹³⁷Ba II and ⁸⁷Sr II. New code developments such as the use of natural orbitals, as well as the addition of polarization effects and Configuration State Function Generators, as implemented in GRASPG, were tested for these heavy elements. The developed strategy allowed us to achieve encouraging results that satisfactorily agree with experiments for all studied levels but

{}^{2}D_{5 / 2}

in the ¹³⁷Ba II isotope. This disagreement was also observed in ¹³⁵Ba II isotope as well as in ⁸⁷Sr II. With two valence electrons, ¹³⁷Ba I is definitely more complex, requiring a multireference approach. Even with the latter, the theory–observation disagreement observed for the hyperfine structure of the low-lying levels remains large in comparison with the alkali-like systems. Possible ongoing developments to remediate this issue are discussed in the conclusions. Full article

(This article belongs to the Special Issue Computational Atomic Physics in Astrophysics)

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13 pages, 1962 KB

Open AccessEditor’s ChoiceArticle

Dielectronic Recombination Strengths and Plasma Rate Coefficients of Lithium-like Argon Ions: Theory and Experiment

by Houke Huang, Zhongkui Huang, Yang Yuan, Hanbing Wang, Zeshan Muhammad, Chang Liu, Weiqiang Wen, Linfan Zhu, Xinwen Ma and Stephan Fritzsche

Atoms 2026, 14(2), 13; https://doi.org/10.3390/atoms14020013 - 13 Feb 2026

Viewed by 1062

Abstract

Dielectronic recombination (DR) is widely recognized as a fundamental atomic process in many astrophysical and laboratory plasmas, where it plays a crucial role in determining ionization balance and level populations over a broad temperature range. Reliable DR resonance strengths and plasma rate coefficients [...] Read more.

Dielectronic recombination (DR) is widely recognized as a fundamental atomic process in many astrophysical and laboratory plasmas, where it plays a crucial role in determining ionization balance and level populations over a broad temperature range. Reliable DR resonance strengths and plasma rate coefficients for such plasma modeling can be computed using the Jena Atomic Calculator (JAC)—a relativistic code based on the multiconfiguration Dirac–Hartree–Fock (MCDHF) method. In this work, we investigate the DR of Li-like Ar¹⁵⁺ ions in their ground state (2s), focusing on resonances associated with the fine-structure core excitations

2 s_{1 / 2} \to 2 p_{1 / 2, 3 / 2}

. The resulting fine-structure-resolved DR resonance strengths and plasma rate coefficients are in good agreement with recent high-resolution DR measurements of Ar¹⁵⁺ ions performed at the Main Cooler Storage Ring (CSRm) in Lanzhou, China. These results provide a stringent benchmark for JAC calculations and support their applicability in plasma modeling. Full article

(This article belongs to the Special Issue Computational Atomic Physics in Astrophysics)

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12 pages, 413 KB

Open AccessEditor’s ChoiceArticle

Two-Atom Superradiance Including Magnetic State Degeneracy

by Paul R. Berman

Atoms 2026, 14(2), 12; https://doi.org/10.3390/atoms14020012 - 6 Feb 2026

Viewed by 751

Abstract

The radiation pattern emitted by two atoms, interacting with each other via the vacuum radiation field, has been calculated, including effects of magnetic state degeneracy for atoms with a ground state having

G = 0

angular momentum and an excited state having [...] Read more.

The radiation pattern emitted by two atoms, interacting with each other via the vacuum radiation field, has been calculated, including effects of magnetic state degeneracy for atoms with a ground state having

G = 0

angular momentum and an excited state having

H = 1

angular momentum. For an initial condition in which both atoms are inverted, the time-integrated radiation pattern is identical to that for non-interacting atoms if the atoms lie on the z-axis, but differs if the atoms lie on the x-axis. The underlying dynamics giving rise to this behavior are examined. Full article

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20 pages, 3504 KB

Open AccessEditor’s ChoiceArticle

Study of the Triplet States in the Autoionizing Electron Spectra of He and Ar Induced by Low-Energy Electrons

by Bratislav P. Marinković, Lorenzo Avaldi and Jozo J. Jureta

Atoms 2026, 14(2), 9; https://doi.org/10.3390/atoms14020009 - 31 Jan 2026

Viewed by 606

Abstract

In this work, the He and Ar triplet autoionizing states have been studied using a non-monochromatic electron beam and a high-resolution electrostatic analyzer at low incident electron energies and three ejection angles: 40°, 90°, and 130°. Low-energy electrons have been used because they [...] Read more.

In this work, the He and Ar triplet autoionizing states have been studied using a non-monochromatic electron beam and a high-resolution electrostatic analyzer at low incident electron energies and three ejection angles: 40°, 90°, and 130°. Low-energy electrons have been used because they have a high probability of exciting triplet states regardless of whether they are discrete isolate states or are embedded in the ionization continuum. Additionally, the He ejected electron spectra have been measured at several ejection angles between 20° and 130° and two incident energies, namely 60.5 eV and 101 eV. The anisotropic angular distributions indicate that orbital angular momentum exchange between the ejected and scattered electrons occurred. The energies of the first triplets 3s3p⁶4s(³S) and 3s3p⁶4p(³P) states of argon are found to be (24.985 ± 0.020) eV and (26.52 ± 0.02) eV, respectively. Full article

(This article belongs to the Special Issue Electronic, Photonic and Ionic Interactions with Atoms and Molecules)

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11 pages, 4878 KB

Open AccessEditor’s ChoiceTechnical Note

NBODYCL: A Program to Generate Regularized Classical Trajectories for the n–Body Coulomb Problem

by Mbuso K. Matfunjwa, Harindranath B. Ambalampitiya and Ilya I. Fabrikant

Atoms 2026, 14(2), 8; https://doi.org/10.3390/atoms14020008 - 23 Jan 2026

Viewed by 1145

Abstract

A program package for calculating regularized classical trajectories for Coulomb n–body problem is developed. The Coulomb singularities from the equations of motion are removed by transformations of variables including the time. This effectively conserves the energy of the time-independent systems to a [...] Read more.

A program package for calculating regularized classical trajectories for Coulomb n–body problem is developed. The Coulomb singularities from the equations of motion are removed by transformations of variables including the time. This effectively conserves the energy of the time-independent systems to a high accuracy for long time propagation. Sample calculations are shown for the cases of 2, 3, 4, and 5 particle systems giving comparisons with the un-regularized trajectories. The program can be used for general purposes including the classical-trajectory Monte-Carlo simulations for charged-particle collisions in free or laser environments. Full article

(This article belongs to the Special Issue Collisions and Applications: Electron, Positron, and Positronium Interactions with Atoms and Molecules)

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18 pages, 799 KB

Open AccessEditor’s ChoiceArticle

Invariant Approach to the Interaction Between Several Fields and an Atom

by Marco A. García-Márquez, Irán Ramos-Prieto and Héctor M. Moya-Cessa

Atoms 2026, 14(1), 4; https://doi.org/10.3390/atoms14010004 - 8 Jan 2026

Viewed by 873

Abstract

We present a general procedure to describe the dynamics of N degenerate quantized fields interacting resonantly with a two–level atom, all coupled with the same strength, within the rotating–wave approximation. Starting from the analysis of the two and three field cases, we generalize [...] Read more.

We present a general procedure to describe the dynamics of N degenerate quantized fields interacting resonantly with a two–level atom, all coupled with the same strength, within the rotating–wave approximation. Starting from the analysis of the two and three field cases, we generalize the method by identifying dynamical invariants that lead to a factorized form of the time–evolution operator. A unitary transformation reduces the problem to an effective Jaynes–Cummings Hamiltonian, where only one field interacts with the atom and the remaining modes contribute as free fields. Assuming initially coherent fields and an atomic superposition, we compute the atomic inversion and the mean photon number, revealing vacuum Rabi oscillations with a frequency determined by an effective coupling constant that exceeds the individual atom–field coupling, as well as the characteristic collapse–revival behavior. Full article

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16 pages, 1936 KB

Open AccessEditor’s ChoiceArticle

L-Shell Photon Excitation Cross Sections for the Chlorine Isonuclear Sequence Cl^{q+ (q=1−4)}: An Experimental Study

by Jean-Paul Mosnier, Eugene T. Kennedy, Denis Cubaynes, Ségolène Guilbaud and Jean-Marc Bizau

Atoms 2026, 14(1), 3; https://doi.org/10.3390/atoms14010003 - 4 Jan 2026

Viewed by 877

Abstract

We report experimental measurements of the absolute photoionization cross sections for chlorine ions in different stages of ionization, over photon energy ranges corresponding to the L-shell (2s and 2p subshells) excitations. Single, double and triple photoionization channels were investigated for the ions Cl [...] Read more.

We report experimental measurements of the absolute photoionization cross sections for chlorine ions in different stages of ionization, over photon energy ranges corresponding to the L-shell (2s and 2p subshells) excitations. Single, double and triple photoionization channels were investigated for the ions Cl⁺, Cl²⁺, Cl³⁺ and Cl⁴⁺. The measurements were performed on the PLéIADES beamline at the SOLEIL radiation storage ring facility, using the Multi-Analysis Ion Apparatus (MAIA). Resonance energies and line strengths are provided for the isonuclear sequence and the evolution of the inner shell photoionization behaviour is demonstrated for the chlorine ions as the degree of ionization is increased. While dominated by photoionization from the corresponding ground state ions, the photoion yields may also contain contributions from low-lying metastable states. The results provide useful data on these ions for plasma modelling and can serve as benchmarking experimental data for future atomic theoretical calculations. Full article

(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)

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15 pages, 10342 KB

Open AccessEditor’s ChoiceArticle

Single Sr Atoms in Optical Tweezer Arrays for Quantum Simulation

by Veronica Giardini, Luca Guariento, Andrea Fantini, Shawn Storm, Massimo Inguscio, Jacopo Catani, Giacomo Cappellini, Vladislav Gavryusev and Leonardo Fallani

Atoms 2026, 14(1), 1; https://doi.org/10.3390/atoms14010001 - 19 Dec 2025

Cited by 1 | Viewed by 2529

Abstract

We report on the realization of a platform for trapping and manipulating individual ⁸⁸Sr atoms in optical tweezers. A first cooling stage based on a blue shielded magneto-optical trap (MOT) operating on the [...] Read more.

We report on the realization of a platform for trapping and manipulating individual ⁸⁸Sr atoms in optical tweezers. A first cooling stage based on a blue shielded magneto-optical trap (MOT) operating on the

|^{1} S_{0} ⟩ \to |^{1} P_{1} ⟩

transition at

461 n m

enables us to trap approximately 4 × 10⁶ atoms at a temperature of 6.8 mK. Further cooling is achieved in a narrow-line red MOT using the

|^{1} S_{0} ⟩ \to |^{3} P_{1} ⟩

intercombination transition at 689 nm, bringing 5 × 10⁵ atoms down to

5 μ K

and reaching a density of 4 × 10¹⁰ cm³. Atoms are then loaded into 813 nm tweezer arrays generated by crossed acousto-optic deflectors and tightly focused onto the atoms with a high-numerical-aperture objective. Through light-assisted collision processes we achieve the collisional blockade, which leads to single-atom occupancy with a probability of about 50%. The trapped atoms are detected via fluorescence imaging with a fidelity of

99.986 (6) %

, while maintaining a survival probability of

97 (2) %

. The release-and-recapture measurement provides a temperature of

12.92 (5) μ K

for the atoms in the tweezers, and the ultra-high-vacuum environment ensures a vacuum lifetime higher than 7 min. These results demonstrate a robust alkaline-earth tweezer platform that combines efficient loading, cooling, and high-fidelity detection, providing the essential building blocks for scalable quantum simulation and quantum information processing with Sr atoms. Full article

(This article belongs to the Special Issue Quantum Technologies with Ultracold Atoms)

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15 pages, 487 KB

Open AccessEditor’s ChoiceArticle

Collective Auger Decay of 4d⁻² Double Inner-Shell Vacancy in Xe

by Jiaolong Zeng, Guoqing Wang, Aihua Deng, Cheng Gao and Jianmin Yuan

Atoms 2025, 13(12), 98; https://doi.org/10.3390/atoms13120098 - 8 Dec 2025

Viewed by 709

Abstract

Auger decay of all levels of the double core-hole states

4 d^{- 2}

of Xe²⁺, including collective Auger decay (CAD) pathways, is investigated using the relativistic distorted-wave approximation. Large-scale configuration interaction calculations were performed to obtain level-to-level Auger decay rates. [...] Read more.

Auger decay of all levels of the double core-hole states

4 d^{- 2}

of Xe²⁺, including collective Auger decay (CAD) pathways, is investigated using the relativistic distorted-wave approximation. Large-scale configuration interaction calculations were performed to obtain level-to-level Auger decay rates. In addition to the typical Auger decay final levels associated with the configurations of

4 d^{- 1} 5 s^{2} 5 p^{4}

,

4 d^{- 1} 5 s^{1} 5 p^{5}

, and

4 d^{- 1} 5 s^{0} 5 p^{6}

, evident contributions are identified from excited channels, leading to configurations such as

4 d^{9} 4 f^{1} 5 s^{2} 5 p^{3}

,

4 d^{9} 5 s^{2} 5 p^{3} 5 d^{1}

,

4 d^{9} 5 s^{2} 5 p^{3} 6 s^{1}

, and

4 d^{9} 5 s^{2} 5 p^{3} 6 p^{1}

. These contributions arise from strong electron correlation between the valence electronic orbitals and the

4 d

inner-shell orbital. The CAD rates and branching ratios (BRs) are determined for each double core-hole level with a minimum CAD BR of 1.28% and a maximum of 4.08% among all CAD channels. The configuration-averaged CAD BR is predicted to be 1.93%, which helps explain recent unexplained experimental findings. The inclusion of CAD processes enriches Auger electron spectroscopy, thereby extending potential applications of this important experimental tool in both fundamental and applied research. Full article

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18 pages, 1413 KB

Open AccessEditor’s ChoiceArticle

Hybrid Basis and Multi-Center Grid Method for Strong-Field Processes

by Kyle A. Hamer, Heman Gharibnejad, Luca Argenti and Nicolas Douguet

Atoms 2025, 13(11), 92; https://doi.org/10.3390/atoms13110092 - 17 Nov 2025

Viewed by 1100

Abstract

We present a time-dependent framework that combines a hybrid basis, consisting of Gaussian-type orbitals (GTOs) and finite-element discrete-variable representation (FEDVR) functions, with a multicenter grid to simulate strong-field and attosecond dynamics in atoms and molecules. The method incorporates the construction of the orthonormal [...] Read more.

We present a time-dependent framework that combines a hybrid basis, consisting of Gaussian-type orbitals (GTOs) and finite-element discrete-variable representation (FEDVR) functions, with a multicenter grid to simulate strong-field and attosecond dynamics in atoms and molecules. The method incorporates the construction of the orthonormal hybrid basis, the evaluation of electronic integrals, a unitary time-propagation scheme, and the extraction of optical and photoelectron observables. Its accuracy and robustness are benchmarked on one-electron systems such as atomic hydrogen and the dihydrogen cation (

H_{2}^{+}

) through comparisons with essentially-exact reference results for bound-state energies, high-harmonic generation spectra, photoionization cross sections, and photoelectron momentum distributions. This work establishes the groundwork for its integration with quantum-chemistry methods, which is already operational but will be detailed in future work, thereby enabling ab initio simulations of correlated polyatomic systems in intense ultrafast laser fields. Full article

(This article belongs to the Special Issue Ab Initio Calculations in Atomic, Molecular, and Optical Physics: A Tribute to Barry Irwin Schneider)

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16 pages, 1425 KB

Open AccessEditor’s ChoiceArticle

Combining Physics and Machine Learning: Hybrid Models for Predicting Interatomic Potentials

by Kaoutar El Haloui, Nicolas Thome and Nicolas Sisourat

Atoms 2025, 13(11), 89; https://doi.org/10.3390/atoms13110089 - 10 Nov 2025

Cited by 4 | Viewed by 2323

Abstract

Constructing accurate Potential Energy Surfaces (PES) is a central task in molecular modeling, as it determines the forces governing nuclear motion and enables reliable quantum dynamics simulations. While ab initio methods can provide accurate PES, they are computationally prohibitive for extensive applications. Alternatively, [...] Read more.

Constructing accurate Potential Energy Surfaces (PES) is a central task in molecular modeling, as it determines the forces governing nuclear motion and enables reliable quantum dynamics simulations. While ab initio methods can provide accurate PES, they are computationally prohibitive for extensive applications. Alternatively, analytical physics-based models such as the Morse potential offer efficient solutions but are limited by their rigidity and poor generalization to excited states. In recent years, neural networks have emerged as powerful tools for determining PES, due to their universal function approximation capabilities, but they require large training datasets. In this work, we investigate hybrid-residual modeling approaches that combine physics-based potentials with neural network corrections, aiming to leverage both physical priors and data adaptability. Specifically, we compare three hybrid models—APHYNITY, Sequential Phy-ML, and PhysiNet—in their ability to reconstruct the potential energy curve of the ground and first excited states of the hydrogen molecule. Each model integrates a simplified physical representation with a neural component that learns the discrepancies from accurate reference data. Our findings reveal that hybrid models significantly outperform both standalone neural networks and pure physics-based models, especially in low-data regimes. Notably, APHYNITY and Sequential Phy-ML exhibit better generalization and maintain accurate estimation of physical parameters, underscoring the benefits of explicit physics incorporation. Full article

(This article belongs to the Special Issue Artificial Intelligence for Quantum Sciences)

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15 pages, 1029 KB

Open AccessEditor’s ChoiceArticle

Single Ionization with Dressed Projectiles: An Improved Theory for Both Long- and Short-Range Interactions

by Nicolás J. Esponda, Michele A. Quinto, Roberto D. Rivarola and Juan M. Monti

Atoms 2025, 13(11), 88; https://doi.org/10.3390/atoms13110088 - 9 Nov 2025

Viewed by 733

Abstract

In this work, we present a theoretical model to investigate electron emission in collisions between dressed ions with He atoms and H₂ molecules. The projectile potential is described as the sum of a long- and short-range terms. The last term includes a [...] Read more.

In this work, we present a theoretical model to investigate electron emission in collisions between dressed ions with He atoms and H₂ molecules. The projectile potential is described as the sum of a long- and short-range terms. The last term includes a screening function that has its maximum at short distances. The present model is based on the Continuum Distorted Wave Eikonal Initial State (CDW-EIS) theory, but the Eikonal approximation is only made within the long-range transition amplitude. This now leads to physically correct predictions, whenever dressed projectiles are involved, in the binary-encounter peak. Indeed, double-differential cross-sections spectra is calculated and compared with existing experimental data, finding that this model is capable of reproducing some well-known phenomena depending on the projectile charge state. Namely, the dependence of the binary-encounter peak magnitude with the projectile charge state. Full article

(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)

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12 pages, 1196 KB

Open AccessEditor’s ChoiceArticle

The Opacity Project: R-Matrix Calculations for Opacities of High-Energy-Density Astrophysical and Laboratory Plasmas

by Anil K. Pradhan and Sultana N. Nahar

Atoms 2025, 13(10), 85; https://doi.org/10.3390/atoms13100085 - 20 Oct 2025

Cited by 2 | Viewed by 1056

Abstract

Accurate determination of opacity is critical for understanding radiation transport in both astrophysical and laboratory plasmas. We employ atomic data from R-Matrix calculations to investigate radiative properties in high-energy-density (HED) plasma sources, focusing on opacity variations under extreme plasma conditions. Specifically, we analyze [...] Read more.

Accurate determination of opacity is critical for understanding radiation transport in both astrophysical and laboratory plasmas. We employ atomic data from R-Matrix calculations to investigate radiative properties in high-energy-density (HED) plasma sources, focusing on opacity variations under extreme plasma conditions. Specifically, we analyze environments such as the base of the convective zone (BCZ) of the Sun (

2 \times 10^{6}

K,

N_{e} = 10^{23}

/cc), and radiative opacity data collected using the inertial confinement fusion (ICF) devices at the Sandia Z facility (

2.11 \times 10^{6}

K,

N_{e} = 3.16 \times 10^{22}

/cc) and the Lawrence Livermore National Laboratory National Ignition Facility. We calculate Rosseland Mean Opacities (RMO) within a range of temperatures and densities and analyze how they vary under different plasma conditions. A significant factor influencing opacity in these environments is line and resonance broadening due to plasma effects. Both radiative and collisional broadening modify line shapes, impacting the absorption and emission profiles that determine the RMO. In this study, we specifically focus on electron collisional and Stark ion microfield broadening effects, which play a dominant role in HED plasmas. We assume a Lorentzian profile factor to model combined broadening and investigate its impact on spectral line shapes, resonance behavior, and overall opacity values. Our results are relevant to astrophysical models, particularly in the context of the solar opacity problem, and provide insights into discrepancies between theoretical calculations and experimental measurements. In addition, we investigate the equation-of-state (EOS) and its impact on opacities. In particular, we examine the “chemical picture” Mihalas–Hummer–Däppen EOS with respect to level populations of excited levels included in the extensive R-matrix calculations. This study should contribute to improving opacity models of HED sources such as stellar interiors and laboratory plasma experiments. Full article

(This article belongs to the Special Issue Electronic, Photonic and Ionic Interactions with Atoms and Molecules)

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14 pages, 865 KB

Open AccessEditor’s ChoiceArticle

Single Electron Capture by Dressed Projectiles Within the Distorted Wave Formalism

by Michele Arcangelo Quinto, Juan Manuel Monti and Roberto Daniel Rivarola

Atoms 2025, 13(10), 84; https://doi.org/10.3390/atoms13100084 - 3 Oct 2025

Cited by 1 | Viewed by 968

Abstract

Single electron capture in collisions involving neutral hydrogen atoms impacted by highly charged dressed projectiles is theoretically investigated using the distorted wave formalism. A series of continuum distorted wave approximations is employed to investigate the electron capture from neutral hydrogen atom impact by [...] Read more.

Single electron capture in collisions involving neutral hydrogen atoms impacted by highly charged dressed projectiles is theoretically investigated using the distorted wave formalism. A series of continuum distorted wave approximations is employed to investigate the electron capture from neutral hydrogen atom impact by boron and carbon projectiles. The projectile potential is described using a two-parameter analytical Green–Sellin–Zachor (GSZ) model potential. The theoretical prediction of total cross sections are compared against other theories and experiments. We looked at a very broad range of collision energies, from 10 keV/u up to 10 MeV/u. In addition, the state-selective cross sections for boron ions are presented. Full article

(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)

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28 pages, 3057 KB

Open AccessEditor’s ChoiceArticle

Proton Interactions with Biological Targets: Inelastic Cross Sections, Stopping Power, and Range Calculations

by Camila Strubbia Mangiarelli, Verónica B. Tessaro, Michaël Beuve and Mariel E. Galassi

Atoms 2025, 13(10), 83; https://doi.org/10.3390/atoms13100083 - 24 Sep 2025

Viewed by 2205

Abstract

Proton therapy enables precise dose delivery to tumors while sparing healthy tissues, offering significant advantages over conventional radiotherapy. Accurate prediction of biological doses requires detailed knowledge of radiation interactions with biological targets, especially DNA, a key site of radiation-induced damage. While most biophysical [...] Read more.

Proton therapy enables precise dose delivery to tumors while sparing healthy tissues, offering significant advantages over conventional radiotherapy. Accurate prediction of biological doses requires detailed knowledge of radiation interactions with biological targets, especially DNA, a key site of radiation-induced damage. While most biophysical models (LEM, mMKM, NanOx) rely on water as a surrogate, this simplification neglects the complexity of real biomolecules. In this work, we calculate the stopping power and range of protons in liquid water, dry DNA, and hydrated DNA using semi-empirical cross sections for ionization, electronic excitation, electron capture, and electron loss by protons and neutral hydrogen in the 10 keV–100 MeV energy range. Additionally, ionization cross sections for uracil are computed to explore potential differences between DNA and RNA damage. Our results show excellent agreement with experimental and ab initio data, highlighting significant deviations in stopping power and range between water and DNA. Notably, the stopping power of DNA exceeds that of water at most energies, reducing proton ranges in dry and hydrated DNA by up to 20% and 26%, respectively. These findings provide improved input for Monte Carlo simulations and biophysical models, enhancing RBE predictions and dose accuracy in hadrontherapy. Full article

(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)

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12 pages, 541 KB

Open AccessEditor’s ChoiceArticle

Integral Cross Sections and Transport Properties for Electron–Radon Scattering over a Wide Energy Range (0–1000 eV) and a Reduced Electric Field Range (0.01–1000 Td)

by Gregory J. Boyle, Dale L. Muccignat, Joshua R. Machacek and Robert P. McEachran

Atoms 2025, 13(10), 82; https://doi.org/10.3390/atoms13100082 - 23 Sep 2025

Cited by 1 | Viewed by 982

Abstract

We report calculations for electron–radon scattering using a complex relativistic optical potential method. The energy range of this study is 0–1000 eV, with results for the elastic (total, momentum-transfer and viscosity-transfer) cross section, summed discrete electronic-state integral excitation cross sections and electron-impact ionization [...] Read more.

We report calculations for electron–radon scattering using a complex relativistic optical potential method. The energy range of this study is 0–1000 eV, with results for the elastic (total, momentum-transfer and viscosity-transfer) cross section, summed discrete electronic-state integral excitation cross sections and electron-impact ionization cross sections presented. Here, we obtain our cross sections from a single theoretical relativistic calculation. Since radon is a heavy element, a relativistic treatment is very desirable. The electron transport coefficients are subsequently calculated for reduced electric fields ranging from 0.01 to 1000 Td, using a multi-term solution of Boltzmann’s equation. Full article

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11 pages, 351 KB

Open AccessEditor’s ChoiceArticle

Short–Range Hard–Sphere Potential and Coulomb Interaction: Deser–Trueman Formula for Rydberg States of Exotic Atomic Systems

by Gregory S. Adkins and Ulrich D. Jentschura

Atoms 2025, 13(9), 81; https://doi.org/10.3390/atoms13090081 - 11 Sep 2025

Cited by 3 | Viewed by 1873

Abstract

In exotic atomic systems with hadronic constituent particles, it is notoriously difficult to estimate the strong-interaction correction to energy levels. It is well known that, due to the strength of the nuclear interaction, the problem cannot be solved using Wigner–Brillouin perturbation theory alone. [...] Read more.

In exotic atomic systems with hadronic constituent particles, it is notoriously difficult to estimate the strong-interaction correction to energy levels. It is well known that, due to the strength of the nuclear interaction, the problem cannot be solved using Wigner–Brillouin perturbation theory alone. Recently, high-angular-momentum Rydberg states of exotic atomic systems with hadronic constituents have been identified as promising candidates in the search for new physics in the low-energy sector of the Standard Model. We thus derive a generalized Deser–Trueman formula for the induced energy shift for a general hydrogenic bound state with principal quantum number n and orbital angular momentum quantum number ℓ, and we find that the energy shift is given by the formula

δ E = 2 α_{n, ℓ} β_{ℓ} {(a_{h} / a_{0})}^{2 ℓ + 1} E_{h} / n^{3}

, where

α_{n, 0} = 1

,

α_{n, ℓ} = \prod_{s = 1}^{ℓ} (s^{- 2} - n^{- 2})

,

β_{ℓ} = (2 ℓ + 1) / {[(2 ℓ + 1)!!]}^{2}

,

E_{h}

is the Hartree energy,

a_{h}

is the hadronic radius and

a_{0}

is the generalized Bohr radius. The square of the double factorial,

{[(2 ℓ + 1)!!]}^{2}

, in the denominator implies a drastic suppression of the effect for higher angular momenta. Full article

(This article belongs to the Section Nuclear Theory and Experiments)

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16 pages, 1120 KB

Open AccessEditor’s ChoiceArticle

Simulated Photoabsorption Spectra for Singly and Multiply Charged Ions

by Stephan Fritzsche, Aloka Kumar Sahoo, Lalita Sharma and Stefan Schippers

Atoms 2025, 13(9), 77; https://doi.org/10.3390/atoms13090077 - 3 Sep 2025

Cited by 1 | Viewed by 1387

Abstract

Simulated (or measured) photoabsorption spectra often provide the first indication of how matter interacts with light when irradiated by some radiation source. In addition to the direct, often slowly varying photoabsorption cross-section as a function of the incident photon frequency, such spectra typically [...] Read more.

Simulated (or measured) photoabsorption spectra often provide the first indication of how matter interacts with light when irradiated by some radiation source. In addition to the direct, often slowly varying photoabsorption cross-section as a function of the incident photon frequency, such spectra typically exhibit numerous resonances and edges arising from the interaction of the radiation field with the subvalence or even inner-shell electrons. Broadly speaking, these resonances reflect photoexcitation, with its subsequent fluorescence, or the autoionization of bound electrons. Here, a (relativistic) cascade model is developed for estimating the photoabsorption of (many) atoms and multiply charged ions with a complex shell structure across the periodic table. This model helps distinguish between level- and shell-resolved, as well as total photoabsorption, cross-sections, starting from admixtures of selected initial-level populations. Examples are shown for the photoabsorption of C⁺ ions near the 1s − 2p excitation threshold and for Xe²⁺ ions in the photon energy range from 10 to 200 eV. While the accuracy and resolution of the predicted photoabsortion spectra remain limited due to the additive treatment of resonances and because of missing electronic correlations in the representation of the levels involved, the present implementation is suitable for ions with quite different open-shell structures and may support smart surveys of resonances along different isoelectronic sequences. Full article

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9 pages, 549 KB

Open AccessEditor’s ChoiceArticle

Interfacing the B-Spline R-Matrix and R-Matrix with Time Dependence Computer Codes: An Update

by Juan C. Del Valle, Aaron T. Bondy, Soumyajit Saha, Kathryn R. Hamilton and Klaus Bartschat

Atoms 2025, 13(9), 75; https://doi.org/10.3390/atoms13090075 - 29 Aug 2025

Cited by 2 | Viewed by 1332

Abstract

As a continuation of Schneider et al., Atoms 2022 10, 26, we report recent progress in the development and deployment of the interface between the computational codes B-Spline R-matrix (BSR) and R-Matrix with Time dependence (RMT). These advances have been achieved within [...] Read more.

As a continuation of Schneider et al., Atoms 2022 10, 26, we report recent progress in the development and deployment of the interface between the computational codes B-Spline R-matrix (BSR) and R-Matrix with Time dependence (RMT). These advances have been achieved within the context of the

L S

-coupling scheme. In its current state, the interface handles atomic target states described by single configurations and supports the Fano–Racah phase convention, as required by RMT. As first example of an application, we use the interface to investigate multiphoton single ionization of helium exposed to a linearly polarized laser field with wavelengths between 280 and 316 nm and a peak intensity of

3 \times 10^{14}

W/cm². As a second example, we consider high-order harmonic generation (HHG) in carbon, driven by an intense 30-cycle laser field at 800 nm and a peak intensity of

1 \times 10^{12}

W/cm². Full article

(This article belongs to the Special Issue Ab Initio Calculations in Atomic, Molecular, and Optical Physics: A Tribute to Barry Irwin Schneider)

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12 pages, 1240 KB

Open AccessEditor’s ChoiceArticle

State-Selective Differential Cross Sections for Single-Electron Capture in Slow He⁺–He Collisions

by Shucheng Cui, Kaizhao Lin, Dadi Xing, Ling Liu, Dongmei Zhao, Dalong Guo, Yong Gao, Shaofeng Zhang, Yong Wu, Chenzhong Dong, Xiaolong Zhu and Xinwen Ma

Atoms 2025, 13(9), 74; https://doi.org/10.3390/atoms13090074 - 28 Aug 2025

Cited by 1 | Viewed by 1476

Abstract

A combined experimental and theoretical study is carried out on the single-electron capture process in He⁺–He collisions at energies ranging from 0.5 keV/u to 5 keV/u. Using cold target recoil ion momentum spectroscopy, we obtain state-selective cross sections and angular differential [...] Read more.

A combined experimental and theoretical study is carried out on the single-electron capture process in He⁺–He collisions at energies ranging from 0.5 keV/u to 5 keV/u. Using cold target recoil ion momentum spectroscopy, we obtain state-selective cross sections and angular differential cross sections. Within the entire studied energy range, the dominant channel is the electron captured into the ground-state, and the relative contribution of the dominant channel shows a decreasing trend with increasing energy. The angular differential cross sections of ground-state capture exhibit obvious oscillatory structures. To understand the oscillatory structures of the differential cross sections, we also performed theoretical calculations using the two-center atomic orbital close-coupling method, which well reproduced the oscillatory structures. The results indicate that these structures are strongly correlated to the oscillatory structures of the impact parameter dependence of electron probability. Full article

(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)

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15 pages, 628 KB

Open AccessEditor’s ChoiceArticle

Accurate Nonrelativistic Energy Calculations for Helium 1snp^1,3P (n = 2 to 27) States via Correlated B-Spline Basis Functions

by Jing Chi, Hao Fang, Yong-Hui Zhang, Xiao-Qiu Qi, Li-Yan Tang and Ting-Yun Shi

Atoms 2025, 13(8), 72; https://doi.org/10.3390/atoms13080072 - 4 Aug 2025

Cited by 2 | Viewed by 1757

Abstract

Rydberg atoms play a crucial role in testing atomic structure theory, quantum computing and simulation. Measurements of transition frequencies from the

2^{1, 3} S

states to Rydberg

{}^{1, 3}P

states have reached a precision of several kHz, which poses [...] Read more.

Rydberg atoms play a crucial role in testing atomic structure theory, quantum computing and simulation. Measurements of transition frequencies from the

2^{1, 3} S

states to Rydberg

{}^{1, 3}P

states have reached a precision of several kHz, which poses significant challenges for theoretical calculations, since the accuracy of variational energy calculations decreases rapidly with increasing principal quantum number n. Recently the complex “triple” Hylleraas basis was employed to attain the ionization energy of helium

24 {}^{1}P

state with high accuracy. Different from it, we extended the correlated B-spline basis functions (C-BSBFs) to calculate the Rydberg states of helium. The nonrelativistic energies of

1 s n p

{}^{1, 3}P

states up to

n = 27

achieve at least 14 significant digits using a unified basis set, thereby greatly reducing the complexity of the optimization process. Results of geometric structure parameters and cusp conditions were presented as well. Both the global operator and direct calculation methods are employed and cross-checked for contact potentials. This C-BSBF method not only obtains high-accuracy energies across all studied levels but also confirms the effectiveness of the C-BSBFs in depicting long-range and short-range correlation effects, laying a solid foundation for future high-accuracy Rydberg-state calculations with relativistic and QED corrections included in helium atom and low-Z helium-like ions. Full article

(This article belongs to the Special Issue Atom and Plasma Spectroscopy)

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13 pages, 359 KB

Open AccessEditor’s ChoiceReview

Numerical Methods for the Time-Dependent Schrödinger Equation: Beyond Short-Time Propagators

by Ryan Schneider and Heman Gharibnejad

Atoms 2025, 13(8), 70; https://doi.org/10.3390/atoms13080070 - 28 Jul 2025

Cited by 1 | Viewed by 3310

Abstract

This article reviews several numerical methods for the time-dependent Schrödinger Equation (TDSE). We consider both the most commonly used approach—short-time propagation, which solves the TDSE by assuming that the Hamiltonian is time-independent over sufficiently small (time) intervals—as well as a number of higher-order [...] Read more.

This article reviews several numerical methods for the time-dependent Schrödinger Equation (TDSE). We consider both the most commonly used approach—short-time propagation, which solves the TDSE by assuming that the Hamiltonian is time-independent over sufficiently small (time) intervals—as well as a number of higher-order alternatives. Our goal is to dispel the notion that the latter are too computationally demanding for practical use. To that end, we cover methods whose numerical building blocks are shared by short-time propagators or can be handled by standard libraries. Moreover, we make the case that these methods are best positioned to take advantage of parallel computing environments. One of the alternatives considered is a “double DVR” solver, which applies an expansion in a product basis of functions in space and time to obtain a solution (over all space and at multiple time points simultaneously) with a single linear system solve. To our knowledge, and despite its simplicity, this approach has not previously been applied to the TDSE. Full article

(This article belongs to the Special Issue Ab Initio Calculations in Atomic, Molecular, and Optical Physics: A Tribute to Barry Irwin Schneider)

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16 pages, 1681 KB

Open AccessEditor’s ChoiceArticle

Thermal–Condensate Collisional Effects on Atomic Josephson Junction Dynamics

by Klejdja Xhani and Nick P. Proukakis

Atoms 2025, 13(8), 68; https://doi.org/10.3390/atoms13080068 - 22 Jul 2025

Cited by 1 | Viewed by 1983

Abstract

We investigate how collisional interactions between the condensate and the thermal cloud influence the distinct dynamical regimes (Josephson plasma, phase-slip-induced dissipative regime, and macroscopic quantum self-trapping) emerging in ultracold atomic Josephson junctions at non-zero subcritical temperatures. Specifically, we discuss how the self-consistent dynamical [...] Read more.

We investigate how collisional interactions between the condensate and the thermal cloud influence the distinct dynamical regimes (Josephson plasma, phase-slip-induced dissipative regime, and macroscopic quantum self-trapping) emerging in ultracold atomic Josephson junctions at non-zero subcritical temperatures. Specifically, we discuss how the self-consistent dynamical inclusion of collisional processes facilitating the exchange of particles between the condensate and the thermal cloud impacts both the condensate and the thermal currents, demonstrating that their relative importance depends on the system’s dynamical regime. Our study is performed within the full context of the Zaremba–Nikuni–Griffin (ZNG) formalism, which couples a dissipative Gross–Pitaevskii equation for the condensate dynamics to a quantum Boltzmann equation with collisional terms for the thermal cloud. In the Josephson plasma oscillation and vortex-induced dissipative regimes, collisions markedly alter dynamics at intermediate-to-high temperatures, amplifying damping in the condensate imbalance mode and inducing measurable frequency shifts. In the self-trapping regime, collisions destabilize the system even at low temperatures, prompting a transition to Josephson-like dynamics on a temperature-dependent timescale. Our results show the interplay between coherence, dissipation, and thermal effects in a Bose–Einstein condensate at a finite temperature, providing a framework for tailoring Josephson junction dynamics in experimentally accessible regimes. Full article

(This article belongs to the Special Issue Quantum Technologies with Ultracold Atoms)

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19 pages, 764 KB

Open AccessEditor’s ChoiceArticle

Subradiance Generation in a Chain of Two-Level Atoms with a Single Excitation

by Nicola Piovella

Atoms 2025, 13(7), 62; https://doi.org/10.3390/atoms13070062 - 1 Jul 2025

Cited by 1 | Viewed by 1349

Abstract

Studies of subradiance in a chain N two-level atoms in the single excitation regime focused mainly on the complex spectrum of the effective Hamiltonian, identifying subradiant eigenvalues. This can be achieved by finding the eigenvalues N of the Hamiltonian or by evaluating the [...] Read more.

Studies of subradiance in a chain N two-level atoms in the single excitation regime focused mainly on the complex spectrum of the effective Hamiltonian, identifying subradiant eigenvalues. This can be achieved by finding the eigenvalues N of the Hamiltonian or by evaluating the expectation value of the Hamiltonian on a generalized Dicke state, depending on a continuous variable k. This has the advantage that the sum above N can be calculated exactly, such that N becomes a simple parameter of the system and no longer the size of the Hilbert space. However, the question remains how subradiance emerges from atoms initially excited or driven by a laser. Here we study the dynamics of the system, solving the coupled-dipole equations for N atoms and evaluating the probability to be in a generalized Dicke state at a given time. Once the subradiant regions have been identified, it is simple to see if subradiance is being generated. We discuss different initial excitation conditions that lead to subradiance and the case of atoms excited by switching on and off a weak laser. This may be relevant for future experiments aimed at detecting subradiance in ordered systems. Full article

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12 pages, 819 KB

Open AccessEditor’s ChoiceArticle

Ionization of CF₃CH₂F by Protons and Photons

by Carlos E. Ferreira, Jorge A. de Souza-Corrêa, Alexandre B. Rocha and Antônio C. F. Santos

Atoms 2025, 13(6), 58; https://doi.org/10.3390/atoms13060058 - 18 Jun 2025

Viewed by 1358

Abstract

(1) Background: Ionizing radiation in the Earth’s atmosphere drives key chemical transformations affecting atmospheric composition. Despite their environmental relevance, experimental data on proton collisions with hydrofluorocarbons remain limited, and theoretical models for total cross-sections and stopping power are still underdeveloped. (2) Methods: This [...] Read more.

(1) Background: Ionizing radiation in the Earth’s atmosphere drives key chemical transformations affecting atmospheric composition. Despite their environmental relevance, experimental data on proton collisions with hydrofluorocarbons remain limited, and theoretical models for total cross-sections and stopping power are still underdeveloped. (2) Methods: This study applies Rudd’s semiempirical model to calculate proton impact ionization cross-sections for the CF₃CH₂F molecule, considering contributions from both outer and inner electron shells. The model enables the estimation of differential cross-sections and the average energy of secondary electrons. In addition, we calculate the photoionization cross-sections using a discretized representation of the continuum—the so-called pseudo-spectrum—obtained through TDDFT with PBE0 as an exchange–correlation functional and compare it with the cross-section obtained for proton impact in the high-energy limit. (3) Results: The Rudd model proves highly adaptable and suitable for numerical applications. However, its validation is hindered by the scarcity of experimental data. Existing models, such as SRIM and Bethe–Bloch, show significant discrepancies due to their limited applicability at intermediate energies and lack of molecular structure consideration. (4) Conclusions: A comparison between the Rudd and BEB models reveals strong agreement in the analyzed energy range. This consistency stems from both models accounting for the molecular structure of the target, as well as from the fact that protons and electrons possess charges of the same magnitude, supporting a coherent description of ionization processes at these energies. Full article

(This article belongs to the Special Issue Electronic, Photonic and Ionic Interactions with Atoms and Molecules)

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19 pages, 857 KB

Open AccessEditor’s ChoiceArticle

An Explicit Numerical Scheme for Milne’s Phase–Amplitude Equations

by Robin Piron and Mikael Tacu

Atoms 2025, 13(6), 57; https://doi.org/10.3390/atoms13060057 - 18 Jun 2025

Viewed by 1022

Abstract

We present an explicit numerical method to solve Milne’s phase–amplitude equations. Existing methods directly solve Milne’s nonlinear equation for amplitude. For that reason, they exhibit high sensitivity to errors and are prone to instability through the growth of a spurious, rapidly varying component [...] Read more.

We present an explicit numerical method to solve Milne’s phase–amplitude equations. Existing methods directly solve Milne’s nonlinear equation for amplitude. For that reason, they exhibit high sensitivity to errors and are prone to instability through the growth of a spurious, rapidly varying component of the amplitude. This makes the systematic use of these methods difficult. On the contrary, the present method is based on solving a linear third-order equation which is equivalent to the nonlinear amplitude equation. This linear equation was derived by Kiyokawa, who used it to obtain analytical results on Coulomb wavefunctions. The present method uses this linear equation for numerical computation, thus resolving the problem of the growth of a rapidly varying component. Full article

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15 pages, 875 KB

Open AccessEditor’s ChoiceArticle

Multi-Configuration Dirac–Hartree–Fock Calculations of Pr⁹⁺ and Nd¹⁰⁺: Configuration Resolution and Probing Fine-Structure Constant Variation

by Songya Zhang, Cunqiang Wu, Chenzhong Dong and Xiaobin Ding

Atoms 2025, 13(6), 54; https://doi.org/10.3390/atoms13060054 - 16 Jun 2025

Cited by 1 | Viewed by 1560

Abstract

We present high-precision multi-configuration Dirac–Hartree–Fock (MCDHF) calculations for the metastable states of

\Pr^{9 +}

and

{Nd}^{10 +}

ions, systematically investigating their energy levels, transition properties, Landé

g_{J}

factors, and hyperfine interaction constants. Our results show excellent agreement with available experimental [...] Read more.

We present high-precision multi-configuration Dirac–Hartree–Fock (MCDHF) calculations for the metastable states of

\Pr^{9 +}

and

{Nd}^{10 +}

ions, systematically investigating their energy levels, transition properties, Landé

g_{J}

factors, and hyperfine interaction constants. Our results show excellent agreement with available experimental data and theoretical benchmarks, while resolving critical configuration assignment discrepancies through detailed angular momentum coupling analysis. The calculations highlight the significant role of Breit interaction and provide the first theoretical predictions of electric quadrupole hyperfine constants (

B_{hfs}

). These findings deliver essential atomic data for the development of next-generation optical clocks and establish lanthanide highly charged ions as exceptional candidates for precision tests of fundamental physics. Full article

(This article belongs to the Special Issue Atomic and Molecular Data and Their Applications: ICAMDATA 2024)

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64 pages, 2080 KB

Open AccessEditor’s ChoiceReview

Triaxial Shapes in Even–Even Nuclei: A Theoretical Overview

by Dennis Bonatsos, Andriana Martinou, Spyridon K. Peroulis, Dimitrios Petrellis, Polytimos Vasileiou, Theodoros J. Mertzimekis and Nikolay Minkov

Atoms 2025, 13(6), 47; https://doi.org/10.3390/atoms13060047 - 31 May 2025

Cited by 6 | Viewed by 2761

Abstract

Triaxial shapes in even–even nuclei have been considered since the early days of the nuclear collective model. Although many theoretical approaches have been used over the years for their description, no effort appears to have been made for grouping them together and identifying [...] Read more.

Triaxial shapes in even–even nuclei have been considered since the early days of the nuclear collective model. Although many theoretical approaches have been used over the years for their description, no effort appears to have been made for grouping them together and identifying regions on the nuclear chart where the appearance of triaxiality might be favored. In addition, over the last few years, discussion has started on the appearance of small triaxiality in nuclei considered so far as purely axial rotors. In the present work, we collect the predictions made by various theoretical approaches and show that pronounced triaxiality appears to be favored within specific stripes on the nuclear chart, with low triaxiality being present in the regions between these stripes, in agreement with parameter-free predictions made by the proxy-SU(3) approximation to the shell model, based on the Pauli principle and the short-range nature of the nucleon–nucleon interaction. The robustness of triaxiality within these stripes is supported by global calculations made in the framework of the Finite-Range Droplet Model (FRDM), which is based on completely different assumptions and possesses parameters fitted in order to reproduce fundamental nuclear properties. Full article

(This article belongs to the Section Nuclear Theory and Experiments)

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12 pages, 9743 KB

Open AccessEditor’s ChoiceArticle

by Peter Van Reeth and John W. Humberston

Atoms 2025, 13(6), 46; https://doi.org/10.3390/atoms13060046 - 28 May 2025

Viewed by 1569

Abstract

Scattering differential cross-sections (DCSs) are important tools, both experimentally and theoretically, in the investigation of scattering processes in lepton–atom collisions. In the present work, the elastic scattering differential cross-sections (EDCSs) for e⁺-H and e⁺-He below the first excitation threshold [...] Read more.

Scattering differential cross-sections (DCSs) are important tools, both experimentally and theoretically, in the investigation of scattering processes in lepton–atom collisions. In the present work, the elastic scattering differential cross-sections (EDCSs) for e⁺-H and e⁺-He below the first excitation threshold of the target were evaluated using the Kohn variational method and found to be very similar. In both cases, the EDCS below the positronium formation threshold, i.e., for pure elastic scattering, had minimum valley features in which significant minima close to 90 degrees were found at ≈2.8 eV for H and ≈2 eV for He. These minima were shown to be linked to the zero in the s-wave phase shift, which gives rise to the Ramsauer minimum in the elastic integrated cross-sections. They were not vortices, but the overall EDCS structure was found to be related to the structures and vortices found in the Ps formation differential cross-sections just above the Ps formation threshold. The valley-type structure in the EDCS went smoothly through the Ps formation threshold, where it linked up with a similar valley structure in both the EDCS above the threshold and the Ps formation DCS. A comparison with the EDCS for e⁻-H and e⁻-He scattering over the same energy range revealed similarities with the positron EDCS, however, with less pronounced structures that had different angular and momentum dependences. Full article

(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)

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14 pages, 1754 KB

Open AccessEditor’s ChoiceArticle

The Single-Active-Electron Approximation with Angular-Momentum-Dependent Potentials: Application to the Helium Atom

by Juan Carlos del Valle and Klaus Bartschat

Atoms 2025, 13(5), 43; https://doi.org/10.3390/atoms13050043 - 14 May 2025

Cited by 1 | Viewed by 2802

Abstract

We discuss an extension of the Single-Active-Electron (SAE) approximation in atoms by allowing the model potential to depend on the angular-momentum quantum number ℓ. We refer to this extension as the ℓ-SAE approximation. The main ideas behind ℓ-SAE are illustrated [...] Read more.

We discuss an extension of the Single-Active-Electron (SAE) approximation in atoms by allowing the model potential to depend on the angular-momentum quantum number ℓ. We refer to this extension as the ℓ-SAE approximation. The main ideas behind ℓ-SAE are illustrated using the helium atom as a benchmark system. We show that introducing ℓ-dependent potentials improves the accuracy of key quantities in atomic structure computed from the Time-Independent Schrödinger Equation (TISE), including energies, oscillator strengths, and static and dynamic polarizabilities, compared to the standard SAE approach. Additionally, we demonstrate that the ℓ-SAE approximation is suitable for quantum simulations of light−atom interactions described by the Time-Dependent Schrödinger Equation (TDSE). As an illustration, we simulate High-order Harmonic Generation (HHG) and the three-sideband (3SB) version of the Reconstruction of Attosecond Beating by Interference of Two-photon Transitions (RABBITT) technique, achieving enhanced accuracy comparable to that obtained in all-electron calculations. One of the main advantages of the ℓ-SAE approach is that existing SAE codes can be easily adapted to handle ℓ-dependent potentials without any additional computational cost. Full article

(This article belongs to the Special Issue Ab Initio Calculations in Atomic, Molecular, and Optical Physics: A Tribute to Barry Irwin Schneider)

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13 pages, 1058 KB

Open AccessEditor’s ChoiceArticle

A Novel Approach to Calculate the Range of High-Energy Charged Particles Within a Medium

by Ioannis Psychogios, Stylianos Vasileios Kontomaris, Anna Malamou and Andreas Stylianou

Atoms 2025, 13(5), 38; https://doi.org/10.3390/atoms13050038 - 27 Apr 2025

Viewed by 986

Abstract

The determination of energy loss of charged particles as they pass through a medium and consequently the calculation of their range within the medium are of tremendous importance in various areas of physics from both theoretical and practical perspectives. Previous works have derived [...] Read more.

The determination of energy loss of charged particles as they pass through a medium and consequently the calculation of their range within the medium are of tremendous importance in various areas of physics from both theoretical and practical perspectives. Previous works have derived approximate equations regarding the range of ions within a medium, focusing on providing simple solutions for practitioners in the radiotherapy field that do not require significant computational cost, unlike traditional Monte Carlo methods. These solutions focus on radiotherapy and are limited to specific ions’ initial speeds, which should be up to 0.65c (where c is the speed of light in vacuum). In this paper, solutions for significantly larger initial velocities are explored. A new analytical equation for determining the range of charged particles within a medium for initial velocities between 0.6c and 0.9c is presented. This equation provides excellent results when compared to the accurate numerical solution. Beyond its theoretical and mathematical interest, this solution is also reliable for radiotherapy applications. It provides excellent results for protons with initial energies between 200 MeV and 350 MeV and has the major advantage of being expressed in terms of elementary functions, making its use more straightforward compared to other approaches. Full article

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10 pages, 4390 KB

Open AccessEditor’s ChoiceArticle

The Laboratory Measurement of the Line Ratios in X-Ray Emission Resulting from the Charge Exchange Between Mg¹¹⁺ and Helium

by Kebao Shu, Caojie Shao, Shuo Zhang, Ruitian Zhang, Cheng Qian, Yingli Xue, Mingwu Zhang, Jinlei Tian, Zhenqiang Wang, Xiaolong Zhu, Liangting Sun, Junxia Ran and Deyang Yu

Atoms 2025, 13(4), 34; https://doi.org/10.3390/atoms13040034 - 14 Apr 2025

Cited by 1 | Viewed by 1377

Abstract

The line ratios in X-ray emission resulting from charge exchange between highly charged ions (HCIs) and neutral atoms are not only crucial for accurately modeling astrophysical X-ray emissions but also offer a unique perspective on the charge exchange processes happening during collisions. The [...] Read more.

The line ratios in X-ray emission resulting from charge exchange between highly charged ions (HCIs) and neutral atoms are not only crucial for accurately modeling astrophysical X-ray emissions but also offer a unique perspective on the charge exchange processes happening during collisions. The K X-ray spectra following charge exchange between Mg¹¹⁺ and He are presented for a collision velocity of 1489 km/s (11.5 keV/amu). The spectra were measured by two Silicon Drift Detectors capable of resolving the Mg¹⁰⁺ Kα, Kβ, Kγ, and Kδ+ lines. The line intensity ratios of Kβ, Kγ, and Kδ+ relative to the Kα line, as well as the hardness ratio, were obtained. The experimental results were compared with the theoretical results from a cascade model that utilizes the state cross-sections produced by multichannel Landau–Zener (MCLZ) calculation. It was discovered that the K X-ray spectrum features can be reproduced well by MCLZ theory when the contributions of both single electron capture (SEC) and autoionizing double capture (ADC) processes are included. This finding implies that the ADC feeding mechanism is significant and should be taken into account for the X-ray emission during charge exchange between highly charged ions and multielectron atoms. Full article

(This article belongs to the Special Issue X-Ray Spectroscopy in Astrophysics)

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10 pages, 2805 KB

Open AccessEditor’s ChoiceArticle

Photoionization of Trans-Fe Ions: Se IV, Se V, and Se VI

by Brendan M. McLaughlin, Joern Wilms and James F. Babb

Atoms 2025, 13(4), 31; https://doi.org/10.3390/atoms13040031 - 8 Apr 2025

Viewed by 1268

Abstract

In the present study, the photoionization cross-sections are calculated for the trans-Fe ions Se IV, Se V, and Se VI over a wide energy region for ground and meta-stable states within the Dirac Atomic R-matrix approach (darc). Our cross-section results, [...] Read more.

In the present study, the photoionization cross-sections are calculated for the trans-Fe ions Se IV, Se V, and Se VI over a wide energy region for ground and meta-stable states within the Dirac Atomic R-matrix approach (darc). Our cross-section results, when benchmarked against the available high-resolution measurements taken at the Advanced Light Source (ALS) for Se IV (Ga-like) and Se VI (Cu-like) selenium ions, show good agreement over the entire photon energy investigated. The present high quality cross-section data are suitable for use in many applications in astrophysics. Full article

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26 pages, 4050 KB

Open AccessEditor’s ChoiceArticle

Vibrational Excitation of HDO Molecule by Electron Impact

by Mehdi Adrien Ayouz, Alexandre Faure, Ioan F. Schneider, János Zsolt Mezei and Viatcheslav Kokoouline

Atoms 2025, 13(4), 32; https://doi.org/10.3390/atoms13040032 - 8 Apr 2025

Viewed by 1545

Abstract

Cross sections and thermally averaged rate coefficients for the vibrational excitation and de-excitation by electron impact on the HDO molecule are computed using a theoretical approach based entirely on first principles. This approach combines scattering matrices obtained from the UK R-matrix codes for [...] Read more.

Cross sections and thermally averaged rate coefficients for the vibrational excitation and de-excitation by electron impact on the HDO molecule are computed using a theoretical approach based entirely on first principles. This approach combines scattering matrices obtained from the UK R-matrix codes for various geometries of the target molecule, three-dimensional vibrational states of HDO, and the vibrational frame transformation. The vibrational states of the molecule are evaluated by solving the Schrödinger equation numerically, without relying on the normal-mode approximation, which is known to be inaccurate for water molecules. As a result, couplings and transitions between the vibrational states of HDO are accurately accounted for. From the calculated cross sections, thermally averaged rate coefficients and their analytical fits are provided. Significant differences between the results for HDO and H₂O are observed. Additionally, an uncertainty assessment of the obtained data is performed for potential use in modeling non-local thermodynamic equilibrium (non-LTE) spectra of water in various astrophysical environments. Full article

(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)

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9 pages, 2679 KB

Open AccessEditor’s ChoiceArticle

Forced Atom Interferometers in Optical Harmonic Potentials

by Mingjie Xin, Wui Seng Leong, Zilong Chen and Shau-Yu Lan

Atoms 2025, 13(4), 30; https://doi.org/10.3390/atoms13040030 - 3 Apr 2025

Cited by 1 | Viewed by 2067

Abstract

We present a study of Doppler-sensitive light-pulse atom interferometers operating within optical dipole potentials, where atomic trajectories are manipulated using momentum transfer from light pulses and optical forces from the trap. Efficient methods are introduced to minimize the inhomogeneous broadening of oscillation frequencies [...] Read more.

We present a study of Doppler-sensitive light-pulse atom interferometers operating within optical dipole potentials, where atomic trajectories are manipulated using momentum transfer from light pulses and optical forces from the trap. Efficient methods are introduced to minimize the inhomogeneous broadening of oscillation frequencies in atoms confined within a three-dimensional optical lattice trap. These techniques enable the preparation of various quantum states, including vacuum, thermal, and squeezed states, for atom interferometry. Additionally, we demonstrate a two-dimensional atom interferometer using a single optical dipole trap, where transverse motion is activated by offsetting the trap position. Our work provides insights into controlling the mechanical motion of neutral atoms in optical harmonic potentials and contributes to advancing applications in quantum sensing and quantum computing. Full article

(This article belongs to the Special Issue Advances in and Prospects for Matter Wave Interferometry)

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26 pages, 414 KB

Open AccessEditor’s ChoiceArticle

Statistics of Quantum Numbers for Non-Equivalent Fermions in Single-j Shells

by Jean-Christophe Pain

Atoms 2025, 13(4), 25; https://doi.org/10.3390/atoms13040025 - 25 Mar 2025

Cited by 2 | Viewed by 1516

Abstract

This work addresses closed-form expressions for the distributions

P (M)

of the magnetic quantum numbers M and

Q (J)

of total angular momentum J for non-equivalent fermions in single-j orbits. Such quantities play an important role in both [...] Read more.

This work addresses closed-form expressions for the distributions

P (M)

of the magnetic quantum numbers M and

Q (J)

of total angular momentum J for non-equivalent fermions in single-j orbits. Such quantities play an important role in both nuclear and atomic physics, through the shell models. Using irreducible representations of the rotation group, different kinds of formulas are presented, involving multinomial coefficients, generalized Pascal triangle coefficients, or hypergeometric functions. Special cases are discussed, and the connections between

P (M)

(and therefore

Q (J)

) and mathematical functions such as elementary symmetric, cyclotomic, and Jacobi polynomials are outlined. Full article

(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)

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12 pages, 1538 KB

Open AccessEditor’s ChoiceArticle

Properties of a Static Dipolar Impurity in a 2D Dipolar BEC

by Neelam Shukla and Jeremy R. Armstrong

Atoms 2025, 13(3), 24; https://doi.org/10.3390/atoms13030024 - 10 Mar 2025

Viewed by 3142

Abstract

We study a system of ultra-cold dipolar Bose gas atoms confined in a two-dimensional (2D) harmonic trap with a dipolar impurity implanted at the center of the trap. Due to recent experimental progress in dipolar condensates, we focused on calculating properties of dipolar [...] Read more.

We study a system of ultra-cold dipolar Bose gas atoms confined in a two-dimensional (2D) harmonic trap with a dipolar impurity implanted at the center of the trap. Due to recent experimental progress in dipolar condensates, we focused on calculating properties of dipolar impurity systems that might guide experimentalists if they choose to study impurities in dipolar gases. We used the Gross–Pitaevskii formalism solved numerically via the split-step Crank–Nicolson method. We chose parameters of the background gas to be consistent with dysprosium (Dy), one of the strongest magnetic dipoles and of current experimental interest, and used chromium (Cr), erbium (Er), terbium (Tb), and Dy for the impurity. The dipole moments were aligned by an external field along what was chosen to be the z-axis, and we studied 2D confinements that were perpendicular or parallel to the external field. We show density contour plots for the two confinements, 1D cross-sections of the densities, calculated self-energies of the impurities while varying both number of atoms in the condensate and the symmetry of the trap. We also calculated the time evolution of the density of an initially pure system where an impurity is introduced. Our results show that while the self-energy increases in magnitude with increasing number of particles, it is reduced when the trap anisotropy follows the natural anisotropy of the gas, i.e., elongated along the z-axis in the case of parallel confinement. This work builds upon work conducted in Bose gases with zero-range interactions and demonstrates some of the features that could be found when exploring dipolar impurities in 2D Bose gases. Full article

(This article belongs to the Section Cold Atoms, Quantum Gases and Bose-Einstein Condensation)

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10 pages, 816 KB

Open AccessEditor’s ChoiceArticle

Theoretical Investigation on Vortex Electron Impact Excitation of a Mg Atom Confined in a Solid-State Environment

by Sophia Strnat, Aloka K. Sahoo, Lalita Sharma, Jonas Sommerfeldt, Daesung Park, Christian Bick and Andrey Surzhykov

Atoms 2025, 13(3), 23; https://doi.org/10.3390/atoms13030023 - 24 Feb 2025

Viewed by 1985

Abstract

We present a theoretical investigation of the inelastic scattering of vortex electrons by many-electron atoms embedded in a solid-state environment. Special emphasis is placed on the probability of exciting a target atom and on the relative population of its magnetic substates as described [...] Read more.

We present a theoretical investigation of the inelastic scattering of vortex electrons by many-electron atoms embedded in a solid-state environment. Special emphasis is placed on the probability of exciting a target atom and on the relative population of its magnetic substates as described by the set of alignment parameters. These parameters are directly related to the angular distribution of the subsequent radiative decay. To demonstrate the application of the developed theoretical approach, we present calculations for the

3 s^{2} {}^{1}S_{0} \to 3 s 3 p {}^{3}P_{1}

excitation of a Mg atom and its subsequent

3 s 3 p {}^{3}P_{1} \to 3 s^{2} {}^{1}S_{0}

radiative decay. Our results highlight the significance of the orbital angular momentum (OAM) projection as well as the relative position of the vortex electron with respect to the target atom. Full article

(This article belongs to the Special Issue 21st International Conference on the Physics of Highly Charged Ions)

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13 pages, 6452 KB

Open AccessEditor’s ChoiceArticle

Evaluation of Spatial Profile of Local Emissions from W¹⁷⁺–W²³⁺ Unresolved Transition Array Spectra

by Ryota Nishimura, Tetsutarou Oishi, Izumi Murakami, Daiji Kato, Hiroyuki A. Sakaue, Hayato Ohashi, Shivam Gupta, Chihiro Suzuki, Motoshi Goto, Yasuko Kawamoto, Tomoko Kawate, Hiroyuki Takahashi and Kenji Tobita

Atoms 2025, 13(2), 21; https://doi.org/10.3390/atoms13020021 - 18 Feb 2025

Cited by 1 | Viewed by 1247

Abstract

Tungsten (W) spectroscopy has attracted significant attention because W is one of the major impurities in ITER and future DEMO reactors. W²²⁺–W³³⁺ spectra at 15–45 Å have been useful for impurity diagnostics. Unresolved Transition Array (UTA) spectra around 200 Å, [...] Read more.

Tungsten (W) spectroscopy has attracted significant attention because W is one of the major impurities in ITER and future DEMO reactors. W²²⁺–W³³⁺ spectra at 15–45 Å have been useful for impurity diagnostics. Unresolved Transition Array (UTA) spectra around 200 Å, which contain W¹⁷⁺–W²³⁺, have potential for diagnostics tungsten ions in even lower charge states. Because multiple charge states overlap with very similar wavelengths, it is challenging to evaluate impurity spatial profiles from UTA spectra around 200 Å. In this study, we conducted tungsten pellet injection experiments in Large Helical Device (LHD) and attempted to evaluate the spatial profiles of UTA spectra around 200 Å, observed at 0.3–0.8 keV of central electron temperature. The results indicated that tungsten ions around W²⁰⁺ were locally profiled in a radial region, r_eff = 0.38 m, where the local electron temperature decreases by 30% to 40% with respect to more central and outer temperatures. These results suggested that the UTA spectrum around 200 Å would be useful for diagnostics of tungsten impurities in lower charge states than the charge states contained in UTA spectra around 15–45 Å. Full article

(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)

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14 pages, 749 KB

Open AccessEditor’s ChoiceArticle

Modelling of X-Ray Spectra Originating from the He- and Li-like Ni Ions for Plasma Electron Temperature Diagnostics Purposes

by Karol Kozioł, Andrzej Brosławski and Jacek Rzadkiewicz

Atoms 2025, 13(2), 18; https://doi.org/10.3390/atoms13020018 - 9 Feb 2025

Viewed by 1185

Abstract

The multi-configurational Dirac–Hartree–Fock method has been used to examine the electron correlation effect on wavelengths and transition rates for

L \to K

transitions occurring in He- and Li-like nickel ions. The collisional-radiative modelling approach has been used to simulate the X-ray spectra, in [...] Read more.

The multi-configurational Dirac–Hartree–Fock method has been used to examine the electron correlation effect on wavelengths and transition rates for

L \to K

transitions occurring in He- and Li-like nickel ions. The collisional-radiative modelling approach has been used to simulate the X-ray spectra, in a 1.585–1.620 Å wavelength range, originating from the He-like nickel ions and their dielectronic Li-, Be-, and B-like satellites for various electron temperature values in the 2 keV to 8 keV range. The presented results may be useful in improving the plasma electron temperature diagnostics based on nickel spectra. Full article

(This article belongs to the Special Issue Atom and Plasma Spectroscopy)

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18 pages, 1928 KB

Open AccessEditor’s ChoiceArticle

Calculated Transition Probabilities for Os VI Spectral Lines of Interest to Nuclear Fusion Research

by Maxime Brasseur, Patrick Palmeri and Pascal Quinet

Atoms 2025, 13(2), 11; https://doi.org/10.3390/atoms13020011 - 21 Jan 2025

Viewed by 1397

Abstract

In this work, we present a new set of transition probabilities for experimentally classified spectral lines in the Os VI spectrum. To do this, two independent computational approaches based on the pseudo-relativistic Hartree–Fock, including core polarization effects (HFR+CPOL) and fully relativistic Multiconfiguration Dirac–Hartree–Fock [...] Read more.

In this work, we present a new set of transition probabilities for experimentally classified spectral lines in the Os VI spectrum. To do this, two independent computational approaches based on the pseudo-relativistic Hartree–Fock, including core polarization effects (HFR+CPOL) and fully relativistic Multiconfiguration Dirac–Hartree–Fock (MCDHF) methods, were used, with the detailed comparison of the results obtained with these two approaches allowing us to estimate the quality of the calculated radiative parameters. These atomic data, corresponding to 367 lines of five-times ionized osmium between 438.720 and 1486.275 Å, are expected to be useful for the analysis of the spectra emitted by fusion plasmas in which osmium could appear as a result of transmutation by the neutron bombardment of tungsten used as component of the reactor wall, such as the ITER divertor. Full article

(This article belongs to the Special Issue Atom and Plasma Spectroscopy)

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12 pages, 617 KB

Open AccessEditor’s ChoiceArticle

Exploring the Nuclear Chart via Precision Mass Spectrometry with the TITAN MR-TOF MS

by Annabelle Czihaly, Soenke Beck, Julian Bergmann, Callum L. Brown, Thomas Brunner, Timo Dickel, Jens Dilling, Eleanor Dunling, Jake Flowerdew, Danny Fusco, Leigh Graham, Zach Hockenbery, Chris Izzo, Andrew Jacobs, Brian Kootte, Yang Lan, Stephan Malbrunot-Ettenauer, Fernando Maldonado Millán, Ali Mollaebrahimi, Erich Leistenschneider, Eleni Marina Lykiardopoulou, Ish Mukul, Stefan F. Paul, Wolfgang R. Plaß, Moritz Pascal Reiter, Christoph Scheidenberger, James L. Tracy, Jr. and A. A. Kwiatkowski Show full author list Hide full author list

Atoms 2025, 13(1), 6; https://doi.org/10.3390/atoms13010006 - 9 Jan 2025

Cited by 1 | Viewed by 2838

Abstract

Isotopes at the limits of nuclear existence are of great interest for their critical role in nuclear astrophysical reactions and their exotic structure. Experimentally, exotic nuclides are challenging to address due to their low production cross-sections, overwhelming amounts of contamination, and lifetimes of [...] Read more.

Isotopes at the limits of nuclear existence are of great interest for their critical role in nuclear astrophysical reactions and their exotic structure. Experimentally, exotic nuclides are challenging to address due to their low production cross-sections, overwhelming amounts of contamination, and lifetimes of typically less than a second. To this end, a Multiple-Reflection Time-of-Flight mass spectrometer at the TITAN-TRIUMF facility was built to determine atomic masses. This device is the preferred tool to work with exotic nuclides due to its ability to resolve the species of interest from contamination and short measurement cycle times, enabling mass measurements of isotopes with millisecond half-lives. With a relative precision of the order 10⁻⁷, we demonstrate why the TITAN MR-TOF MS is the tool of choice for precision mass surveys for nuclear structure and astrophysics. The capabilities of the device are showcased in this work, including new mass measurements of short-lived tin isotopes (^104–107Sn) approaching the proton dripline as well as ⁸⁹Zr, ⁹⁰Y, and ⁹¹Y. The last three illustrate how the broadband surveys of MR-TOF MS reach beyond the species of immediate interest. Full article

(This article belongs to the Special Issue Advances in Ion Trapping of Radioactive Ions)

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11 pages, 1889 KB

Open AccessEditor’s ChoiceArticle

Chemical Lasers Based on Polyatomic Reaction Dynamics: Research of Vibrational Excitation in a Reactive

by José Daniel Sierra Murillo

Atoms 2025, 13(1), 5; https://doi.org/10.3390/atoms13010005 - 9 Jan 2025

Cited by 3 | Viewed by 1464

Abstract

The research presented by the author investigates a polyatomic reaction occurring in the gas phase. This study employs the Quasi-Classical Trajectory (QCT) approach using the Wu–Schatz–Lendvay–Fang–Harding (WSLFH) potential energy surface (PES), recognized as one of the most reliable PES models for this type [...] Read more.

The research presented by the author investigates a polyatomic reaction occurring in the gas phase. This study employs the Quasi-Classical Trajectory (QCT) approach using the Wu–Schatz–Lendvay–Fang–Harding (WSLFH) potential energy surface (PES), recognized as one of the most reliable PES models for this type of analysis. The substantial sample size enables the derivation of detailed results that corroborate previous findings while also identifying potential objectives for future experimental work. The Gaussian Binning (GB) technique is utilized to more effectively highlight the variation in the total angular momentum (J′) of the excited product molecule, HOD*. A key aim of the study is to explore the reaction dynamics due to their importance in excitation and emission processes, which may contribute to the development of a chemical laser based on this reaction. Increasing the vibrational level, v, of one reactant, D₂, significantly enhances the excitation of HOD* and shifts the P(J′) distributions towards higher J′ values, while also broadening the distribution. Although the current research focuses on a few initial conditions, the author plans to extend the study to encompass a wider range of initial conditions within the reaction chamber of this type of chemical laser. Full article

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13 pages, 1408 KB

Open AccessEditor’s ChoiceArticle

Cooper Pairs in 2D Trapped Atoms Interacting Through Finite-Range Potentials

by Erick Manuel Pineda-Ríos and Rosario Paredes

Atoms 2025, 13(1), 4; https://doi.org/10.3390/atoms13010004 - 7 Jan 2025

Viewed by 2273

Abstract

This work deals with the key constituent behind the existence of superfluid states in ultracold fermionic gases confined in a harmonic trap in 2D, namely, the formation of Cooper pairs in the presence of a Fermi sea in inhomogeneous confinement. For a set [...] Read more.

This work deals with the key constituent behind the existence of superfluid states in ultracold fermionic gases confined in a harmonic trap in 2D, namely, the formation of Cooper pairs in the presence of a Fermi sea in inhomogeneous confinement. For a set of finite-range models representing particle–particle interaction, we first ascertain the simultaneity of the emergence of bound states and the divergence of the s-wave scattering length in 2D as a function of the interaction potential parameters in free space. Then, through the analysis of two particles interacting in 2D harmonic confinement, we evaluate the energy shift with respect to the discrete harmonic oscillator levels for both repulsive and attractive cases. All of these results are the basis for determining the energy gaps of Cooper pairs arising from two particles interacting in the presence of a Fermi sea consisting of particles immersed in a 2D harmonic trap. Full article

(This article belongs to the Special Issue Quantum Technologies with Cold Atoms)

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11 pages, 1434 KB

Open AccessEditor’s ChoiceArticle

Emergence of Quantum Vortices in the Ionization of Helium by Proton Impact, and How to Measure Them

by Tamara A. Guarda, Francisco Navarrete and Raúl O. Barrachina

Atoms 2025, 13(1), 3; https://doi.org/10.3390/atoms13010003 - 6 Jan 2025

Viewed by 1927

Abstract

This study investigates how the presence of quantum vortices affects the ionization cross-section of helium atoms by 75 keV proton impact, with special attention to the region near the electron capture to the continuum (ECC) cusp. It has been found that these vortices [...] Read more.

This study investigates how the presence of quantum vortices affects the ionization cross-section of helium atoms by 75 keV proton impact, with special attention to the region near the electron capture to the continuum (ECC) cusp. It has been found that these vortices cause a significant reduction in the intensity of the

{| T |}^{2}

distribution in the low-energy region of the ECC cusp, leading to a considerable distortion that facilitates its experimental determination. Furthermore, the analysis shows that one of the vortices coincides with the Thomas angle (a parameter coming from the classical ion-electron Thomas mechanism). Full article

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11 pages, 260 KB

Open AccessEditor’s ChoiceArticle

Nuclear Hyperfine Mixing Effect in Highly Charged ²⁰⁵Pb Ions

by Wu Wang, Yong Li and Xu Wang

Atoms 2025, 13(1), 2; https://doi.org/10.3390/atoms13010002 - 3 Jan 2025

Cited by 3 | Viewed by 1696

Abstract

In highly charged ions, significant nuclear hyperfine mixing (NHM) effects can arise when the electromagnetic field generated by the electrons interacts strongly with the nucleus, leading to mixing of nuclear states. While previous studies have primarily attributed the NHM effect to unpaired valence [...] Read more.

In highly charged ions, significant nuclear hyperfine mixing (NHM) effects can arise when the electromagnetic field generated by the electrons interacts strongly with the nucleus, leading to mixing of nuclear states. While previous studies have primarily attributed the NHM effect to unpaired valence electrons, we present a reformulation of the theoretical framework using dressed hyperfine states and investigate the NHM effect in ²⁰⁵Pb⁷⁶⁺, ²⁰⁵Pb⁷⁵⁺, ²⁰⁵Pb⁷⁴⁺, and ²⁰⁵Pb⁷³⁺ ions. Our numerical results show that significant NHM effects occurred in all of the studied ions, even in the absence of unpaired valence electrons in ²⁰⁵Pb⁷⁶⁺ and ²⁰⁵Pb⁷⁴⁺. We found that the lifetime of the isomeric state was reduced by 2–4 orders of magnitude compared with the bare ²⁰⁵Pb nucleus, depending on the charge state of the ion. These results indicate that it is the active valence electrons rather than unpaired electrons which play a key role in the NHM effect, thereby deepening our understanding of this phenomenon. Full article

(This article belongs to the Special Issue 21st International Conference on the Physics of Highly Charged Ions)

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