Atoms

18 pages, 2145 KiB

Open AccessArticle

Modified Ji-Huan He’s Frequency Formulation for Large-Amplitude Electron Plasma Oscillations

by Stylianos Vasileios Kontomaris, Anna Malamou, Ioannis Psychogios and Gamal M. Ismail

Atoms 2024, 12(12), 68; https://doi.org/10.3390/atoms12120068 - 12 Dec 2024

This paper examines oscillations governed by the generic nonlinear differential equation

{u^{″} = ω}_{p 0}^{2} (1 - u \mp \frac{2 β^{2}}{u^{γ}}),

where

ω_{p 0}, β

and

γ

are positive constants. The aforementioned differential [...] Read more.

This paper examines oscillations governed by the generic nonlinear differential equation

{u^{″} = ω}_{p 0}^{2} (1 - u \mp \frac{2 β^{2}}{u^{γ}}),

where

ω_{p 0}, β

and

γ

are positive constants. The aforementioned differential equation is of particular importance, as it describes electron plasma oscillations influenced by temperature effects and large oscillation amplitudes. Since no analytical solution exists for the oscillation period in terms of

ω_{p 0}, β, γ

and the oscillation amplitude, accurate approximations are derived. A modified He’s approach is used to account for the non-symmetrical oscillation around the equilibrium position. The motion is divided into two parts:

u_{m i n} \leq u < u_{e q}

and

u_{e q} < u \leq u_{m a x}

, where

u_{m i n}

and

u_{m a x}

are the minimum and maximum values of

u

, and

u_{e q}

is its equilibrium value. The time intervals for each part are calculated and summed to find the oscillation period. The proposed method shows remarkable accuracy compared to numerical results. The most significant result of this paper is that He’s approach can be readily extended to strongly non-symmetrical nonlinear oscillations. It is also demonstrated that the same approach can be extended to any case where each segment of the function

f (u)

in the differential equation

u^{″} + f (u) = 0

(for

u_{m i n} \leq u < u_{e q}

and for

u_{e q} < u \leq u_{m a x}

) can be approximated by a fifth-degree polynomial containing only odd powers. Full article

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

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17 pages, 1138 KiB

Open AccessArticle

Charge Transfer Excitation of NeAr⁺ Ions in Collisions with Electrons

by Alexander Narits, Konstantin Kislov and Vladimir Lebedev

Atoms 2024, 12(12), 67; https://doi.org/10.3390/atoms12120067 - 12 Dec 2024

Abstract

We study the resonant processes of the excitation of weakly bound

{NeAr}^{+}

ions in collisions with the free electrons of Ne/Ar mixture plasma under conditions typical of the active media of gas lasers and plasma-based UV radiation sources. The transitions leading to [...] Read more.

We study the resonant processes of the excitation of weakly bound

{NeAr}^{+}

ions in collisions with the free electrons of Ne/Ar mixture plasma under conditions typical of the active media of gas lasers and plasma-based UV radiation sources. The transitions leading to the population of charge transfer electronic terms are considered. Using an original theoretical approach developed recently, we study the dependences of the cross-sections of several competing resonant processes on the incident electron energy and the gas temperature of the plasma. The role of the continuous states of internuclear motion is discussed. We highlight the specific features of the processes considered that stem from the low binding energy of

{NeAr}^{+}

ions and demonstrate that, in the weakly bound systems, the efficiencies of different charge transfer excitation channels differ greatly from those obtained for ions with moderate dissociation energies. Full article

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

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17 pages, 6807 KiB

Open AccessArticle

Many-Body Effects in a Composite Bosonic Josephson Junction

by Sudip Kumar Haldar and Anal Bhowmik

Atoms 2024, 12(12), 66; https://doi.org/10.3390/atoms12120066 - 11 Dec 2024

Abstract

In standard bosonic Josephson junctions (BJJs), particles tunnel between two single-well potentials linked by a finite barrier. The dynamics of standard BJJs have been extensively studied, both at the many-body and mean-field levels of theory. In the present work, we introduce the concept [...] Read more.

In standard bosonic Josephson junctions (BJJs), particles tunnel between two single-well potentials linked by a finite barrier. The dynamics of standard BJJs have been extensively studied, both at the many-body and mean-field levels of theory. In the present work, we introduce the concept of a composite BJJ. In a composite BJJ, particles tunnel between two double-well potentials linked by a finite potential barrier between them. We focused on the many-body facets of quantum dynamics and investigate how the complex structure of the junction influences the tunneling. Employing the multiconfigurational time-dependent Hartree method for bosons, highly accurate many-boson wavefunctions were obtained, from which properties were computed. We analyzed the dynamics using the survival probability, the degree of fragmentation of the junction, and the fluctuations of the observables, and discuss how the many-boson tunneling behaved, and how it may be controlled, using the composite nature of the junction. A central result of this work relates to the degree of fragmentation of composite BJJs with different numbers of bosons. We provide strong evidence that a universal degree of fragmentation into multiple time-dependent modes takes place. Further applications are briefly discussed. Full article

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

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11 pages, 983 KiB

Open AccessReview

A Critical Look at Density Functional Theory in Chemistry: Untangling Its Strengths and Weaknesses

by Konstantinos P. Zois and Demeter Tzeli

Atoms 2024, 12(12), 65; https://doi.org/10.3390/atoms12120065 - 11 Dec 2024

Abstract

Density functional theory (DFT) is a commonly used methodology favored by experts and non-experts alike. It is a useful tool for the investigation of atomic, molecular and surface systems, offering an efficient and often reliable approach to calculate ground state properties such as [...] Read more.

Density functional theory (DFT) is a commonly used methodology favored by experts and non-experts alike. It is a useful tool for the investigation of atomic, molecular and surface systems, offering an efficient and often reliable approach to calculate ground state properties such as electron density, total energy and molecular structure. However, fundamental issues are not rare. Of course, no one can really question the bold impact of DFT on modern chemical science. It is not only the way research is conducted that has been influenced by DFT, but also textbooks, datasets and our chemical intuition as well. In this review, issues pertaining to DFT are discussed, and it is pointed out that without a clear understanding of why we use calculations, an effective combination of experiment and theory will never be accomplished. Using low-level theoretical frameworks surely does not shed light on profound problems. To excel in our scientific field and make good use of our tools, we must very carefully decide which methodologies we are to employ. Full article

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

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16 pages, 1489 KiB

Open AccessArticle

Theoretical Study of the Dissociative Recombination and Vibrational (De-)Excitation of HCNH⁺ and Its Isomers by Electron Impact

by Mehdi Adrien Ayouz and Arnaud Buch

Atoms 2024, 12(12), 64; https://doi.org/10.3390/atoms12120064 - 3 Dec 2024

Abstract

Protonated hydrogen cyanide, HCNH⁺, is one of the most important molecules of interest in the astrophysical and astrochemical fields. This molecule not only plays the role of a reaction intermediary in various types of interstellar reactions but was also identified in [...] Read more.

Protonated hydrogen cyanide, HCNH⁺, is one of the most important molecules of interest in the astrophysical and astrochemical fields. This molecule not only plays the role of a reaction intermediary in various types of interstellar reactions but was also identified in Titan’s upper atmosphere. The cross sections for the dissociative recombination (DR) and vibrational (de-)excitation (VE and VDE) of HCNH⁺ and its

{CNH}_{2}^{+}

isomer are computed using a theoretical approach based on a combination of the normal mode approximation for the vibrational states of the target ions and the UK R-matrix code to evaluate electron-ion scattering matrices for fixed geometries of ions. The theoretical convoluted DR cross section for HCNH⁺ agrees well with the experimental data and a previous study. It was also found that the DR of the

{CNH}_{2}^{+}

isomer is important, which suggests that this ion might be present in DR experiments of HCNH⁺. Moreover, the ab initio calculations performed on the H₂CN⁺ isomer predict that this ion is a transition state. This result was confirmed by the study of the reaction path of the HCNH⁺ isomerization that was carried out by evaluating the intrinsic reaction coordinate (IRC). Finally, thermally averaged rate coefficients derived from the cross sections are provided for temperatures in the 10–10,000 K range. A comprehensive set of calculations is performed to assess the uncertainty of the obtained data. These results should help in modeling non-LTE spectra of HCNH⁺, taking into account the role of its most stable isomer, in various astrophysical environments. Full article

(This article belongs to the Special Issue Interaction of Electrons with Atoms and Molecules in Ionized Environments)

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12 pages, 2269 KiB

Open AccessArticle

Cross-Sections for Projectile Ionization, Electron Capture, and System Breakdown of C⁵⁺ and Li²⁺ Ions with Atomic Hydrogen

by Saed J. Al Atawneh

Atoms 2024, 12(12), 63; https://doi.org/10.3390/atoms12120063 - 2 Dec 2024

Abstract

For many disciplines of science, all conceivable collisional cross-sections and reactions must be precisely known. Although recent decades have seen a trial of large-scale research to obtain such data, many essential atomic and molecular cross-section data are still missing, and the reliability of [...] Read more.

For many disciplines of science, all conceivable collisional cross-sections and reactions must be precisely known. Although recent decades have seen a trial of large-scale research to obtain such data, many essential atomic and molecular cross-section data are still missing, and the reliability of the existing cross-sections has to be validated. In this paper, we present projectile ionization, electron capture, and system breakdown cross-sections in carbon (C⁵⁺) ions and lithium (Li²⁺) ion collisions with atomic hydrogen based on the Monte Carlo models of classical and quasi-classical trajectories. According to our expectation, the QCTMC results show higher results in comparison to standard CTMC data, emphasizing the role of the Heisenberg correction constraint, especially in the low-energy regime. On the other hand, at high energy, the Heisenberg correction term has less influence as the projectile momentum increases. We present the total cross-sections of projectile ionization, electron capture, and system breakdown in C⁵⁺ ions and Li²⁺ ion collisions with atomic hydrogen in the impact energy range from 10 keV to 160 keV, which is of interest in astrophysical plasmas, atmospheric sciences, plasma laboratories, and fusion research. Full article

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

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18 pages, 763 KiB

Open AccessArticle

Critical Impact of Isospin Asymmetry in Elucidating Magicity Across Isotonic Chains of Different Mass Regions Using Relativistic Energy Density Functional

by Praveen K. Yadav, N. Biswal, R. N. Panda, S. Mishra, Raj Kumar and M. Bhuyan

Atoms 2024, 12(12), 62; https://doi.org/10.3390/atoms12120062 - 28 Nov 2024

Abstract

This study provides a comprehensive examination of the surface properties—particularly the symmetry energy and its contributing components—of isotonic chains across various mass ranges, including light, medium, heavy, and superheavy nuclei. We establish a correlation between nuclear symmetry energy and isospin asymmetry in different [...] Read more.

This study provides a comprehensive examination of the surface properties—particularly the symmetry energy and its contributing components—of isotonic chains across various mass ranges, including light, medium, heavy, and superheavy nuclei. We establish a correlation between nuclear symmetry energy and isospin asymmetry in different mass regions along isotonic chains with magic and semi-magic neutron numbers of N = 20, 40, 82, 126, and 172. Our approach integrates the coherent density fluctuation model within the relativistic mean-field (RMF) framework, utilizing both the non-linear NL3 and density-dependent DD-ME2 parameter sets. The methodology employs the Brueckner energy density functional in conjunction with our recently developed relativistic energy density functional (relativistic-EDF). The relativistic parameterization of the EDF at local density facilitates a consistent exploration of isospin-dependent surface properties across the nuclear landscape. In the present work, we successfully reproduce established shell closures and demonstrate that the relativistic approach yields significantly improved predictions for recognized magic numbers, particularly Z = 28 and 50. Additionally, we present compelling evidence for the presence of novel shell and sub-shell closures, specifically at Z = 34, 58, 92, and 118. These findings contribute to a nuanced understanding of nuclear surface properties while serving as a benchmark for future investigations and validations of nuclear models. Full article

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

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12 pages, 456 KiB

Open AccessArticle

Mutual Neutralization in Collisions of Li⁺ with O⁻

by Åsa Larson and Ann E. Orel

Atoms 2024, 12(12), 61; https://doi.org/10.3390/atoms12120061 - 28 Nov 2024

Abstract

The total and differential cross-sections and final state distribution for mutual neutralization in collisions of Li⁺ with O⁻ were calculated using an ab initio quantum mechanical approach based on potential energy curves and non-adiabatic coupling elements computed with the multi-reference configuration [...] Read more.

The total and differential cross-sections and final state distribution for mutual neutralization in collisions of Li⁺ with O⁻ were calculated using an ab initio quantum mechanical approach based on potential energy curves and non-adiabatic coupling elements computed with the multi-reference configuration interaction method. The final state distributions favored channels with excited oxygen states, indicating a strong effect of electron correlation, and the electron transfer could not be described by a simple one-electron exchange process. Full article

(This article belongs to the Special Issue Applications of Ab-Initio Calculations in Atomic, Molecular, and Optical Physics)

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15 pages, 1189 KiB

Open AccessArticle

Application of Atomic Spectroscopy of Trapped Radioactive Ions in Nuclear Physics

by Ruben P. de Groote

Atoms 2024, 12(12), 60; https://doi.org/10.3390/atoms12120060 - 21 Nov 2024

Abstract

A review is given of precision measurements of hyperfine constants and nuclear g-factors measured with ions confined in ion traps. The nuclear physics observables which can be extracted from these types of measurements are discussed. The feasibility of future nuclear structure studies [...] Read more.

A review is given of precision measurements of hyperfine constants and nuclear g-factors measured with ions confined in ion traps. The nuclear physics observables which can be extracted from these types of measurements are discussed. The feasibility of future nuclear structure studies using precision atomic spectroscopy of trapped radioactive atoms, produced with accelerator-driven approaches, is discussed. Full article

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

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8 pages, 287 KiB

Open AccessArticle

Dataset for Optical Processes in Dense Astrophysical and Laboratory Plasmas

by Nenad M. Sakan, Vladimir A. Srećković, Zoran J. Simić and Momchil Dechev

Atoms 2024, 12(11), 59; https://doi.org/10.3390/atoms12110059 - 14 Nov 2024

Abstract

The interest in the modeling of laboratory and astrophysical plasma behavior from mid up to strong non-ideality (NI), e.g., plasma in which a Coulomb interaction becomes dominant, led us to further investigate the optical properties of such systems. An expanded set of results [...] Read more.

The interest in the modeling of laboratory and astrophysical plasma behavior from mid up to strong non-ideality (NI), e.g., plasma in which a Coulomb interaction becomes dominant, led us to further investigate the optical properties of such systems. An expanded set of results and properties like wave functions, dipole matrix elements, etc., for such systems is presented in this submission. The methodologies of our research, as well as the current and future elements of their applications, are explained. In addition to being helpful to other researchers for achieving a variety of goals, the data from this study could be useful the interdisciplinary fields of machine learning, astrochemistry and fusion physics. The dataset is available online at the repository Figshare. Full article

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9 pages, 430 KiB

Open AccessArticle

On Resonance Enhancement of E1-E2 Nondipole Photoelectron Asymmetries in Low-Energy Ne 2p Photoionization

by Valeriy K. Dolmatov and Steven T. Manson

Atoms 2024, 12(11), 58; https://doi.org/10.3390/atoms12110058 - 7 Nov 2024

Abstract

Earlier, a significant enhancement of the nondipole parameters

γ_{2 p}

,

δ_{2 p}

, and

ζ_{2 p} = γ_{2 p} + 3 δ_{2 p}

in the photoelectron angular distribution for Ne

2 p

photoionization was predicted, owing to [...] Read more.

Earlier, a significant enhancement of the nondipole parameters

γ_{2 p}

,

δ_{2 p}

, and

ζ_{2 p} = γ_{2 p} + 3 δ_{2 p}

in the photoelectron angular distribution for Ne

2 p

photoionization was predicted, owing to resonance interference between dipole (

E 1

) and quadrupole (

E 2

) transitions. This enhancement manifests as narrow resonance spikes in the parameters due to the low-energy

2 s \to 3 p

and

2 s \to 4 p

dipole, as well as the

2 s \to 3 d

quadrupole autoionizing resonances. Given the unique nature of this predicted enhancement, it requires further validation, specifically regarding whether these narrow spikes in

γ_{2 p}

,

δ_{2 p}

and

ζ_{2 p}

will or will not retain their values for experimental observation if one accounts for a typical finite frequency spread in the ionizing radiation. To address this, we revisit the previous study, now incorporating the effect of frequency spread in the ionizing radiation, assuming a spread as large as 5 meV at the half-maximum of the radiation’s intensity. In the present paper we demonstrate that while the frequency spread does affect the resonance enhancement of

γ_{2 p}

,

δ_{2 p}

and

ζ_{2 p}

, these parameters still retain quantitatively significant values to be observed experimentally. The corresponding calculations were performed using the random phase approximation with exchange, which accounts for interchannel coupling in both dipole and quadrupole photoionization amplitudes. Full article

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

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11 pages, 426 KiB

Open AccessArticle

Excitation of Helium by Proton and Antiproton Impact

by Zsuzsánna Bálint, Sándor Borbély and Ladislau Nagy

Atoms 2024, 12(11), 57; https://doi.org/10.3390/atoms12110057 - 3 Nov 2024

Abstract

The electron transitions in atoms caused by charged particle impact are benchmarks for the study of electron dynamics. In the present paper we focus on the excitation of helium by proton and antiproton impact. We perform both ab initio and perturbational calculations, revealing [...] Read more.

The electron transitions in atoms caused by charged particle impact are benchmarks for the study of electron dynamics. In the present paper we focus on the excitation of helium by proton and antiproton impact. We perform both ab initio and perturbational calculations, revealing the importance of electron correlations and higher-order effects. The influence of the projectile charge sign on the excitation cross section is also studied. Full article

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

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14 pages, 361 KiB

Open AccessArticle

On a Study of Photoionization of Atoms and Ions from Endohedral Anions

by Valeriy K. Dolmatov, Larissa V. Chernysheva and Victor G. Yarzhemsky

Atoms 2024, 12(11), 56; https://doi.org/10.3390/atoms12110056 - 30 Oct 2024

Abstract

We study the relationship between the results of two qualitatively different semi-empirical models for photoionization cross sections,

σ_{n ℓ}

, of neutral atoms (A) and their cations (

A^{+}

) centrally encapsulated inside a fullerene anion,

C_{N}^{q}

[...] Read more.

We study the relationship between the results of two qualitatively different semi-empirical models for photoionization cross sections,

σ_{n ℓ}

, of neutral atoms (A) and their cations (

A^{+}

) centrally encapsulated inside a fullerene anion,

C_{N}^{q}

, where q represents the negative excess charge on the shell. One of the semi-empirical models, broadly employed in previous studies, assumes a uniform excess negative charge distribution over the entire fullerene cage, by analogy with a charged metallic sphere. The other model, presented here, considers the quantum states of the excess electrons on the shell, determined by specific n and ℓ values of their quantum numbers. Remarkably, both models yield similar photoionization cross sections for the encapsulated species. Consequently, we find that the photoionization of the encapsulated atoms or cations inside the

C_{N}^{q}

anion is influenced only slightly by the quantum states of the excess electrons on the fullerene cage. Furthermore, we demonstrate that the influence decreases even further as the size of the fullerene cage increases. All this holds true at least under the assumption that the encapsulated atom or cation is compact, i.e., its electron density remains primarily within itself rather than being drawn into the fullerene shell. This remarkable finding results from Hartree–Fock calculations combined with a popular modeling of the fullerene shell which is simulated by an attractive spherical annular potential. Full article

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12 pages, 5333 KiB

Open AccessArticle

Impact of Calcium Doping on the Electronic and Optical Characteristics of Strontium Hydride (SrH₂): A DFT Study

by Hamza Errahoui, Mohamed Karouchi, Abdelkebir Ejjabli, Aymane El haji, Abdelmounaim Laassouli, Omar Ait El Alia, Salah Chaji, Youssef Lachtioui and Omar Bajjou

Atoms 2024, 12(11), 55; https://doi.org/10.3390/atoms12110055 - 29 Oct 2024

Abstract

This study investigates the electronic and optical properties of calcium-doped strontium hydride (SrH₂) using first-principles density functional theory (DFT) calculations via the CASTEP code with generalized gradient approximation (GGA). We explore the impact of calcium (Ca) doping on the electronic band [...] Read more.

This study investigates the electronic and optical properties of calcium-doped strontium hydride (SrH₂) using first-principles density functional theory (DFT) calculations via the CASTEP code with generalized gradient approximation (GGA). We explore the impact of calcium (Ca) doping on the electronic band structure, density of states (DOS), and optical absorption spectra of SrH₂. Our results show that Ca doping significantly alters the electronic properties of SrH₂, notably increasing the indirect bandgap from 1.3 eV to 1.6 eV. The DOS analysis reveals new states near the Fermi level, primarily from Ca 3d orbitals. Moreover, the optical absorption spectra display enhanced absorption in the visible range, suggesting the potential for optoelectronic applications. This research highlights the feasibility of tuning the electronic and optical characteristics of SrH₂ through Ca doping, thus opening the way for the generation of advanced materials with tailored properties. Full article

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

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17 pages, 354 KiB

Open AccessArticle

Gordon Decomposition of the Magnetizability of a Dirac One-Electron Atom in an Arbitrary Discrete Energy State

by Patrycja Stefańska

Atoms 2024, 12(11), 54; https://doi.org/10.3390/atoms12110054 - 25 Oct 2024

Abstract

We present a Gordon decomposition of the magnetizability of a Dirac one-electron atom in an arbitrary discrete energy eigenstate, with a pointlike, spinless, and motionless nucleus of charge

Z e

. The external magnetic field, by which the atomic state is perturbed, is [...] Read more.

We present a Gordon decomposition of the magnetizability of a Dirac one-electron atom in an arbitrary discrete energy eigenstate, with a pointlike, spinless, and motionless nucleus of charge

Z e

. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, static, and uniform. Using the Sturmian expansion of the generalized Dirac–Coulomb Green function proposed by Szmytkowski in 1997, we derive a closed-form expressions for the diamagnetic (

χ_{d}

) and paramagnetic (

χ_{p}

) contributions to

χ

. Our calculations are purely analytical; the received formula for

χ_{p}

contains the generalized hypergeometric functions ₃F₂ of the unit argument, while

χ_{d}

is of an elementary form. For the atomic ground state, both results reduce to the formulas obtained earlier by other author. This work is a prequel to our recent article, where the numerical values of

χ_{d}

and

χ_{p}

for some excited states of selected hydrogenlike ions with

1 ⩽ Z ⩽ 137

were obtained with the use of the general formulas derived here. Full article

8 pages, 1199 KiB

Open AccessArticle

CO Dissociation Induced by 1 keV/u Ar²⁺ Ion

by Chijun Zhang, Ruitian Zhang, Shaofeng Zhang and Xinwen Ma

Atoms 2024, 12(10), 53; https://doi.org/10.3390/atoms12100053 - 18 Oct 2024

Abstract

CO is one of the important molecules in dense molecular clouds, and its dissociation induced by cosmic ray heavy ions is a fundamental process for molecular breaking up and rearrangement in astronomical networks. Extensive laboratory simulations are required to understand molecular evolution in [...] Read more.

CO is one of the important molecules in dense molecular clouds, and its dissociation induced by cosmic ray heavy ions is a fundamental process for molecular breaking up and rearrangement in astronomical networks. Extensive laboratory simulations are required to understand molecular evolution in astrophysical contexts. Here, we investigate the CO dissociation induced by 1 keV/u

{Ar}^{2 +}

using cold target recoil ion momentum spectroscopy. Kinetic energy release for double electron capture

{Ar}^{2 +} + CO \to {Ar}^{0} + C^{+} + O^{+}

and transfer ionization

{Ar}^{2 +} + CO \to {Ar}^{+} + C^{+} + O^{+} + e^{-}

was obtained. The dissociation mechanisms are attributed to different KER distributions. The autoionization process is identified below the

{CO}^{2 +}

double ionization threshold. Full article

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

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9 pages, 532 KiB

Open AccessArticle

An Extensive Analysis of Tsallis Statistics: π^±, K^± Mesons, and

p \bar{p}

Baryon in Inelastic pp Collisions

by Uzma Tabassam, Zain Ul Abidin, Khadija Gul and Irfan Siddique

Atoms 2024, 12(10), 52; https://doi.org/10.3390/atoms12100052 - 15 Oct 2024

Abstract

This study explores the inelastic doubly differential transverse momentum spectra of the primary charged particles,

(π^{+} + π^{-})

,

(K^{+} + K^{-})

and

(p \bar{p})

, as a function of observables associated [...] Read more.

This study explores the inelastic doubly differential transverse momentum spectra of the primary charged particles,

(π^{+} + π^{-})

,

(K^{+} + K^{-})

and

(p \bar{p})

, as a function of observables associated with underlying event (UE) at

\sqrt{s} = 13 T e V

. The particle production is measured on the basis of different angular regions like toward, transverse and away, elucidated with respect to the direction of leading particle of an event. To study the thermal freeze-out parameters, the non-extensive Tsallis distribution function is used to extract the temperature

T_{e f f}

and chemical potential

μ

, which provide a basis to explain the QCD matter. The Tsallis distribution function describes transverse momentum spectra in pseudorapidity region of

| η | < 0.8

. It is observed that effective temperature

T_{e f f}

changes from away to towards and forward region. Full article

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10 pages, 4757 KiB

Open AccessReview

High-Precision Experiments with Trapped Radioactive Ions Produced at Relativistic Energies

by Timo Dickel, Wolfgang R. Plaß, Emma Haettner, Christine Hornung, Sivaji Purushothaman, Christoph Scheidenberger and Helmut Weick

Atoms 2024, 12(10), 51; https://doi.org/10.3390/atoms12100051 - 8 Oct 2024

Abstract

Research on radioactive ion beams produced with in-flight separation of relativistic beams has advanced significantly over the past decades, with contributions to nuclear physics, nuclear astrophysics, atomic physics, and other fields. Central to these advancements are improved production, separation, and identification methods.The FRS [...] Read more.

Research on radioactive ion beams produced with in-flight separation of relativistic beams has advanced significantly over the past decades, with contributions to nuclear physics, nuclear astrophysics, atomic physics, and other fields. Central to these advancements are improved production, separation, and identification methods.The FRS Ion Catcher at GSI/FAIRexemplifies these technological advancements. The system facilitates high-precision experiments by efficiently stopping and extracting exotic nuclei as ions and making these available at thermal energies. High-energy synchrotron beams enhance the system’s capabilities, enabling unique experimental techniques such as multi-step reactions, mean range bunching, and optimized stopping, as well as novel measurement methods for observables such as beta-delayed neutron emission probabilities. The FRS Ion Catcher has already contributed to various scientific fields, and the future with the Super-FRS at FAIR promises to extend research to even more exotic nuclei and new applications. Full article

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

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19 pages, 2533 KiB

Open AccessArticle

Fisher Information-Based Optimization of Mapped Fourier Grid Methods

by Sotiris Danakas and Samuel Cohen

Atoms 2024, 12(10), 50; https://doi.org/10.3390/atoms12100050 - 8 Oct 2024

Abstract

The mapped Fourier grid method (mapped-FGM) is a simple and efficient discrete variable representation (DVR) numerical technique for solving atomic radial Schrödinger differential equations. It is set up on equidistant grid points, and the mapping, a suitable coordinate transformation to the radial variable, [...] Read more.

The mapped Fourier grid method (mapped-FGM) is a simple and efficient discrete variable representation (DVR) numerical technique for solving atomic radial Schrödinger differential equations. It is set up on equidistant grid points, and the mapping, a suitable coordinate transformation to the radial variable, deals with the potential energy peculiarities that are incompatible with constant step grids. For a given constrained number of grid points, classical phase space and semiclassical arguments help in selecting the mapping function and the maximum radial extension, while the energy does not generally exhibit a variational extremization trend. In this work, optimal computational parameters and mapping quality are alternatively assessed using the extremization of (coordinate and momentum) Fisher information. A benchmark system (hydrogen atom) is employed, where energy eigenvalues and Fisher information are traced in a standard convergence procedure. High-precision energy eigenvalues exhibit a correlation with the extrema of Fisher information measures. Highly efficient mapping schemes (sometimes classically counterintuitive) also stand out with these measures. Same trends are evidenced in the solution of Dalgarno–Lewis equations, i.e., inhomogeneous counterparts of the radial Schrödinger equation occurring in perturbation theory. A detailed analysis of the results, implications on more complex single valence electron Hamiltonians, and future extensions are also included. Full article

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