Atoms

15 pages, 43137 KB

Open AccessEditorial

Barry I. Schneider (1940–2024): Memories by His Colleagues

by Nicolas Douguet

Atoms 2026, 14(10), 81; https://doi.org/10.3390/atoms14100081 - 9 Oct 2026

A collection of short stories about Barry Irwin Schneider (1940–2024), to whom this Special Issue of Atoms is dedicated. 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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26 pages, 398 KB

Open AccessArticle

Exponentially Correlated Hylleraas–Configuration Interaction Studies of Atomic Systems—IV: Energies for the Five Lowest ¹S and ¹P States of He and Oscillator Strengths, Including Bounds, for Their Allowed Transitions

by James S. Sims, Bholanath Padhy and María Belén Ruiz

Atoms 2026, 14(10), 80; https://doi.org/10.3390/atoms14100080 - 6 Oct 2026

Abstract

The Exponentially Correlated Hylleraas–Configuration Interaction method (E-Hy-CI) is a generalization of the Hylleraas–Configuration Interaction method (Hy-CI), in which the single \(r_{ij}\) is generalized to a form of the generic type \(r_{ij}^{\nu_{ij}}\text{e}^{-\omega_{ij}r_{ij}}\). This paper extends our earlier work of exploring whether wave functions containing [...] Read more.

The Exponentially Correlated Hylleraas–Configuration Interaction method (E-Hy-CI) is a generalization of the Hylleraas–Configuration Interaction method (Hy-CI), in which the single \(r_{ij}\) is generalized to a form of the generic type \(r_{ij}^{\nu_{ij}}\text{e}^{-\omega_{ij}r_{ij}}\). This paper extends our earlier work of exploring whether wave functions containing both linear and exponential \(r_{ij}\) factors converge more rapidly. In the present study, we calculate the five lowest \(^1S\) and \(^1P\) states of He I in two wave functions. These two wave functions are used to calculate oscillator strengths, including upper and lower bounds, for the allowed transitions between these states. The results of this study are oscillator strengths for the \(n\) \(^1S\) \(\rightarrow\) \(m\) \(^1P\) transitions for \(n = 1-5\), \(m= 2-6\) with rigorous upper and lower bounds, which in the best case (1 \(^1S \rightarrow 2\ ^1P\)) are 0.00000001 % and probable precision ≤ 0.0000000001. Full article

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

22 pages, 784 KB

Open AccessArticle

Exploring the Parameter Space of pvCD-Bonn Potentials Under Constraints from Nuclear Saturation Properties

by Ke Nan, Chencan Wang, Jinniu Hu, Ying Zhang and Hong Shen

Atoms 2026, 14(10), 79; https://doi.org/10.3390/atoms14100079 - 26 Sep 2026

Abstract

We explore the parameter space of the pvCD-Bonn B potential within the relativistic Brueckner–Hartree–Fock framework under the constraints from the empirical saturation properties of symmetric nuclear matter. We first examined the effects of the scalar-meson and pion coupling constants. Changing the

σ

-meson [...] Read more.

We explore the parameter space of the pvCD-Bonn B potential within the relativistic Brueckner–Hartree–Fock framework under the constraints from the empirical saturation properties of symmetric nuclear matter. We first examined the effects of the scalar-meson and pion coupling constants. Changing the

σ

-meson couplings in the

{}^{1}S_{0}

and

{}^{3}S_{1}

–

{}^{3}D_{1}

channels alone cannot reproduce the empirical saturation density and binding energy at the same time, whereas increasing

g_{π}

moves the saturation point toward the empirical region. However, changing

g_{π}

alone also affects the deuteron properties and tensor-sensitive observables. We therefore extended the parameter search by varying the

ρ

-meson tensor coupling

f_{ρ} / g_{ρ}

and readjusting the effective

σ

-meson couplings in the

{}^{1}S_{0}

and

{}^{3}P_{0}

channels. Four representative parameter sets with

g_{π}^{2} / 4 π = 14.7

–15.0 give deuteron properties close to the experimental values and maintain a reasonable description of the main neutron–proton phase shifts and differential cross sections at

E_{lab} = 50

and 212 MeV. Their saturation densities lie in the range

0.159

–

0.161 {fm}^{- 3}

, with saturation energies between

- 15.00

and

- 15.38 MeV

. For the interactions obtained by varying

g_{π}

, the neutron-star mass–radius relations show only a weak dependence on the pion coupling, with maximum masses of about

2.24

–

2.28 M_{⊙}

and radii of about

12.3

–

12.6 km

at

1.4 M_{⊙}

. These results show that including the

ρ

-meson tensor coupling and partial-wave-dependent

σ

-meson couplings provides a better balance between free-space two-nucleon observables and nuclear-matter saturation properties than varying the pion coupling alone. Full article

(This article belongs to the Special Issue Advances in Nuclear Ab Initio Calculations)

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24 pages, 3532 KB

Open AccessArticle

The Winds, UV Line Blanketing, Rotational Velocities and Mass Loss Rate of the Hot, Contact Binary Star TU Muscae (HD 100213)

by Raymond J. Pfeiffer

Atoms 2026, 14(9), 78; https://doi.org/10.3390/atoms14090078 - 18 Sep 2026

Abstract

An empirical model of the TU Muscae binary star system has been developed by a study of 23 high resolution SWP spectrophotometric images that were obtained with the International Ultraviolet Explorer (IUE) satellite telescope including some that were downloaded from the NASA/MAST IUE [...] Read more.

An empirical model of the TU Muscae binary star system has been developed by a study of 23 high resolution SWP spectrophotometric images that were obtained with the International Ultraviolet Explorer (IUE) satellite telescope including some that were downloaded from the NASA/MAST IUE Archive. The images are well distributed in Keplerian orbital phase thereby permitting a simultaneous fitting of the C IV wind-line profile by the SEI method and the light curve for the blanketed continuum (1450–1490 Å) bandpass by means of a program developed by the author. The result is a set of parameters characterizing the physical and geometric properties of the wind envelopes surrounding the stars. Surprisingly, there is no evidence for a P Cygni profile or strong, distinguishable shock front in the system, as has been found for similar investigations of EM Carinae and HD 159176. This is probably a result of the contact nature of the binary and the high-temperature environment of such a shock. That is, most of the carbon ions in the shock are more highly ionized. Based on the parameters for the SEI fit to the C IV profile, the value for the ionization fraction of C IV in the wind was calculated to be 10⁻⁴. With this value, the mass loss rate, Ṁ, calculated from two independent equations, was found to be about 10⁻⁶ solar masses per year (M_ʘ/yr). The UV line blanketing in the 1500 to 1600 Ångstrom bandpass was found to be erratically variable with orbital phase and time, indicating a variable amount of fast moving, dense clouds in the winds and/or a great amount of turbulence. The meaning of rotational velocities for the stars is problematic and depends on what point on the photospheres one is considering. Full article

(This article belongs to the Special Issue Atomic Processes and Their Role in Astrophysical Phenomena)

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13 pages, 1168 KB

Open AccessArticle

Instrument Development for Lunar Interior Investigation Using Atom Interferometry

by Yun-Jhih Chen, Filippo Borselli, Sheng-wey Chiow and Nan Yu

Atoms 2026, 14(9), 77; https://doi.org/10.3390/atoms14090077 - 15 Sep 2026

Abstract

The Atomic Lunar Seismometer (ALS) is an atom-interferometer instrument concept for measuring the lunar gravity and vibration modes at long time scales. Compared to other seismometer techniques, atom interferometers offer a pathway toward an ultra-low drift seismometer for signals around and below the [...] Read more.

The Atomic Lunar Seismometer (ALS) is an atom-interferometer instrument concept for measuring the lunar gravity and vibration modes at long time scales. Compared to other seismometer techniques, atom interferometers offer a pathway toward an ultra-low drift seismometer for signals around and below the mHz frequency range. The ALS instrument concept is also applicable to other terrestrial bodies such as Mars. In this paper, we present our instrument design based on a 5 cm tall atomic fountain and summarize the test results obtained in a laboratory environment. This development is specifically to optimize and accommodate in lunar environment. Presently, the instrument’s short-term sensitivity is 1.4 × 10⁻⁶ m/s²/

\sqrt{Hz}

(140

μ

Gal/

\sqrt{Hz}

), limited by the vibration noise in our lab, and it averages down to 6.7 × 10⁻⁸ m/s² (6.7

μ

Gal) after 445 s. Full article

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

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56 pages, 21070 KB

Open AccessArticle

Atomic Data for Yb-like Ions from Ta IV to Pt IX Relevant to Tungsten Transmutation in Fusion Plasmas

by Maxime Brasseur, Patrick Palmeri and Pascal Quinet

Atoms 2026, 14(9), 76; https://doi.org/10.3390/atoms14090076 - 12 Sep 2026

Abstract

Accurate atomic data for heavy ions are required for spectroscopic diagnostics and impurity transport modeling in magnetic-confinement fusion devices, particularly for tungsten and its neutron-induced transmutation products. In the present work, we investigate the ytterbium-like ions Ta IV, W V, Re VI, Os [...] Read more.

Accurate atomic data for heavy ions are required for spectroscopic diagnostics and impurity transport modeling in magnetic-confinement fusion devices, particularly for tungsten and its neutron-induced transmutation products. In the present work, we investigate the ytterbium-like ions Ta IV, W V, Re VI, Os VII, Ir VIII, and Pt IX using complementary pseudo-relativistic Hartree–Fock (HFR) and fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) approaches. Semi-empirical calculations were first performed using the HFR method including core polarization corrections (HFR+CPOL). The evolution of correlation effects along the isoelectronic sequence was then analyzed through an alternative HFR(CV) model in which the most important core-excited configurations were introduced explicitly to account for core–valence interactions. Extensive least-squares fits to the available experimental energy levels were carried out for all ions considered. The results reveal that the HFR+CPOL approach provides an adequate description of Ta IV and W V, while explicit treatment of core–valence correlations becomes increasingly important from Re VI onwards owing to the growing interaction between the 5d5f and 5p⁵5d³ configurations. New energy level classifications, level compositions, oscillator strengths, and transition probabilities are reported and critically assessed through comparisons between HFR and MCDHF calculations. The resulting dataset extends previous investigations of rhenium and osmium ions and provides benchmark atomic data for heavy-ion spectroscopy and future fusion-plasma applications. Full article

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

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10 pages, 2261 KB

Open AccessArticle

High-Precision Measurement of the Landé g_J-Factor of the ²D_3/2 State in the ¹⁷¹Yb⁺ Ion

by Kristina P. Galstyan, Ilia V. Zalivako, Alexander S. Borisenko, Yury P. Anosov and Nikolay N. Kolachevsky

Atoms 2026, 14(9), 75; https://doi.org/10.3390/atoms14090075 - 7 Sep 2026

Abstract

In this work, we report a high-precision experimental determination of the ratio

g_{F, D} / g_{F, S} = 0.998060 (5)

between the Landé g-factors for states

{}^{2}S_{1 / 2} (F = 1)

[...] Read more.

In this work, we report a high-precision experimental determination of the ratio

g_{F, D} / g_{F, S} = 0.998060 (5)

between the Landé g-factors for states

{}^{2}S_{1 / 2} (F = 1)

and

{}^{2}D_{3 / 2} (F = 1)

in ¹⁷¹Yb⁺. Together with the recently calculated g-factor of the

{}^{2}S_{1 / 2}

state

g (S_{1 / 2}) = 2.002615 (70)

, this yields a value of

g (D_{3 / 2}) = 0.79917 (3)

for

{}^{2}D_{3 / 2}

with a precision more than an order of magnitude higher than that of previous measurements. The experiment was performed by microwave spectroscopy of hyperfine transitions in the

{}^{2}S_{1 / 2}

and

{}^{2}D_{3 / 2}

manifolds of trapped ions confined in a linear Paul trap. We also obtain the hyperfine splitting

W_{D_{3 / 2}} = 857, 178, 077 (3)

Hz, agreeing with previous measurements. Precise knowledge of the

{}^{2}D_{3 / 2}

state Landé g-factor is essential for evaluating systematic shifts in ¹⁷¹Yb⁺ optical clocks and for tests of fundamental theories using such frequency standards. Full article

(This article belongs to the Special Issue Atomic and Molecular Data and Their Applications : ICAMDATA 2026)

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36 pages, 1004 KB

Open AccessReview

Recent Progress in Ab Initio Nuclear Theory for Precision Physics Searches in Muonic Atoms and Superallowed β Decays

by Simone Salvatore Li Muli and Michael Gennari

Atoms 2026, 14(9), 74; https://doi.org/10.3390/atoms14090074 - 4 Sep 2026

Abstract

Precision tests of the Standard Model at low energy are increasingly limited by nuclear-structure theory rather than by experiments. We review two such cases: the two-photon-exchange correction to the Lamb shift in muonic atoms, and the γW box radiative correction to superallowed β [...] Read more.

Precision tests of the Standard Model at low energy are increasingly limited by nuclear-structure theory rather than by experiments. We review two such cases: the two-photon-exchange correction to the Lamb shift in muonic atoms, and the γW box radiative correction to superallowed β decays. Although they probe different physics, both are governed by the same generalized hadronic tensor, so that the chiral effective field theory Hamiltonians and currents, Lanczos-based response methods, and Bayesian uncertainty quantification developed for one carry over directly to the other. We summarize recent ab initio progress in light nuclei and its impact on nuclear charge radii, on the helium isotope-shift puzzle, and on the extraction of V_ud for the top-row CKM unitarity test, and state a future outlook. Full article

(This article belongs to the Special Issue Advances in Nuclear Ab Initio Calculations)

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13 pages, 536 KB

Open AccessArticle

Construction of Intrinsically Screened Heavy-Particle Potentials in Dense Plasmas from First-Principles Pseudopotentials

by Nenad M. Sakan, Vladimir Srećković, Biljana Stankov and Zoran Simić

Atoms 2026, 14(9), 73; https://doi.org/10.3390/atoms14090073 - 1 Sep 2026

Abstract

We present a computational framework for constructing effective, intrinsically screened heavy-particle potentials in dense plasmas from first-principles pseudopotentials. Starting from available projector-augmented-wave (PAW) data in the Unified Pseudopotential Format (UPF), the angular-momentum-dependent channel potentials (s, p, d, f) [...] Read more.

We present a computational framework for constructing effective, intrinsically screened heavy-particle potentials in dense plasmas from first-principles pseudopotentials. Starting from available projector-augmented-wave (PAW) data in the Unified Pseudopotential Format (UPF), the angular-momentum-dependent channel potentials (s, p, d, f) are reconstructed and mixed according to Boltzmann occupation probabilities at the plasma temperature. The intrinsic screening by thermally populated valence electrons is included through a self-consistent Hartree potential computed for each charge state, yielding element-specific temperature-dependent effective scattering potentials for neutral atoms and ions. The Saha ionisation equilibrium, corrected for ionisation-potential depression via the Stewart–Pyatt model, determines the species composition. A number-density-weighted mixture average then produces a single effective heavy-particle potential for multi-component plasmas. The procedure is implemented in D_plas_V, a C++17 code with zero external dependencies, and all methods are validated against analytical test cases. Full article

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

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24 pages, 477 KB

Open AccessArticle

Study of the Hyperfine Structure of the Low-Lying Ca II and Ra I–II Levels: Applying the MCDHF Models Developed for Ba I–II

by Lorenzo Nezosi, Patrick Palmeri and Per Jönsson

Atoms 2026, 14(9), 72; https://doi.org/10.3390/atoms14090072 - 25 Aug 2026

Abstract

Building on our previous multi-configuration Dirac–Hartree–Fock (MCDHF) computational strategies tailored for the hyperfine structure (HFS) of low-lying levels in one-valence electron Sr II and Ba II ions and in two-valence electrons in a Ba I atom, we successfully extend these methodologies along the [...] Read more.

Building on our previous multi-configuration Dirac–Hartree–Fock (MCDHF) computational strategies tailored for the hyperfine structure (HFS) of low-lying levels in one-valence electron Sr II and Ba II ions and in two-valence electrons in a Ba I atom, we successfully extend these methodologies along the alkaline-earth elements to the lighter Ca II and heavier Ra I–II ions. MCDHF-recommended HFS constants, along with their uncertainty estimates, are reported for the first time and critically discussed. Where applicable, the Bohr–Weisskopf correction is applied to the HFS constants, and its effects are analyzed. This is particularly valuable for cases where no measurement is available such as for the [Rn]

{6 d}^{2} D_{3 / 2, 5 / 2}

levels in ^223,225Ra II, for the [Rn]

{7 s 6 d}^{3} D_{1, 2, 3}

and ¹

D_{2}

levels in ²²³Ra I, for the [Rn]

7 s {6 d}^{3} D_{2, 3}

and

{}^{1}D_{2}

levels in ²²³Ra I, and for the [Rn]

7 s {7 p}^{3} P_{2}^{o}

level in ²²⁵Ra I. In all cases, our MCDHF values agree with the ones found in the literature within our error bars. For the

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

levels in Ca II and Ra II, the discrepancies with the experiment observed in Sr II and Ba II for the HFS A constant are not seen. Full article

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

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17 pages, 1911 KB

Open AccessArticle

Transformation Between Regular-Irregular Schrödinger Equation Solution Pairs by Means of the Corresponding Milne Function Properties

by Sotirios Danakas and Samuel Cohen

Atoms 2026, 14(8), 71; https://doi.org/10.3390/atoms14080071 - 17 Aug 2026

Abstract

In scattering and tunnelling-to-continuum problems, the regular and irregular solution pairs to the one-particle radial Schrödinger equation follow various amplitude and phase difference conventions at infinity. The Milne transformation of the Schrödinger equation (a.k.a. the Phase-Amplitude Method) leads to a solution pair whose [...] Read more.

In scattering and tunnelling-to-continuum problems, the regular and irregular solution pairs to the one-particle radial Schrödinger equation follow various amplitude and phase difference conventions at infinity. The Milne transformation of the Schrödinger equation (a.k.a. the Phase-Amplitude Method) leads to a solution pair whose form inherently complies with scattering theory’s requirements of common amplitude and phase difference of

π / 2

at the

r \to \infty

limit. On occasion, applications favoured the adoption of the reverse phase convention. In this work we present a formal framework that permits switching of the regular/irregular solution pairs between representations. To showcase the formalism, two exemplar potential curves are investigated: a repulsive Coulomb barrier and the Coulomb-Stark potential, the latter corresponding to the hydrogen atom in the presence of a static homogeneous electric field. Analysis of the results, assessment of the methodology and a discussion of possible extensions are also included. Ultimately, this work shows that it is the regular solution that acts as the thread that binds together the different representations. Full article

(This article belongs to the Special Issue Quantum and Optical Phenomena in Atomic Systems)

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23 pages, 425 KB

Open AccessArticle

Efficient Methods for Dynamic Correlation in Atoms

by Kenneth G. Dyall

Atoms 2026, 14(8), 70; https://doi.org/10.3390/atoms14080070 - 15 Aug 2026

Abstract

An algorithm for large-scale correlated calculations on atoms is presented that significantly reduces the scaling of these calculations with the number of single-particle functions used to construct the N-particle states. The reduction is provided in the stage in which the Hamiltonian matrix is [...] Read more.

An algorithm for large-scale correlated calculations on atoms is presented that significantly reduces the scaling of these calculations with the number of single-particle functions used to construct the N-particle states. The reduction is provided in the stage in which the Hamiltonian matrix is contracted with the coefficients or amplitudes of the basis states in an iterative procedure such as the Davidson method. The algorithm relies on the representation of the radial one-particle functions on a grid, and it makes use of the multipole expansion of the electron–electron interaction in a sequence of transformations on the spinors, coefficients, and potentials. It also uses prototyping for the angular integrals and evaluation of recoupling coefficients for the configuration state functions (CSFs) separately rather than for pairs of CSFs. The scaling is verified with calculations on two-electron atoms and analyzed in terms of the number of operations required for each stage of both the proposed algorithm and the conventional methods. 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, 607 KB

Open AccessArticle

Ab Initio Quadrupole-Invariant Analysis of Neutron-Rich Deformed Nuclei Around N = 28

by Liu-Yuan Shen, Xin-Peng Wang, Hong-Hui Li, Hong-Yu Zhu, Wei Zuo and Qi Yuan

Atoms 2026, 14(8), 69; https://doi.org/10.3390/atoms14080069 - 12 Aug 2026

Abstract

We present an ab initio quadrupole-invariant study of neutron-rich nuclei around

N = 28

. Effective Hamiltonians and consistently evolved

E 2

operators are obtained from chiral NN+3N interactions using the ab initio valence-space in-medium similarity renormalization group, and the resulting

E 2

[...] Read more.

We present an ab initio quadrupole-invariant study of neutron-rich nuclei around

N = 28

. Effective Hamiltonians and consistently evolved

E 2

operators are obtained from chiral NN+3N interactions using the ab initio valence-space in-medium similarity renormalization group, and the resulting

E 2

matrix elements are used to extract the deformation parameters. Along the even–even

N = 28

isotonic chain, the

β

values increase systematically from ⁴⁸Ca to ⁴⁰Mg, providing a direct deformation signature of the weakening of the

N = 28

shell closure. The extracted

β

and

γ

values show a prolate–oblate–triaxial evolution of the

0_{1}^{+}

states from ⁴⁰Mg to ⁴²Si and ⁴⁴S, while the

0_{2}^{+}

states remain mainly in the prolate-to-triaxial region. Extending the analysis to the neighboring

N = 27

and 29 isotones, we find a systematic evolution from strongly prolate Mg isotopes, to oblate-side Si isotopes, and to prolate-to-triaxial S isotopes. These results provide a unified picture of quadrupole deformation, triaxiality, and configuration coexistence around

N = 28

. Full article

(This article belongs to the Special Issue Advances in Nuclear Ab Initio Calculations)

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18 pages, 9081 KB

Open AccessArticle

Reactive Collision Dynamics and Effective Cross-Sections in a Reduced-Dimensional Model Potential

by Sanja Tošić, Vladimir A. Srećković and Veljko Vujčić

Atoms 2026, 14(8), 68; https://doi.org/10.3390/atoms14080068 - 11 Aug 2026

Abstract

We investigate reactive collision dynamics and effective interaction cross-sections using classical trajectory simulations on a reduced-dimensional reactive potential-energy surface containing reactant and product wells separated by an intermediate barrier region. The simulations are performed over a range of collision velocities for which direct [...] Read more.

We investigate reactive collision dynamics and effective interaction cross-sections using classical trajectory simulations on a reduced-dimensional reactive potential-energy surface containing reactant and product wells separated by an intermediate barrier region. The simulations are performed over a range of collision velocities for which direct scattering, transient trapping, and reactive trajectories coexist within the same interaction landscape. Trajectories are propagated using a velocity-Verlet integration scheme, while reaction probabilities are analyzed as functions of the impact parameter and initial projectile velocity. The calculated probability distributions exhibit strongly localized reactive windows in phase space separated by extended nonreactive regions, indicating pronounced sensitivity of the dynamics to both collision geometry and initial conditions. Probability maps in the (v_x,b) plane reveal a fragmented phase-space structure and highly nonuniform accessibility of the interaction region across the investigated parameter range. The simulations further show substantial variations in the relative importance of reactive, trapped, and back-scattering trajectories with increasing collision velocity, together with non-monotonic behavior of the effective reactive cross-sections. Despite the intentionally reduced dimensionality of the model, the trajectory ensembles reproduce several characteristic features of complex reactive scattering dynamics, including transient trapping, competing dynamical pathways, and broad residence-time distributions. The present results demonstrate that reduced-dimensional classical trajectory approaches can already capture important phase-space mechanisms governing dynamical accessibility and channel competition in reactive molecular collisions. Full article

(This article belongs to the Special Issue Electron-Impact Ionization: Fragmentation and Cross-Section)

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22 pages, 404 KB

Open AccessReview

A Survey on Atomic Clocks in GNSS and Beyond

by Georgios Tzanoulinos, Spiros Makris and Vaios Lappas

Atoms 2026, 14(8), 67; https://doi.org/10.3390/atoms14080067 - 2 Aug 2026

Abstract

Space-based navigation systems rely on atomic clocks aboard satellites to provide precise time and positioning information through synchronized radio-frequency signals. At the core are Atomic Frequency References (AFRs), which stabilize a local oscillator using atomic transitions to achieve exceptional accuracy and stability. To [...] Read more.

Space-based navigation systems rely on atomic clocks aboard satellites to provide precise time and positioning information through synchronized radio-frequency signals. At the core are Atomic Frequency References (AFRs), which stabilize a local oscillator using atomic transitions to achieve exceptional accuracy and stability. To maintain 1 m positioning precision, timing uncertainties below 3 ns are required, achievable only with high-quality atomic clocks. This paper surveys the principles, architectures, and performance of AFRs in satellite navigation, including the types deployed in major Global Navigation Satellite System (GNSS) constellations such as GPS, Galileo, GLONASS, and BeiDou, and discusses current practices and emerging trends in satellite timing technologies, including the nascent Low-Earth-Orbit Positioning, Navigation, and Timing (LEO-PNT) paradigm. Full article

(This article belongs to the Special Issue Ultra-Precise Atomic Clocks)

12 pages, 1054 KB

Open AccessArticle

Semirelativistic BSR–RMT Interface: Photoionization of Highly Charged Two-Electron Ions

by Aaron T. Bondy and Klaus Bartschat

Atoms 2026, 14(8), 66; https://doi.org/10.3390/atoms14080066 - 1 Aug 2026

Abstract

We outline an intermediate step toward a semirelativistic BSR–RMT interface by using inner-region structure information generated with the B-spline R-matrix (BSR) method as the input to the Seaton/Badnell STGF/STGBF outer-region asymptotic codes used in R-matrix photoionization calculations. The long-term goal is to exploit [...] Read more.

We outline an intermediate step toward a semirelativistic BSR–RMT interface by using inner-region structure information generated with the B-spline R-matrix (BSR) method as the input to the Seaton/Badnell STGF/STGBF outer-region asymptotic codes used in R-matrix photoionization calculations. The long-term goal is to exploit the compact, nonorthogonal, term-dependent target descriptions available in BSR for time-dependent R-matrix calculations with the R matrix with time dependence (RMT) method, especially for processes sensitive to semirelativistic and spin-orbit effects. To probe these effects, we consider the ground-state photoionization of Ne⁸⁺, Ar¹⁶⁺, Fe²⁴⁺, and Kr³⁴⁺, focusing on resonance structures and the singlet-triplet separation of the predominantly

{2 s 2 p}^{3} P^{o}

and

{2 s 2 p}^{1} P^{o}

autoionizing states and their spin-orbit mixing. For Fe²⁴⁺, we also analyze higher resonances and the region between the ionic thresholds, with R-matrix I (RM-I) calculations using Badnell’s version for comparison. The BSR results agree well overall with the available Iron Project data and with the NIST separations between the predominantly

{2 s 2 p}^{3} P^{o}

and

{2 s 2 p}^{1} P^{o}

levels. Since semirelativistic RMT currently uses RM-I input; the successful interfacing of BSR inner-region data with STGF/STGBF codes that likewise use RM-I input represents a direct precursor to semirelativistic BSR–RMT capability. 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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22 pages, 455 KB

Open AccessArticle

“Square-Root” Klein–Gordon Equation: The Harmonic and Morse Potentials

by Luis A. Poveda, Bill Poirier and Arthur R. B. de Magalhães

Atoms 2026, 14(8), 65; https://doi.org/10.3390/atoms14080065 - 1 Aug 2026

Abstract

Quantum relativistic solutions of a “square-root” version of the Klein–Gordon equation, for a particle in a one-dimensional Morse potential, are presented using methods previously proposed and applied to a particle in a harmonic oscillator. The methods lead to both numerical and analytical solutions, [...] Read more.

Quantum relativistic solutions of a “square-root” version of the Klein–Gordon equation, for a particle in a one-dimensional Morse potential, are presented using methods previously proposed and applied to a particle in a harmonic oscillator. The methods lead to both numerical and analytical solutions, with the latter allowing smooth variation of the system parameters from non-relativistic to ultra-relativistic limits. Analytical expressions for the energy levels and wavefunctions are obtained, as solutions to a Schrödinger-type equation, including relativistic effects through a state-dependent rescaled mass. The eigenstates of the Morse potential exhibit suitable and smooth behavior and approach the corresponding harmonic oscillator solutions as the depth of the Morse potential well increases, as expected. A comparison is also presented between the relativistic harmonic oscillator obtained with this method and the so-called “Klein–Gordon oscillator”. Full article

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

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16 pages, 2050 KB

Open AccessArticle

Configuration Assignments to K = 1/2 Three-Quasiparticle Bands

by Manpreet Kaur, Sushil Kumar, Sukhjeet Singh and A. K. Jain

Atoms 2026, 14(8), 64; https://doi.org/10.3390/atoms14080064 - 1 Aug 2026

Abstract

In the present work, configuration assignments to K = 1/2 bandheads of given three-quasiparticle (3qp) quadruplets experimentally observed and yet to be observed in odd-A nuclei lying in the rare-earth mass region are carried out based on an improved version of an earlier [...] Read more.

In the present work, configuration assignments to K = 1/2 bandheads of given three-quasiparticle (3qp) quadruplets experimentally observed and yet to be observed in odd-A nuclei lying in the rare-earth mass region are carried out based on an improved version of an earlier empirical formulation. The important contributions of the irrotational component, residual n-p interactions, and rotor–particle coupling terms are explored and highlighted. The magnitude of the RPC term is found to be comparatively smaller (≈5–10 keV) than the irrotational and residual interactions and can affect the 3qp bandheads with small energy separation. We confirm the tentative configuration assignments of three K = 1/2 bandheads having configurations 1/2[411]_π⊗7/2[523]_π⊗5/2[523]_ν and 1/2[411]_π⊗9/2[514]_π⊗7/2[514]_ν in ¹⁷⁵Yb and 9/2[514]_π⊗7/2[514]_ν⊗1/2[521]_ν in ¹⁷⁷Ta nuclides. The average deviation between experimental data and present model calculations for ¹⁷⁵Yb and ¹⁷⁷Ta is 37.9 keV and 163.2 keV, as compared to the earlier model estimates, which yielded a deviation of 249.7 keV and 222.3 keV, respectively. We also resolved some issues pertaining to ambiguous configuration assignments of 3qp quadruplets observed in ¹⁷⁷Lu, ¹⁷³Ta, and ¹⁷⁹Ta nuclides. Encouraged by the good overall agreement among experimental and calculated bandhead energies, we have extended these calculations to predict the locations of 18 K = 1/2 bandheads, which are members of 3qp quadruplets of ^171,175,177Lu, ^173,179,181Ta, and ^179,183Re nuclides but have not been observed experimentally and will be useful for predicting bandheads associated with various 3qp states. Full article

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Open AccessArticle

First Direct Mass Measurement of ¹⁸⁴Ta and Surrounding Nuclei

by Jinn Ming Yap, Peter Schury, Sarah Naimi, Gemma Bartram, Alison M. Bruce, Navodhayan Chandrakumar, Jiulong Chen, James G. Cubiss, Siddharth Doshi, Sunil Dutt, Jilehu Gada, Song Guo, Yoshikazu Hirayama, George Hudson-Chang, Sota Kimura, Filip G. Kondev, Gregory Lane, Jenny Lee, Guangshun Li, Yury Litvinov, Zhong Liu, Pengcong Ma, Sorin Pascu, Zsolt Podolyák, Aiko Takamine, Michiharu Wada, Philip Walker, Hiroshi Watanabe and Yutaka X. Watanabe Show full author list Hide full author list

Atoms 2026, 14(8), 63; https://doi.org/10.3390/atoms14080063 - 1 Aug 2026

Abstract

Mass measurements of isotopes around the

A = 184

region near stability were performed at the KEK Isotope Separation System within the RIKEN Nishina Center, Japan. The isotopes were produced via multi-nucleon transfer reactions with a ¹³⁶Xe beam of 7.2 MeV/u impinging [...] Read more.

Mass measurements of isotopes around the

A = 184

region near stability were performed at the KEK Isotope Separation System within the RIKEN Nishina Center, Japan. The isotopes were produced via multi-nucleon transfer reactions with a ¹³⁶Xe beam of 7.2 MeV/u impinging on a natural tungsten target. We report the first direct mass measurement of ¹⁸⁴Ta, showing a 62(27) keV deviation compared to previous indirect measurements. Full article

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