Atoms

18 pages, 799 KB

Open AccessArticle

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

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 AccessArticle

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

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 C [...] 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 C^l+, 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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13 pages, 1356 KB

Open AccessArticle

Fractatomic Physics: Atomic Stability and Rydberg States in Fractal Spaces

by Nhat A. Nghiem and Trung V. Phan

Atoms 2026, 14(1), 2; https://doi.org/10.3390/atoms14010002 - 31 Dec 2025

Abstract

We explore the physical quantum properties of atoms in fractal spaces, both as a theoretical generalization of normal integer-dimensional Euclidean spaces and as an experimentally realizable setting. We identify the threshold of fractality at which Ehrenfest atomic instability emerges, where the Schrödinger equation [...] Read more.

We explore the physical quantum properties of atoms in fractal spaces, both as a theoretical generalization of normal integer-dimensional Euclidean spaces and as an experimentally realizable setting. We identify the threshold of fractality at which Ehrenfest atomic instability emerges, where the Schrödinger equation describing the wavefunction of a single electron orbiting around an atom becomes scale-free, and discuss the potential of observing this phenomena in laboratory settings. We then study the Rydberg states of stable atoms using the Wentzel–Kramers–Brillouin approximation, along with a proposed extension for the Langer modification, in general fractal dimensionalities. We show that fractal space atoms near instability explode in size even at low-number excited state, making them highly suitable to induce strong entanglements and foster long-range many-body interactions. We argue that atomic physics in fractal spaces—“fractatomic physics”—is a rich research avenue deserving of further theoretical and experimental investigations. Full article

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15 pages, 10342 KB

Open AccessArticle

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

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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19 pages, 3573 KB

Open AccessArticle

Time-Dependent Theory of Electron Emission Perpendicular to Laser Polarization for Reconstruction of Attosecond Harmonic Beating by Interference of Multiphoton Transitions

by Matías L. Ocello, Sebastián D. López, Martín Barlari and Diego G. Arbó

Atoms 2025, 13(12), 99; https://doi.org/10.3390/atoms13120099 - 10 Dec 2025

Abstract

We present a time-dependent nonperturbative theory of the reconstruction of attosecond beating by interference of multiphoton transitions (RABBIT) for photoelectron emission from hydrogen atoms in the transverse direction relative to the laser polarization axis. Extending our recent semiclassical strong-field approximation (SFA) model developed [...] Read more.

We present a time-dependent nonperturbative theory of the reconstruction of attosecond beating by interference of multiphoton transitions (RABBIT) for photoelectron emission from hydrogen atoms in the transverse direction relative to the laser polarization axis. Extending our recent semiclassical strong-field approximation (SFA) model developed for parallel emission, we deduce analytical expressions for the transition amplitudes and demonstrate that the photoelectron probability distribution can be factorized into interhalf- and intrahalfcycle interference contributions, the latter modulating the intercycle pattern responsible for sideband formation. We identify the intrahalfcycle interference arising from trajectories released within the same half cycle as the mechanism governing attosecond phase delays in the perpendicular geometry. Our results reveal the suppression of even-order sidebands due to destructive interhalfcycle interference, leading to a characteristic spacing between adjacent peaks that doubles the standard spacing observed along the polarization axis. Comparisons with numerical calculations of the SFA and the ab initio solution of the time-dependent Schrödinger equation confirm the accuracy of the semiclassical description. This work provides a unified framework for understanding quantum interferences in attosecond chronoscopy, bridging the cases of parallel and perpendicular electron emission in RABBIT-like protocols. Full article

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15 pages, 487 KB

Open AccessArticle

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

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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22 pages, 648 KB

Open AccessArticle

The Validity of Long Wavelength Approximation in the Evaluation of Two-Photon Decay Rate

by George-Tony Constantin and Cristian Iorga

Atoms 2025, 13(12), 97; https://doi.org/10.3390/atoms13120097 - 4 Dec 2025

Abstract

This paper investigates the validity of the long wavelength approximation in the calculation of two-photon decay of

2 s_{1 / 2}

level in hydrogen-like ions with nuclear charge

Z = 1 - 100

based on time-dependent second-order perturbation theory and angular momentum [...] Read more.

This paper investigates the validity of the long wavelength approximation in the calculation of two-photon decay of

2 s_{1 / 2}

level in hydrogen-like ions with nuclear charge

Z = 1 - 100

based on time-dependent second-order perturbation theory and angular momentum algebra. While the relativistic structure effects on the two-photon decay rates are highlighted in the literature, the role of slowing effects in the photon electric dipole operators are not discussed extensively. The rate is computed by the sum-over-states method, with bound-bound and bound-free electric dipole matrix elements obtained in the Babushkin and Coulomb gauges, which satisfy the Lorenz gauge condition, as well as their non-relativistic limits in the long-wavelength approximation (Length and Velocity forms, respectively). The present results explicitly show how this approximation breaks gauge invariance by overestimating the Babushkin values by ∼24%

{(α Z)}^{2}

while underestimating the Coulomb rates by ∼

31 % {(α Z)}^{2}

. Using analytical eigenfunctions of the Dirac equation, we found that the contributions of the negative continuum states to the rate scale are ∼

0.0134 {(α Z)}^{4}

in the Babushkin gauge and ∼

1.46 {(α Z)}^{4}

in the Coulomb gauge, making the latter gauge more susceptible to errors when attempting to achieve basis completeness in multiphoton calculations. The present results are useful in assessing the complexity requirements of radiative transition rates for atomic systems of interest. Full article

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

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14 pages, 1283 KB

Open AccessArticle

A Comparative Study of COMPLET Code Predictions with Experimental Data on Alpha Particle-Induced Reactions on Cobalt Isotope up to 120 MeV

by Cherie Sisay Mekonen and Ayyagari Venkata Mohan Rao

Atoms 2025, 13(12), 96; https://doi.org/10.3390/atoms13120096 - 4 Dec 2025

Abstract

A comparative study of alpha-induced reactions on cobalt isotope with the predictions by COMPLET code is presented for nine excitation functions, ⁵⁹Co(α,p5n)⁵⁷Ni, ⁵⁹Co (α,p6n)⁵⁶Ni, ⁵⁹Co(α,2pn)⁶⁰Co, ⁵⁹Co(α,3pn)⁵⁹Fe, ⁵⁹Co(α,αn)⁵⁸Co, ⁵⁹ [...] Read more.

A comparative study of alpha-induced reactions on cobalt isotope with the predictions by COMPLET code is presented for nine excitation functions, ⁵⁹Co(α,p5n)⁵⁷Ni, ⁵⁹Co (α,p6n)⁵⁶Ni, ⁵⁹Co(α,2pn)⁶⁰Co, ⁵⁹Co(α,3pn)⁵⁹Fe, ⁵⁹Co(α,αn)⁵⁸Co, ⁵⁹Co(α,α2n)⁵⁷Co, ⁵⁹Co(α,α3n)⁵⁶Co, ⁵⁹Co(α,2αn)⁵⁴Mn, and ⁵⁹Co(α,2α3n)⁵²Mn. The experimental values were taken from the EXFOR data base. Theoretical cross-sections were calculated using initial exciton number n₀ = 4 (4p0h) and level density parameter a (=ACN/10) globally. While several reactions showed excellent agreement with experimental data, others displayed a notable discrepancy. This is because of the limitations of the COMPLET code to take the alpha emission in a pre-equilibrium phase. Full article

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11 pages, 257 KB

Open AccessOpinion

Effective Action Approach to Quantum and Thermal Effects: From One Particle to Bose–Einstein Condensates

by Luca Salasnich

Atoms 2025, 13(12), 95; https://doi.org/10.3390/atoms13120095 - 1 Dec 2025

Abstract

We present a detailed derivation of the quantum and quantum–thermal effective action for non-relativistic systems, starting from the single-particle case and extending to the Gross–Pitaevskii (GP) field theory for weakly interacting bosons. In the single-particle framework, we introduce the one-particle-irreducible (1PI) effective action [...] Read more.

We present a detailed derivation of the quantum and quantum–thermal effective action for non-relativistic systems, starting from the single-particle case and extending to the Gross–Pitaevskii (GP) field theory for weakly interacting bosons. In the single-particle framework, we introduce the one-particle-irreducible (1PI) effective action formalism, taking explicitly into account the choice of the initial quantum state, its saddle-point plus Gaussian-fluctuation approximation, and its finite-temperature extension via Matsubara summation, yielding a clear physical interpretation in terms of zero-point and thermal contributions to the Helmholtz free energy. The formalism is then applied to the GP action, producing the 1PI effective potential at zero and finite temperature, including beyond-mean-field Lee–Huang–Yang and thermal corrections. We discuss the gapless and gapped Bogoliubov spectra, their relevance to equilibrium and non-equilibrium regimes, and the role of regularization. Applications include the inclusion of an external potential within the local density approximation, the derivation of finite-temperature Josephson equations, and the extension to D-dimensional systems, with particular attention to the zero-dimensional limit. This unified approach provides a transparent connection between microscopic quantum fluctuations and effective macroscopic equations of motion for Bose–Einstein condensates. Full article

14 pages, 6427 KB

Open AccessArticle

Electron Scattering from Superheavy Elements: Copernicium and Oganesson

by Shruti Sarswat, Saumyashree Baral and Jobin Jose

Atoms 2025, 13(11), 94; https://doi.org/10.3390/atoms13110094 - 20 Nov 2025

Abstract

Superheavy elements are an ideal testbed for studying relativistic, exchange, and correlation effects in scattering phenomena. In this work, we investigate electron scattering from copernicium

(Z = 112)

and oganesson

(Z = 118)

atoms. Both the relativistic Dirac and [...] Read more.

Superheavy elements are an ideal testbed for studying relativistic, exchange, and correlation effects in scattering phenomena. In this work, we investigate electron scattering from copernicium

(Z = 112)

and oganesson

(Z = 118)

atoms. Both the relativistic Dirac and non-relativistic partial wave methods are employed to analyze the scattering dynamics, with the interaction between the projectile and target atom modeled within the framework of the optical potential approach. Our results demonstrate that relativistic, exchange, and correlation effects play a significant role in modifying the scattering cross-sections and scattering length, highlighting the influence of these interactions on the scattering processes from superheavy atomic systems. The work also attempts to identify common features of the scattering cross-section by comparing those of lighter elements in the same group. Full article

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

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13 pages, 914 KB

Open AccessArticle

Antiprotonic Atoms as Gateways to HCI

by Lidia Lappo, Jakub Zieliński, Fredrik P. Gustafsson, Malgorzata Grosbart, Georgy Kornakov and Michael Doser

Atoms 2025, 13(11), 93; https://doi.org/10.3390/atoms13110093 - 19 Nov 2025

Abstract

The present study investigates the production of highly charged ions (HCIs) through the novel application of antiprotonic atoms and explores their potential for studying atomic and nuclear structures. Utilizing the Geant4 simulation toolkit, comprehensive simulations were conducted for all known isotopes with atomic [...] Read more.

The present study investigates the production of highly charged ions (HCIs) through the novel application of antiprotonic atoms and explores their potential for studying atomic and nuclear structures. Utilizing the Geant4 simulation toolkit, comprehensive simulations were conducted for all known isotopes with atomic numbers below 100. These simulations recorded key parameters of the resulting nuclear fragments, including mass, momentum, charge, and yield. The results obtained from this study offer valuable insights into the mechanisms of HCI production and provide a foundation for planning and analyzing future experimental investigations. This work demonstrates the feasibility of using antiprotonic atoms to advance nuclear and atomic physics research. Full article

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

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18 pages, 1413 KB

Open AccessArticle

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

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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20 pages, 2241 KB

Open AccessArticle

Computational and Spectroscopic Investigation of Diaminomethane Formation: The Simplest Geminal Diamine of Astrochemical Interest

by Pravi Mishra, Parmanand Pandey, Rachana Singh, Manisha Yadav, Shivani, Aftab Ahamad, Alka Misra, Amritanshu Shukla and Poonam Tandon

Atoms 2025, 13(11), 91; https://doi.org/10.3390/atoms13110091 - 12 Nov 2025

Abstract

A high-level ab initio characterization and formation of diaminomethane (DAM), the simplest geminal diamine, is presented to support its spectroscopic detection and astrochemical relevance in the interstellar medium. The C_2v DAM conformer is identified as the global minimum, while C₁ [...] Read more.

A high-level ab initio characterization and formation of diaminomethane (DAM), the simplest geminal diamine, is presented to support its spectroscopic detection and astrochemical relevance in the interstellar medium. The C_2v DAM conformer is identified as the global minimum, while C₁ DAM and C₂ DAM represent higher-energy local minima. The proposed reaction pathways are exothermic and proceed without activation barriers. Simulated infrared spectrum reproduces accurate key spectral signatures with several vibrational modes exhibiting strong IR intensities (>80 km mol⁻¹), particularly in the 800–3000 cm⁻¹ range and band shapes. Dipole moments and accurate rovibrational spectroscopic parameters, including rotational constants, anharmonic vibrational frequencies, quartic and sextic distortion constants, and nuclear quadrupole coupling constants are reported to assist with high-resolution spectroscopic identification. This study provides significant theoretical benchmarks for its formation and offers guidance for future laboratory spectroscopy and molecular searches in interstellar environments. Full article

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14 pages, 6876 KB

Open AccessArticle

Improving Quantitative Analysis of Lithium in Brines Using Laser-Induced Breakdown Spectroscopy with τ–Algorithm (τLIBS)

by Juan Molina M., Carlos Aragón, José A. Aguilera, César Costa-Vera and Diego M. Díaz Pace

Atoms 2025, 13(11), 90; https://doi.org/10.3390/atoms13110090 - 12 Nov 2025

Abstract

In this work, a quantitative analysis of Li in natural brines was carried out by laser-induced breakdown spectroscopy (LIBS) assisted by the τ–algorithm for detailed analysis of the experimental line shapes (τLIBS). Brine samples were collected from different salars located in the Puna [...] Read more.

In this work, a quantitative analysis of Li in natural brines was carried out by laser-induced breakdown spectroscopy (LIBS) assisted by the τ–algorithm for detailed analysis of the experimental line shapes (τLIBS). Brine samples were collected from different salars located in the Puna plateau (Northwest Argentina) and analyzed by LIBS in the form of solid pressed pellets. The emission intensities of Li I, H_α, and Mg I–II lines were measured and spatially integrated along the line of sight with temporal resolution by using a high-spectral-resolution spectrometer equipped with an intensified charge-coupled device (iCCD) detector. The plasma was characterized through the determination of the electron density and the temperature. The τ–algorithm calculated the optical thicknesses of the Li I lines to generate synthetic intensity profiles that were subsequently fitted to the experimental spectra. By applying the developed τLIBS approach, valuable spectroscopic insight was recovered about the physical processes occurring in the plasma, such as self-absorption. The analytical process involved an univariate external calibration process using the resonant Li I line at 6707.7 Å measured from a series of Li standard samples. Self-absorption effects were evaluated and subsequently compensated. The final LIBS results, with an enhanced accuracy of 15%, were validated by crosschecking them against those obtained with the standard AAS method. Full article

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Graphical abstract

16 pages, 1425 KB

Open AccessArticle

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

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 AccessArticle

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

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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38 pages, 792 KB

Open AccessArticle

First and Second Law of Thermodynamics Constraints in the Lifshitz Theory of Dispersion Forces

by Fabrizio Pinto

Atoms 2025, 13(11), 87; https://doi.org/10.3390/atoms13110087 - 5 Nov 2025

Abstract

The presence of dominant interatomic dispersion forces on the nanoscale holds the promise for breakthrough applications in key areas of quantum sensing, such as accelerometry, as well as nano-manipulation and energy storage. In order to do work, nano-machines enabled by dispersion forces must [...] Read more.

The presence of dominant interatomic dispersion forces on the nanoscale holds the promise for breakthrough applications in key areas of quantum sensing, such as accelerometry, as well as nano-manipulation and energy storage. In order to do work, nano-machines enabled by dispersion forces must exchange energy with the surrounding environment. Such processes can be described in terms of thermodynamical engine cycles involving individual atoms or material boundaries, separated by possibly empty gaps and interacting via time-dependent dispersion forces. The fundamental strategy indispensable to achieve dispersion force time-modulation, demonstrated experimentally by independent groups on different scales, is based on the illumination of interacting, semiconducting elements by appropriate radiation beams. Here we analyze the operation of ideal nano-engines in the quasi-static regime by means of the Lifshitz theory of dispersion forces involving semiconducting boundary or atom irradiation. Firstly, we verify that the First Law of Thermodynamics is satisfied so that the total energy of the system is rigorously conserved. Secondly, we show that, within this first approximate treatment, the Second Law of Thermodynamics may be violated for extremely small interboundary gap widths. We identify important limitations to be addressed to determine whether this is a reliable conclusion. The technological and historic backdrops are presented, and important topics for future research are identified. Full article

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8 pages, 467 KB

Open AccessArticle

The Arrow of Time in Quantum Theory

by Jean-Patrick Connerade

Atoms 2025, 13(11), 86; https://doi.org/10.3390/atoms13110086 - 26 Oct 2025

Abstract

In Classical Mechanics, time is reversible, i.e., it implies no particular choice: only the observer knows in which direction it flows. The present article re-examines whether this remains true in Quantum Mechanics. In the context of Atomic Physics, it is concluded that the [...] Read more.

In Classical Mechanics, time is reversible, i.e., it implies no particular choice: only the observer knows in which direction it flows. The present article re-examines whether this remains true in Quantum Mechanics. In the context of Atomic Physics, it is concluded that the existence of an arrow of time depends on the manner in which the radiation field is introduced, which must be non-perturbative. Full article

12 pages, 1196 KB

Open AccessArticle

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 1

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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