Atoms

18 pages, 1213 KB

Open AccessArticle

An Analytical Model for the Time Distribution of Muonic Oxygen X-Rays in Muonic Experiments

by Petar Danev, Iavor Boradjiev and Hristo Tonchev

Atoms 2026, 14(5), 37; https://doi.org/10.3390/atoms14050037 - 27 Apr 2026

We propose an analytical model and perform numerical simulations to study the time distribution of the characteristic muonic oxygen X-ray emission following muon transfer from muonic hydrogen to oxygen in a H₂ + O₂ gas mixture. The model accounts for all [...] Read more.

We propose an analytical model and perform numerical simulations to study the time distribution of the characteristic muonic oxygen X-ray emission following muon transfer from muonic hydrogen to oxygen in a H₂ + O₂ gas mixture. The model accounts for all fundamental processes that alter the kinetic energy and spin distribution of muonic hydrogen atoms. The impact of the uncertainties in various experimental parameters on the precision of the computed results is studied in detail by means of the Monte Carlo method. Specifically, we observe the presence of a minimum in the time dependence of the relative standard deviation of X-ray emission for realistic parameter combinations, which can serve as a benchmark for comparing experiments and numerical simulations. Verification against available experimental data reveals the potential of this approach for both description and parameter optimization in the planning and analysis of muonic experiments Full article

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

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16 pages, 607 KB

Open AccessArticle

Ionization of Helium by Proton Impact in a Quasi-Sturmian Approach Built upon the 3C Model

by Sergey A. Zaytsev, Darya S. Zaytseva, Alexander S. Zaytsev, Lorenzo U. Ancarani, Konstantin A. Kouzakov and Yury V. Popov

Atoms 2026, 14(5), 36; https://doi.org/10.3390/atoms14050036 - 26 Apr 2026

Abstract

We investigate theoretically the 75 keV proton-impact ionization of atomic helium. The convoluted quasi-Sturmian approach is extended to treat, on an equal footing, both the direct mechanism and the electron capture to the continuum. This is achieved by proposing an ansatz of the [...] Read more.

We investigate theoretically the 75 keV proton-impact ionization of atomic helium. The convoluted quasi-Sturmian approach is extended to treat, on an equal footing, both the direct mechanism and the electron capture to the continuum. This is achieved by proposing an ansatz of the Green’s function of the three-body Coulomb system

(e^{-}, {H e}^{+}, p^{+})

that is compatible with the well-known 3C correlated continuum wave function. The model that stems from this approximation, named

3 \tilde{C}

, is tested numerically using parabolic Sturmian expansions. Calculations of fully differential cross sections are presented for different regimes of energy losses, namely for ejected electron energies below, nearly equal to, and above the cusp energy. Our results are compared with recent experimental measurements and other theoretical calculations. The proposed

3 \tilde{C}

model yields very encouraging results and paves the way towards a more advanced Lippmann–Schwinger approach based on the 3C model. Full article

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

15 pages, 441 KB

Open AccessArticle

Rci-q: An Improved QED Correction Model for the Grasp2018 Package

by Karol Kozioł

Atoms 2026, 14(5), 35; https://doi.org/10.3390/atoms14050035 - 24 Apr 2026

Abstract

The Rci-Q package is an extension to the Grasp2018 suite, improving the model of estimating the quantum electrodynamics corrections to the energy levels. The Flambaum–Ginges radiative potential method is used to estimate the leading self-energy correction to electron energy in many electron [...] Read more.

The Rci-Q package is an extension to the Grasp2018 suite, improving the model of estimating the quantum electrodynamics corrections to the energy levels. The Flambaum–Ginges radiative potential method is used to estimate the leading self-energy correction to electron energy in many electron atoms. The new fitting prefactors to parameterize radiative potential are presented. The correction to self-energy originating from finite nucleus size is included. The Wichmann–Kroll part of the vacuum polarization potential is also implemented. 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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18 pages, 978 KB

Open AccessArticle

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

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

Atoms 2026, 14(5), 34; https://doi.org/10.3390/atoms14050034 - 23 Apr 2026

Abstract

We present fully relativistic calculations of integral cross sections and swarm transport properties for positron–radon scattering over a wide energy range (0–1000 eV) and reduced electric field range (0.01–1000 Td). Elastic (total, momentum-transfer and viscosity-transfer), discrete excitation, direct annihilation, positronium formation and positron-impact [...] Read more.

We present fully relativistic calculations of integral cross sections and swarm transport properties for positron–radon scattering over a wide energy range (0–1000 eV) and reduced electric field range (0.01–1000 Td). Elastic (total, momentum-transfer and viscosity-transfer), discrete excitation, direct annihilation, positronium formation and positron-impact ionization cross sections are obtained using a complex relativistic optical potential method. Owing to the large atomic number of radon and the absence of experimental scattering data, a consistent relativistic treatment is essential. The present work provides the first fully relativistic, internally consistent cross-section dataset for positron swarms in radon gas. Using a multi-term solution of Boltzmann’s equation, steady-state transport coefficients are calculated and found to be strongly influenced by energy-dependent reactive loss, particularly positronium formation. Significant divergence between bulk and flux transport coefficients is observed, including non-monotonic bulk drift velocities and pronounced suppression of longitudinal bulk diffusion at intermediate fields (0.3–1000 Td). Time-dependent field-free calculations further quantify thermalization and annihilation dynamics through the evolution of the mean energy and

⟨ Z_{eff} ⟩ (t)

. These results provide a robust theoretical foundation for modelling positron transport and annihilation in radon and other heavy noble gases where relativistic and reactive effects are crucial. Full article

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

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11 pages, 1880 KB

Open AccessArticle

State-Selective Single-Electron Capture from H₂O at Low Collision Energies Using the Classical Trajectory Monte Carlo Method

by James A. Perez and Josh A. Muller

Atoms 2026, 14(4), 33; https://doi.org/10.3390/atoms14040033 - 10 Apr 2026

Abstract

A three-body classical trajectory Monte Carlo method is used to investigate state-specific electron capture from H₂O by highly charged ions. The radial and momentum distributions of the target electron are modeled using a one-center molecular orbital wave function. Total single-electron capture [...] Read more.

A three-body classical trajectory Monte Carlo method is used to investigate state-specific electron capture from H₂O by highly charged ions. The radial and momentum distributions of the target electron are modeled using a one-center molecular orbital wave function. Total single-electron capture cross sections, as well as cross sections for capture into specific

n l

-states, are calculated for the highly charged ion projectiles, C⁶⁺, N⁷⁺, Ne¹⁰⁺, and Ar¹⁸⁺, at relative collision energies ranging from 0.01 keV/amu to 50 keV/amu. Comparisons of relative

n

-state capture populations and total single-electron capture cross sections are made with experimental results. The results show a marked improvement in the prediction of relative

n

-states populated, with the overall single-electron single capture cross sections being slightly low compared with experimental values. Overall, this method of calculating

n l

-states of the captured electron appears to be a promising approach for those wishing to model X-ray and Extreme Ultraviolet (EUV) emissions from comets bombarded by solar wind ions, and fusion researchers trying to determine the effects of impurities in Tokomak reactors. Full article

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13 pages, 281 KB

Open AccessTutorial

Long-Lived 3d Levels in Highly Charged Iron Ions

by Elmar Träbert

Atoms 2026, 14(4), 32; https://doi.org/10.3390/atoms14040032 - 10 Apr 2026

Abstract

In Na- through Ca-like ions of Fe, rather low-lying 3d levels feature level lifetimes in the range from picoseconds to many seconds. This lifetime range is somewhat wider than that of the 3p resonance levels of the same ions. When trying to measure [...] Read more.

In Na- through Ca-like ions of Fe, rather low-lying 3d levels feature level lifetimes in the range from picoseconds to many seconds. This lifetime range is somewhat wider than that of the 3p resonance levels of the same ions. When trying to measure such level lifetimes, the width of the range exceeds the capabilities of a single measurement scheme. However, there also is the fundamental problem of multi-exponential decay curves and the reliability of their analysis. This problem has arisen afresh for the analysis of long-lived 3p levels in the ground configurations of many isoelectronic sequences that are replenished by cascades from long-lived 3d levels that have no

E 1

decay channels, but consequently feature lifetimes of the same order of magnitude as those in the ground configuration. This tutorial addresses the measurement situation for lifetimes of 3d levels in a number of ions of Fe and nearby elements. Full article

(This article belongs to the Special Issue Current Studies and Applications of Radiative and Collisional Processes in Atoms)

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12 pages, 416 KB

Open AccessArticle

Ionization in C⁶⁺+He Collisions: Singly Differential Cross-Sections

by Sh. U. Alladustov, K. H. Spicer, N. W. Antonio, A. M. Kotian and A. S. Kadyrov

Atoms 2026, 14(4), 31; https://doi.org/10.3390/atoms14040031 - 9 Apr 2026

Abstract

Differential ionization in

C^{6 +} +

He collisions is investigated using the single- and two-center wave-packet convergent close-coupling (WP-CCC) method for projectile energies of 1–6 MeV/u. We present three types of singly differential cross-sections (SDCSs) as functions of the ejection angle, ejection [...] Read more.

Differential ionization in

C^{6 +} +

He collisions is investigated using the single- and two-center wave-packet convergent close-coupling (WP-CCC) method for projectile energies of 1–6 MeV/u. We present three types of singly differential cross-sections (SDCSs) as functions of the ejection angle, ejection energy, and projectile scattering angle. The two-center framework incorporates couplings across all channels as well as electron correlations. Overall, both the single- and two-center WP-CCC results agree well with existing experimental and theoretical data (apart from the first Born ones) for the SDCS as a function of electron energy and the SDCS as a function of ejection angle, laying a foundation for investigation of doubly and fully differential ionization cross-sections. The cross-sections differential in the projectile scattering angle are presented for the first time. Full article

(This article belongs to the Special Issue Electronic Dynamics in Atomic and Molecular Collisions)

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9 pages, 1281 KB

Open AccessArticle

Charge Exchange Studies with n-, l-, and spin-Quantum State Population in Ar⁷⁺-He Collisions

by Yijiao Wu, Hao Yin, Bingsheng Tu, Tianming Meng, Pufang Ma, Xu Tan, Ke Yao, Jun Xiao, Yaming Zou and Baoren Wei

Atoms 2026, 14(4), 30; https://doi.org/10.3390/atoms14040030 - 8 Apr 2026

Abstract

The energy-dependent population of fine quantum states in single electron capture (SEC) reflects the intrinsic collision dynamics. Here we report experimental studies of Ar⁷⁺ ions colliding with He in the energy range of 1.05–17.5 keV/u. Owing to the high resolution of a [...] Read more.

The energy-dependent population of fine quantum states in single electron capture (SEC) reflects the intrinsic collision dynamics. Here we report experimental studies of Ar⁷⁺ ions colliding with He in the energy range of 1.05–17.5 keV/u. Owing to the high resolution of a recoil-ion momentum spectrometer, the n-, l-, and spin-state electron capture populations are well resolved, and a strong energy dependence of the SEC cross sections is observed. Most importantly, a clear inversion of the cross-section ratio between the spin-resolved triplet and singlet 3s3d configurations is found, demonstrating a breakdown of spin statistics. Together with recent spin-resolved studies of C³⁺-He collisions (PRL 133, 173002 (2024)), these results suggest that the breakdown of spin statistics is likely a general feature of charge exchange in open-shell highly charged ion systems. Full article

(This article belongs to the Special Issue Electronic Dynamics in Atomic and Molecular Collisions)

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97 pages, 1163 KB

Open AccessArticle

A Program Library for Computing Pure Spin-Angular Coefficients for One- and Two-Particle Operators in Non-Relativistic Atomic Theory

by Gediminas Gaigalas

Atoms 2026, 14(4), 29; https://doi.org/10.3390/atoms14040029 - 1 Apr 2026

Cited by 2

Abstract

A program library, libang77, for computing pure spin-angular coefficients for any one- and scalar two-particle operator is presented. The method is based on the combination of the second quantization and quasi-spin techniques with angular momentum theory and the method of irreducible tensorial sets. [...] Read more.

A program library, libang77, for computing pure spin-angular coefficients for any one- and scalar two-particle operator is presented. The method is based on the combination of the second quantization and quasi-spin techniques with angular momentum theory and the method of irreducible tensorial sets. A non-relativistic approach is used, in which relativistic corrections may be included in the Breit–Pauli approximation. This program library, libang77, is integrated into the Atomic Structure Package ATSP2K [ATSP2K, C. Froese Fischer, G. Tachiev, G. Gaigalas, and M.R. Godefroid, Comput. Phys. Commun. (2007). DOI: 10.1016/j.cpc.2007.01.006], but it can be implemented in other program packages too. 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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9 pages, 328 KB

Open AccessArticle

Single-Electron Capture in Intermediate-Energy He⁺ + Ne Collisions

by Hanfeng Yu, Dalong Guo, Xiaolong Zhu, Xuexia Pang, Yong Gao, Dongmei Zhao, Kaizhao Lin, Jinjian Yu, Shaofeng Zhang and Xinwen Ma

Atoms 2026, 14(4), 28; https://doi.org/10.3390/atoms14040028 - 1 Apr 2026

Abstract

State-selective single-electron capture in He⁺ + Ne collisions was studied at laboratory He⁺ projectile kinetic energies of 30–100 keV (corresponding to 7.5–25 keV/u) using a reaction microscope. Q-value spectra were obtained through recoil-ion momentum reconstruction, enabling the decomposition of the [...] Read more.

State-selective single-electron capture in He⁺ + Ne collisions was studied at laboratory He⁺ projectile kinetic energies of 30–100 keV (corresponding to 7.5–25 keV/u) using a reaction microscope. Q-value spectra were obtained through recoil-ion momentum reconstruction, enabling the decomposition of the capture yield into three distinct contributions: (i) capture into excited states of the projectile without target excitation, (ii) capture into the projectile ground state accompanied by excitation of the residual Ne⁺ ion, and (iii) capture involving simultaneous excitation of both He and Ne⁺. Across the studied energy range, capture into the projectile ground state accompanied by target excitation is the dominant pathway. With increasing impact energy, the fraction of joint projectile–target excitation increases markedly, whereas the target-excitation-only contribution decreases; the projectile-excitation-only fraction remains at a low, nearly constant level. These findings underscore the significance of multi-electron dynamics in intermediate-energy collisions involving many-electron targets. Full article

(This article belongs to the Special Issue Electronic Dynamics in Atomic and Molecular Collisions)

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6 pages, 236 KB

Open AccessCommunication

Ionization of Hydrogenic Systems by Positron and Electron Impacts

by Anand K. Bhatia

Atoms 2026, 14(4), 27; https://doi.org/10.3390/atoms14040027 - 1 Apr 2026

Abstract

The ionizations of the 1S state of hydrogenic systems with a nuclear charge of Z = 2 and 3 have been carried out using the hybrid theory. This is a continuation of the work started earlier. The present results are compared with the [...] Read more.

The ionizations of the 1S state of hydrogenic systems with a nuclear charge of Z = 2 and 3 have been carried out using the hybrid theory. This is a continuation of the work started earlier. The present results are compared with the published cross-sections for Z = 1 [Bhatia, A.K. 2025]. The distortion of the orbit is considered irrespective of the position of the incident particle, whether it is outside or inside the orbit. Only the distortion of the target orbit in the initial state is considered, but the distortion in the final state is not considered. Cross-sections decrease as the nuclear charge increases. Full article

(This article belongs to the Special Issue Interactions of Positrons with Matter and Radiation: Second Edition)

19 pages, 546 KB

Open AccessArticle

Multichannel Quantum Defect Theory with Numerical Reference Functions: Applications to Cold Atomic Collisions

by Dibyendu Sardar, Arpita Rakshit, Somnath Naskar and Bimalendu Deb

Atoms 2026, 14(3), 26; https://doi.org/10.3390/atoms14030026 - 21 Mar 2026

Abstract

We develop a method for calculating multichannel wavefunctions in the spirit of quantum defect theory, based on numerically calculated reference functions. We benchmark the method by calculating cold collisional properties of ⁸⁵Rb and ⁶Li in the presence of external magnetic fields [...] Read more.

We develop a method for calculating multichannel wavefunctions in the spirit of quantum defect theory, based on numerically calculated reference functions. We benchmark the method by calculating cold collisional properties of ⁸⁵Rb and ⁶Li in the presence of external magnetic fields tuned across specific s-wave Feshbach resonances and thereby reproducing known results. We then apply the method to calculate experimentally observed d-wave Feshbach resonance in ⁸⁷Rb-⁸⁵Rb cold collisions. Our numerical results for this d-wave resonance show good agreement with the experimental observations. The method is applicable to arbitrary interaction potentials and to any energy range near the scattering threshold. The implementation of our method to any multichannel two-body scattering problem is straightforward. Full article

(This article belongs to the Section Quantum Chemistry, Computational Chemistry and Molecular Physics)

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1 pages, 129 KB

Open AccessCorrection

Correction: Pawelkiewicz et al. Introducing Machine Learning in Teaching Quantum Mechanics. Atoms 2025, 13, 66

by M. K. Pawelkiewicz, Filippo Gatti, Didier Clouteau, Viatcheslav Kokoouline and Mehdi Adrien Ayouz

Atoms 2026, 14(3), 25; https://doi.org/10.3390/atoms14030025 - 19 Mar 2026

Abstract

Missing Supplementary Materials [...] Full article

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

8 pages, 480 KB

Open AccessArticle

Ni- and Co-like Xe Ion EUV Spectra Produced by Excitation Around the Ionisation Threshold of Xe XXVII

by Elmar Träbert

Atoms 2026, 14(3), 24; https://doi.org/10.3390/atoms14030024 - 12 Mar 2026

Abstract

A high-resolution flat-field grating spectrometer has been employed at the Livermore EBIT-I electron beam ion trap for observations of extreme-uv spectra of Ni-like ions Xe²⁶⁺ and Co-like ions Xe²⁷⁺. Multistep ionisation involving the long-lived 3d⁹4s ³D₃ [...] Read more.

A high-resolution flat-field grating spectrometer has been employed at the Livermore EBIT-I electron beam ion trap for observations of extreme-uv spectra of Ni-like ions Xe²⁶⁺ and Co-like ions Xe²⁷⁺. Multistep ionisation involving the long-lived 3d⁹4s ³D₃ level in the Ni-like ion as a stepping stone has a significant influence on the charge state distribution at a given electron beam energy, as has been reported elsewhere. Complementing those observations of 3d-4s

E 2

and

M 3

transitions from long-lived levels, the present report shows spectra of 3d-4p and 3d-4f

E 1

transitions that arise from the decays of short-lived levels in both ions and their neighbouring ions of higher charge states and provide bright reference signals for the changes in the charge state distribution. Their observation is serendipitously furthered by the visual absence of 3d-4d transitions from the observed spectra, although

M 1

and

E 2

transitions between these configurations are permitted. Full article

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

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24 pages, 1742 KB

Open AccessReview

Quantum Encryption in Phase Space

by Randy Kuang

Atoms 2026, 14(3), 23; https://doi.org/10.3390/atoms14030023 - 11 Mar 2026

Abstract

Quantum Encryption in Phase Space (QEPS) is a physical-layer encryption framework that harnesses the quantum-mechanical properties of coherent states to secure optical communications against both classical and quantum computational threats. By applying randomized phase shifts, displacements, or their dynamic combinations—implemented as unitary transformations [...] Read more.

Quantum Encryption in Phase Space (QEPS) is a physical-layer encryption framework that harnesses the quantum-mechanical properties of coherent states to secure optical communications against both classical and quantum computational threats. By applying randomized phase shifts, displacements, or their dynamic combinations—implemented as unitary transformations in phase space—QEPS disrupts the phase reference essential for coherent detection, establishing aphase synchronization barrier. This review synthesizes the theoretical foundations, security mechanisms, and experimental progress of the QEPS framework, encompassing its three principal variants: the round-trip Quantum Public Key Envelope (QPKE) protocol—a public-key-like scheme built upon phase randomization (QEPS-p), the symmetric phase-only QEPS-p, and the displacement-based QEPS-d. Experimental validations demonstrate that authorized users achieve bit-error rates (BERs) below the forward-error-correction threshold, whereas eavesdroppers are confined to BERs near 50%, equivalent to random guessing—all while utilizing standard coherent optical transceivers at data rates up to 200 Gb/s over 80 km of fiber. We further examine QEPS’s robustness to channel impairments, its seamless compatibility with existing digital signal processing (DSP) pipelines, and its distinctive position within the post-quantum cryptography landscape. Finally, we outline key challenges and future research directions toward deploying QEPS as a practical, quantum-resistant security layer for next-generation optical networks. Full article

(This article belongs to the Special Issue Quantum Optics and Quantum Information)

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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

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 1

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

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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12 pages, 527 KB

Open AccessPerspective

Diabatic Potential Energy Matrices at the Interface of Nonadiabatic Dynamics, Machine Learning, and Quantum Computing

by Yuchen Wang

Atoms 2026, 14(3), 19; https://doi.org/10.3390/atoms14030019 - 8 Mar 2026

Abstract

The accurate description of nonadiabatic quantum molecular dynamics represents one of the most significant challenges in modern computational chemistry, serving as a gateway to understanding complex phenomena ranging from photochemistry and electron transfer to surface scattering and biological exciton transport. A key difficulty [...] Read more.

The accurate description of nonadiabatic quantum molecular dynamics represents one of the most significant challenges in modern computational chemistry, serving as a gateway to understanding complex phenomena ranging from photochemistry and electron transfer to surface scattering and biological exciton transport. A key difficulty lies in bridging high-level electronic structure theory for ground and excited states with accurate quantum dynamics theory. Although on-the-fly semiclassical approaches are increasingly viable, most quantum dynamics simulations still rely on pre-constructed potential energy surfaces, or in the nonadiabatic context, diabatic potential energy matrices (DPEMs). This perspective paper addresses the theoretical foundations, construction methodologies, and emerging frontiers of DPEMs. We examine the mathematical framework of the adiabatic-to-diabatic transformation, addressing the inherent topological challenges imposed by the geometric phase and the curl condition. We further analyze the transformative impact of machine learning, detailing how machine learning algorithms, such as permutation invariant polynomial neural networks and deep learning architectures, are reshaping the construction of global, high-dimensional DPEMs. Finally, we explore the disruptive potential of quantum computing, discussing how quantum algorithms are automating the direct simulation of nonadiabatic dynamics. In emerging quantum-centric workflows, DPEMs will continue to provide the critical bridge which enables the mapping of realistic, time-dependent molecular Hamiltonians onto quantum hardware. Full article

(This article belongs to the Section Quantum Chemistry, Computational Chemistry and Molecular Physics)

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