Atoms

1 pages, 152 KiB

Open AccessCorrection

Correction: Stambulchik, E. Stark Broadening of Lyman-α in the Presence of a Strong Magnetic Field. Atoms 2023, 11, 120

by Evgeny Stambulchik

Atoms 2024, 12(9), 45; https://doi.org/10.3390/atoms12090045 - 9 Sep 2024

Abstract

In the original publication [...] Full article

16 pages, 7071 KiB

Open AccessArticle

Applicability of Bispectral Analysis to Causality Determination within and between Ensembles of Unstable Plasma Waves

by Renaud Stauber and Mark Koepke

Atoms 2024, 12(9), 44; https://doi.org/10.3390/atoms12090044 - 5 Sep 2024

Abstract

Turbulence implies nonlinear wave–wave coupling, and determining cause and effect of either is important to understand mixing responsible for enhanced number, momentum, or energy (NME) transport. To explain the identification of parent and daughter modes via a look-up table, we sketch the framework [...] Read more.

Turbulence implies nonlinear wave–wave coupling, and determining cause and effect of either is important to understand mixing responsible for enhanced number, momentum, or energy (NME) transport. To explain the identification of parent and daughter modes via a look-up table, we sketch the framework of bispectral analysis without repeating the mathematical formalism of earlier bispectrum researchers. We then apply this technique to a test signal and plasma fluctuation data from the WVU-Q machine, where the inhomogeneous energy density-driven spectrum exhibited a degree of coupling to lower frequencies that was absent in the case of the related, single-eigenmode, current-driven spectrum. Full article

(This article belongs to the Special Issue Plasma Physics Highlights: Non-equilibrium Dynamics, Interfaces and Mixing)

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13 pages, 414 KiB

Open AccessArticle

Cooperative Decay of an Ensemble of Atoms in a One-Dimensional Chain with a Single Excitation

by Nicola Piovella

Atoms 2024, 12(9), 43; https://doi.org/10.3390/atoms12090043 - 28 Aug 2024

Abstract

We propose a new expression of the cooperative decay rate of a one-dimensional chain of N two-level atoms in the single-excitation configuration. From it, the interference nature of superradiance and subradiance arises naturally, without the need to solve the eigenvalue problem of the [...] Read more.

We propose a new expression of the cooperative decay rate of a one-dimensional chain of N two-level atoms in the single-excitation configuration. From it, the interference nature of superradiance and subradiance arises naturally, without the need to solve the eigenvalue problem of the atom–atom interaction Green function. The cooperative decay rate can be interpreted as the imaginary part of the expectation value of the effective non-Hermitian Hamiltonian of the system, evaluated over a generalized Dicke state of N atoms in the single-excitation manifold. Whereas the subradiant decay rate is zero for an infinite chain, it decreases as

1 / N

for a finite chain. A simple approximated expression for the cooperative decay rate is obtained as a function of the lattice constant d and the atomic number N. The results are obtained first for the scalar model and then extended to the vectorial light model, assuming all the dipoles aligned. Full article

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9 pages, 2276 KiB

Open AccessArticle

Detection of Optogalvanic Spectra Using Driven Quasi-Periodic Oscillator Dynamics

by Mark Koepke

Atoms 2024, 12(8), 42; https://doi.org/10.3390/atoms12080042 - 19 Aug 2024

Abstract

The narrowband light from a scannable, single-mode dye laser influences the electrical properties of gas discharges. The variation in these properties as the laser wavelength λ is scanned yields the optogalvanic spectrum of the discharge (i.e., electrical conductivity vs. frequency). By connecting a [...] Read more.

The narrowband light from a scannable, single-mode dye laser influences the electrical properties of gas discharges. The variation in these properties as the laser wavelength λ is scanned yields the optogalvanic spectrum of the discharge (i.e., electrical conductivity vs. frequency). By connecting a neon lamp, capacitor, and power supply in parallel, an undriven relaxation oscillator is formed whose natural frequency f₀ is affected by neon-resonant laser light and this λ-dependence of the relaxation oscillator frequency f₀ yields a variant optogalvanic spectrum (i.e., f₀ vs. frequency). In this paper, a driving force is effectively applied to an otherwise undriven oscillator when the incident light is chopped periodically at f_d. For f_d ≈ f₀ and a sufficiently large driving force amplitude (laser intensity and the degree of neon resonance), the relaxation oscillator can be entrained so that f₀ is locked on f_d and is independent of λ. For the new chopped-light technique described here, f_d is adjusted to be the subthreshold of the entrainment range, where the λ-dependence of f₀ is advantageously exaggerated by periodic pulling, and the beat frequency |f_d − f₀| vs. λ provides an optogalvanic spectrum with appealingly amplified signal-to-noise qualities. Beat frequency neon spectra are reported for the cases f_d < f₀ and f_d > f₀ and are compared with spectra obtained using the unchopped-light (i.e., undriven) method. Full article

(This article belongs to the Special Issue Plasma Physics Highlights: Non-equilibrium Dynamics, Interfaces and Mixing)

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System’s oscillation frequency and system’s beat frequency as a function of chopping frequency, i.e., driving frequency. (a) Beat frequency and (b) system’s oscillation frequency shows effects of periodic pulling and entrainment when driving and oscillation frequency values are close. Full article ">Figure 2
Beat frequency (increasing vertically) vs. driving force frequency (increasing from left to right). Effect of incident laser light’s resonance with neon influences the relaxation oscillator’s natural frequency, while the Arnol’d tongue feature remains dominant. Here, the system’s natural frequency, approximated by the entrainment’s midpoint along fd axis, decreases slightly as the laser light is scanned through the neon line. The blue line is the optogalvanic beat frequency spectrum (see Figure 6) for a given value of laser chopping frequency, i.e., driving frequency. Of interest is the blue line that is immediately to the left of the zero-beat-frequency region, i.e., entrainment region. Full article ">Figure 3
Natural frequency vs. duty cycle. (a) Increasing laser intensity increases optogalvanic effect until heating effects dominate. (b) Optogalvanic effect increases (relaxation oscillator’s national frequency decreases) as chopping duty cycle increases. Full article ">Figure 4
Isolation of two effects (widening and shifting). (a) Center of entrainment shifts as optogalvanic effect increases. (b) Entrainment width broadens as optogalvanic effect increases. Full article ">Figure 5
Schematic diagram of experimental setup. Full article ">Figure 6
Beat frequency spectra. Influence of optogalvanic effect on beat frequency for driving force frequency smaller or larger than the relaxation oscillator’s natural frequency. Full article ">Figure 7
Influence of laser intensity and chopping duty cycle (D.C.) on optogalvanic spectral line amplitude and shape. Beat freq spectra for 100%-100%, 100%-50%, 50%-100% (ratio of intensity to duty cycle). Full article ">

5 pages, 2337 KiB

Open AccessObituary

Claudio Mendoza (1951–2024)

by Manuel Bautista Plaza

Atoms 2024, 12(8), 41; https://doi.org/10.3390/atoms12080041 - 9 Aug 2024

Abstract

I met Claudio in 1989 when I was starting the last year of my physics bachelor’s degree [...] Full article

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

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11 pages, 351 KiB

Open AccessArticle

Calculation of Low-Lying Electronic Excitations of Magnesium Monofluoride: How Well Do Coupled-Cluster Methods Work?

by Marko Horbatsch

Atoms 2024, 12(8), 40; https://doi.org/10.3390/atoms12080040 - 8 Aug 2024

Abstract

Magnesium monofluoride is a polar molecule amenable to laser cooling which has caused renewed interest in its spectroscopy. In this work, we consider the case of three low-lying electronic excitations, namely

X^{2} Σ^{+}

→

A^{2} Π

, [...] Read more.

Magnesium monofluoride is a polar molecule amenable to laser cooling which has caused renewed interest in its spectroscopy. In this work, we consider the case of three low-lying electronic excitations, namely

X^{2} Σ^{+}

→

A^{2} Π

,

X^{2} Σ^{+}

→

B^{2} Σ^{+}

,

X^{2} Σ^{+}

→

C^{2} Σ^{+}

, using well-developed quantum chemistry approaches, i.e., without reference to the spin-orbit splitting of the

A^{2} Π

states. Accurate experimental data for these transitions have been available for over 50 years. Here, we explore the linear response method at the level of CC2 theory, as well as equation of motion methods at the level of CCSD and CC3, using two families of basis sets. Excellent agreement is obtained for the first three transitions when using the correlation-consistent basis sets and extrapolation to the complete basis limit within EOM-CC3 (at a relative precision of

10^{- 4}

), and qualitative agreement for the other two methods. The purpose of this paper is to serve as a guide on how to approach the accurate calculation of excitations in polar diatomic molecules. Full article

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11 pages, 2412 KiB

Open AccessArticle

A Collisional-Radiative Model for Kr III Ions

by Shikha Rathi and Lalita Sharma

Atoms 2024, 12(8), 39; https://doi.org/10.3390/atoms12080039 - 29 Jul 2024

Abstract

A collisional radiative model for Kr III in the ultraviolet regime is developed. For this purpose, atomic parameters for

4 s^{2} 4 p^{4}

,

4 s 4 p^{5}

,

4 s^{2} 4 p^{3} n l

, and [...] Read more.

A collisional radiative model for Kr III in the ultraviolet regime is developed. For this purpose, atomic parameters for

4 s^{2} 4 p^{4}

,

4 s 4 p^{5}

,

4 s^{2} 4 p^{3} n l

, and

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

configurations with n ranging from 5 to 7 and

l = s, p

, using the multiconfiguration Dirac–Hatree–Fock method are calculated. The effects of Breit and radiative quantum electrodynamic corrections are also included. Electron impact excitation cross-sections from the ground state, along with four metastable states arising from the

4 s^{2} 4 p^{4}

configuration to all fine structure levels of interest, are calculated using the relativistic distorted wave method. The reliability of the model is tested by comparing the predicted results with the previous measurements. Full article

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

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Comparison of the present transition rates (<math display="inline"><semantics> <msub> <mi>A</mi> <mi>Present</mi> </msub> </semantics></math>) with the measured transition rates (<math display="inline"><semantics> <msub> <mi>A</mi> <mi>Other</mi> </msub> </semantics></math>) of [<a href="#B8-atoms-12-00039" class="html-bibr">8</a>]. Full article ">Figure 2
EIE cross-sections for transitions from the (a) <math display="inline"><semantics> <mrow> <mn>4</mn> <msup> <mi>s</mi> <mn>2</mn> </msup> <mn>4</mn> <msup> <mi>p</mi> <mn>4</mn> </msup> <mo> </mo> <mmultiscripts> <mi>P</mi> <mn>2</mn> <none/> <mprescripts/> <none/> <mn>3</mn> </mmultiscripts> </mrow> </semantics></math> and (b) <math display="inline"><semantics> <mrow> <mn>4</mn> <msup> <mi>s</mi> <mn>2</mn> </msup> <mn>4</mn> <msup> <mi>p</mi> <mn>4</mn> </msup> <mo> </mo> <mmultiscripts> <mi>P</mi> <mn>0</mn> <none/> <mprescripts/> <none/> <mn>3</mn> </mmultiscripts> </mrow> </semantics></math>, levels of Kr III to higher excited levels. Full article ">Figure 3
EIE cross-sections for transitions from the <math display="inline"><semantics> <mrow> <mn>4</mn> <msup> <mi>s</mi> <mn>2</mn> </msup> <mn>4</mn> <msup> <mi>p</mi> <mn>4</mn> </msup> <mo> </mo> <mmultiscripts> <mi>P</mi> <mn>2</mn> <none/> <mprescripts/> <none/> <mn>3</mn> </mmultiscripts> </mrow> </semantics></math> level of Kr III to higher excited levels belonging to (a–d) <math display="inline"><semantics> <mrow> <mn>4</mn> <msup> <mi>s</mi> <mn>2</mn> </msup> <mn>4</mn> <msup> <mi>p</mi> <mn>3</mn> </msup> <mn>4</mn> <mi>d</mi> </mrow> </semantics></math> and (e–h) <math display="inline"><semantics> <mrow> <mn>4</mn> <msup> <mi>s</mi> <mn>2</mn> </msup> <mn>4</mn> <msup> <mi>p</mi> <mn>3</mn> </msup> <mn>5</mn> <mi>p</mi> </mrow> </semantics></math> configurations. Full article ">Figure 4
The variation in deviation parameter for a range of temperatures and densities. Full article ">Figure 5
Comparison of normalized measured intensities of [<a href="#B8-atoms-12-00039" class="html-bibr">8</a>] with the intensities stimulated from the present CR model. Full article ">

15 pages, 734 KiB

Open AccessReview

Electron and Positron Impact Ionization of Molecules

by Ladislau Nagy, István Tóth and Radu I. Campeanu

Atoms 2024, 12(8), 38; https://doi.org/10.3390/atoms12080038 - 23 Jul 2024

Abstract

We review our group’s most significant results concerning the collision of positrons and electrons with small molecules. Total and triple differential cross sections for the ionization of these targets were calculated in the distorted wave Born approximation using Gaussian molecular orbitals. Different models [...] Read more.

We review our group’s most significant results concerning the collision of positrons and electrons with small molecules. Total and triple differential cross sections for the ionization of these targets were calculated in the distorted wave Born approximation using Gaussian molecular orbitals. Different models were tested. The obtained theoretical results reproduced, in most cases, the features observed in the experimental data. Full article

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

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9 pages, 726 KiB

Open AccessArticle

The Optical Model Absorption Term in the Frame of Fractional Derivatives

by Ibrahim Ghabar, Aliaa Burqan and Gharib Gharib

Atoms 2024, 12(7), 37; https://doi.org/10.3390/atoms12070037 - 10 Jul 2024

Abstract

The complex optical model has been widely used to describe the elastic scattering of the nucleon–nucleus. The imaginary term of the optical potential takes into account the non-elastic scattering processes. This term was taken to be a Woods–Saxon form factor or its derivative [...] Read more.

The complex optical model has been widely used to describe the elastic scattering of the nucleon–nucleus. The imaginary term of the optical potential takes into account the non-elastic scattering processes. This term was taken to be a Woods–Saxon form factor or its derivative to simulate the volume absorption or the absorption localized at the surface of the target, respectively. In this study, a fractional derivative of the Woods–Saxon potential with

0 < α < 1

was used, where

α = 0

and

α = 1

give the volume and the surface absorption form factor, respectively. Full article

(This article belongs to the Special Issue Over a Century of Nuclear Isomers: Challenges and Prospects)

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19 pages, 475 KiB

Open AccessArticle

Calculations of Positron Scattering from Boron, BH, BF, BF₂, and BF₃

by Nicolas A. Mori, Haadi Umer, Liam H. Scarlett, Igor Bray and Dmitry V. Fursa

Atoms 2024, 12(7), 36; https://doi.org/10.3390/atoms12070036 - 10 Jul 2024

Abstract

The single-center convergent close-coupling (CCC) method is applied to calculate positron scattering from boron. A model potential approach is utilized to extract the positronium formation, direct ionization, and values between the positronium formation and ionization thresholds. We present results for total, electron loss, [...] Read more.

The single-center convergent close-coupling (CCC) method is applied to calculate positron scattering from boron. A model potential approach is utilized to extract the positronium formation, direct ionization, and values between the positronium formation and ionization thresholds. We present results for total, electron loss, elastic, momentum transfer, total bound state excitation, positronium formation, direct ionization, stopping power, and mean excitation energy from

10^{- 5}

eV to 5000 eV. For boron, there is only one other set of theoretical positron calculations for elastic and momentum transfer above 500 eV, which is in excellent agreement with the current CCC results. Using the current results for boron atoms and previous CCC calculations for hydrogen and fluorine atoms, positron scattering from BF,

{BF}_{2}

,

{BF}_{3}

, and BH molecules is calculated for energies between 0.1 eV and 5000 eV with a modified independent atom approach. Full article

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

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16 pages, 459 KiB

Open AccessArticle

Experimental and Theoretical Electron Collision Broadening Parameters for Several Ti II Spectral Lines of Industrial and Astrophysical Interest

by Lucía Isidoro-García, Isabel de Andrés-García, Juan Porro, Francisco Fernández and Cristóbal Colón

Atoms 2024, 12(7), 35; https://doi.org/10.3390/atoms12070035 - 9 Jul 2024

Abstract

A Q-switched Nd:YAG laser was focused on the Pb–Ti alloy samples in several laser-induced breakdown experiments in order to measure the Stark parameters of several spectral lines (58) of singly ionized titanium, including the 3504.89 Å and 3510.83 Å lines (where we achieved [...] Read more.

A Q-switched Nd:YAG laser was focused on the Pb–Ti alloy samples in several laser-induced breakdown experiments in order to measure the Stark parameters of several spectral lines (58) of singly ionized titanium, including the 3504.89 Å and 3510.83 Å lines (where we achieved new experimental and theoretical values). The diagnostics of the laser-induced plasmas (electron density and electron temperature) were performed using Balmer’s H alpha line (6562.7 Å). The temperatures were obtained by the Boltzmann plot technique with spectral lines of Pb I (after correction for its evident self-absorption). Subsequently, the calculations by the Griem approach of the Stark broadening parameters for several spectral lines were performed using the Gaunt factors proposed by van Regemorter and those proposed by Douglas H. Sampson. In the latter case, the values obtained were very close to the experimental values. This enables us to assume that the calculations performed for the spectral lines of Ti II, without experimental information, are more accurate using the Gaunt factors proposed by Sampson. Full article

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

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15 pages, 3029 KiB

Open AccessArticle

Efficient Time-Dependent Method for Strong-Field Ionization of Atoms with Smoothly Varying Radial Steps

by Nicolas Douguet, Mikhail Guchkov, Klaus Bartschat and Samantha Fonseca dos Santos

Atoms 2024, 12(7), 34; https://doi.org/10.3390/atoms12070034 - 3 Jul 2024

Cited by 1

Abstract

We present an efficient numerical method to solve the time-dependent Schrödinger equation in the single-active electron picture for atoms interacting with intense optical laser fields. Our approach is based on a non-uniform radial grid with smoothly increasing steps for the electron distance from [...] Read more.

We present an efficient numerical method to solve the time-dependent Schrödinger equation in the single-active electron picture for atoms interacting with intense optical laser fields. Our approach is based on a non-uniform radial grid with smoothly increasing steps for the electron distance from the residual ion. We study the accuracy and efficiency of the method, as well as its applicability to investigate strong-field ionization phenomena, the process of high-order harmonic generation, and the dynamics of highly excited Rydberg states. Full article

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

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Figure 1
Schematic representation of the non-uniform radial grid used to represent the radial components of the electronic wave function. Full article ">Figure 2
Comparison between ionization spectra calculated for a 6-cycle 400 nm pulse with a peak intensity of <math display="inline"><semantics> <msup> <mn>10</mn> <mn>14</mn> </msup> </semantics></math> W/cm2: (a) uniform grid results in LG with various equidistant steps h, (b) non-uniform grid results in LG, and (c) non-uniform grid results in VG. See text for details. Full article ">Figure 3
Comparison between calculated ionization spectra for the benchmark (uniform) and non-uniform grids: (a) results for the 800 nm, 6-cycle, <math display="inline"><semantics> <msup> <mn>10</mn> <mn>14</mn> </msup> </semantics></math> W/cm2 pulse, and (b) results for the 150 nm, 100-cycle, <math display="inline"><semantics> <msup> <mn>10</mn> <mn>13</mn> </msup> </semantics></math> W/cm2 pulse. See text for details. Full article ">Figure 4
Comparison between the HHG spectra produced by an 800 nm pulse with 6 cycles at a peak intensity of <math display="inline"><semantics> <msup> <mn>10</mn> <mn>14</mn> </msup> </semantics></math> W/cm2, calculated using a uniform grid (<math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mi>max</mi> </msub> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>) and a non-uniform grid (<math display="inline"><semantics> <mrow> <msub> <mi>h</mi> <mi>max</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>) in LG and VG. See text for details. Full article ">Figure 5
Ionization spectra (positive energy—solid lines) and renormalized Rydberg states excitation probability (negative energy—connected squares) for two different frequency pulses. See text for details. Full article ">

20 pages, 1930 KiB

Open AccessArticle

Elastic Electron Scattering from Be, Mg, and Ca

by Mehrdad Adibzadeh, Constantine E. Theodosiou and Nicholas J. Harmon

Atoms 2024, 12(6), 33; https://doi.org/10.3390/atoms12060033 - 18 Jun 2024

Abstract

We present a comprehensive set of theoretical results for differential, integrated, and momentum transfer cross sections for the elastic scattering of electrons by beryllium, magnesium, and calcium at energies below 1 keV. In addition, we provide Sherman function values for elastic electron scattering [...] Read more.

We present a comprehensive set of theoretical results for differential, integrated, and momentum transfer cross sections for the elastic scattering of electrons by beryllium, magnesium, and calcium at energies below 1 keV. In addition, we provide Sherman function values for elastic electron scattering from calcium in the same energy range. This study extends the application of our method of calculations, already employed for barium and strontium, to all stable alkaline-earth-metal atoms. Our semi-empirical approach to treating target polarization has produced in our earlier work a satisfactory agreement with experimental values and precise theoretical results such as convergent close-coupling calculations for barium. The present data are expected to be of similar high accuracy, based on our previous success in similar calculations for barium and all inert gases. Full article

(This article belongs to the Special Issue Calculations and Measurements of Atomic and Molecular Collisions)

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19 pages, 2622 KiB

Open AccessArticle

Sensitivity of a Point-Source-Interferometry-Based Inertial Measurement Unit Employing Large Momentum Transfer and Launched Atoms

by Jinyang Li, Timothy Kovachy, Jason Bonacum and Selim M. Shahriar

Atoms 2024, 12(6), 32; https://doi.org/10.3390/atoms12060032 - 11 Jun 2024

Abstract

We analyze theoretically the sensitivity of accelerometry and rotation sensing with a point source interferometer employing large momentum transfer (LMT) and present a design of an inertial measurement unit (IMU) that can measure rotation around and acceleration along each of the three axes. [...] Read more.

We analyze theoretically the sensitivity of accelerometry and rotation sensing with a point source interferometer employing large momentum transfer (LMT) and present a design of an inertial measurement unit (IMU) that can measure rotation around and acceleration along each of the three axes. In this design, the launching technique is used to realize the LMT process without the need to physically change directions of the Raman pulses, thus significantly simplifying the apparatus. We also describe an explicit scheme for such an IMU. Full article

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

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26 pages, 723 KiB

Open AccessReview

Time-Dependent Density Functional Theory for Atomic Collisions: A Progress Report

by Tom Kirchner

Atoms 2024, 12(6), 31; https://doi.org/10.3390/atoms12060031 - 1 Jun 2024

Abstract

In this paper, the current status of time-dependent density functional theory (TDDFT)-based calculations for ion–atom collision problems is reviewed. Most if not all reported calculations rely on the semiclassical approximation of heavy particle collision physics and the time-dependent Kohn–Sham (TDKS) scheme for computing [...] Read more.

In this paper, the current status of time-dependent density functional theory (TDDFT)-based calculations for ion–atom collision problems is reviewed. Most if not all reported calculations rely on the semiclassical approximation of heavy particle collision physics and the time-dependent Kohn–Sham (TDKS) scheme for computing the electronic density of the system. According to the foundational Runge–Gross theorem, all information available about the electronic many-body system is encoded in the density; however, in practice it is often not known how to extract it without resorting to modelling and approximations. This is in addition to a necessarily approximate implementation of the TDKS scheme due to the lack of precise knowledge about the potential that drives the equations. Notwithstanding these limitations, an impressive body of work has been accumulated over the past few decades. A sample of the results obtained for various collision systems is discussed here, in addition to the formal underpinnings and theoretical and practical challenges of the application of TDDFT to atomic collision problems, which are expounded in mostly nontechnical terms. Open problems and potential future directions are outlined as well. Full article

(This article belongs to the Special Issue Editorial Board Members’ Collection Series: Atomic Collision and Atomic Spectroscopy)

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16 pages, 386 KiB

Open AccessArticle

Natural Orbitals and Targeted Non-Orthogonal Orbital Sets for Atomic Hyperfine Structure Multiconfiguration Calculations

by Mingxuan Ma, Yanting Li, Michel Godefroid, Gediminas Gaigalas, Jiguang Li, Jacek Bieroń, Chongyang Chen, Jianguo Wang and Per Jönsson

Atoms 2024, 12(6), 30; https://doi.org/10.3390/atoms12060030 - 29 May 2024

Cited by 1

Abstract

Hyperfine structure constants have many applications, but are often hard to calculate accurately due to large and canceling contributions from different terms of the hyperfine interaction operator, and also from different closed and spherically symmetric core subshells that break up due to electron [...] Read more.

Hyperfine structure constants have many applications, but are often hard to calculate accurately due to large and canceling contributions from different terms of the hyperfine interaction operator, and also from different closed and spherically symmetric core subshells that break up due to electron correlation effects. In multiconfiguration calculations, the wave functions are expanded in terms of configuration state functions (CSFs) built from sets of one-electron orbitals. The orbital sets are typically enlarged within the layer-by-layer approach. The calculations are energy-driven, and orbitals in each new layer of correlation orbitals are spatially localized in regions where the weighted total energy decreases the most, overlapping and breaking up different closed core subshells in an irregular pattern. As a result, hyperfine structure constants, computed as expectation values of the hyperfine operators, often show irregular or oscillating convergence patterns. Large orbital sets, and associated large CSF expansions, are needed to obtain converged values of the hyperfine structure constants. We analyze the situation for the states of the

{2 s^{2} 2 p^{3}, 2 s^{2} 2 p^{2} 3 p, 2 s^{2} 2 p^{2} 4 p}

odd and

{2 s^{2} 2 p^{2} 3 s, 2 s 2 p^{4}, 2 s^{2} 2 p^{2} 4 s, 2 s^{2} 2 p^{2} 3 d}

even configurations in N I, and show that the convergence with respect to the increasing sets of orbitals is radically improved by introducing separately optimized orbital sets targeted for describing the spin- and orbital-polarization effects of the

1 s

and

2 s

core subshells that are merged with, and orthogonalized against, the ordinary energy-optimized orbitals. In the layer-by-layer approach, the spectroscopic orbitals are kept frozen from the initial calculation and are not allowed to relax in response to the introduced layers of correlation orbitals. To compensate for this lack of variational freedom, the orbitals are transformed to natural orbitals prior to the final calculation based on single and double substitutions from an increased multireference set. The use of natural orbitals has an important impact on the states of the

2 s^{2} 2 p^{2} 3 s

configuration, bringing the corresponding hyperfine interaction constants in closer agreement with experiment. Relying on recent progress in methodology, the multiconfiguration calculations are based on configuration state function generators, cutting down the time for spin-angular integration by factors of up to 50, compared to ordinary calculations. Full article

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15 pages, 1097 KiB

Open AccessArticle

PyQCAMS: Python Quasi-Classical Atom–Molecule Scattering

by Rian Koots and Jesús Pérez-Ríos

Atoms 2024, 12(5), 29; https://doi.org/10.3390/atoms12050029 - 11 May 2024

Cited by 1

Abstract

We present Python Quasi-classical atom–molecule scattering (PyQCAMS v0.1.0), a new Python package for atom–diatom scattering within the quasi-classical trajectory approach. The input consists of the mass, collision energy, impact parameter, and pair-wise/three-body interactions. As the output, the code provides the vibrational quenching, dissociation, [...] Read more.

We present Python Quasi-classical atom–molecule scattering (PyQCAMS v0.1.0), a new Python package for atom–diatom scattering within the quasi-classical trajectory approach. The input consists of the mass, collision energy, impact parameter, and pair-wise/three-body interactions. As the output, the code provides the vibrational quenching, dissociation, and reactive cross sections along with the rovibrational energy distribution of the reaction products. We benchmark the program for a reaction involving a molecular ion in a high-density ultracold gas, RbBa⁺ + Rb. Furthermore, we treat H₂ + Ca → CaH + H reactions as a prototypical example to illustrate the properties and performance of the software. Finally, we study the parallelization performance of the code by looking into the speedup of the program as a function of the number of CPUs used. Full article

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18 pages, 5583 KiB

Open AccessArticle

Interaction of Protons with Noble-Gas Atoms: Total and Differential Cross Sections

by Musab Al-Ajaleen and Károly Tőkési

Atoms 2024, 12(5), 28; https://doi.org/10.3390/atoms12050028 - 7 May 2024

Abstract

We present a classical treatment of the ionization and electron-capture processes in the interaction of protons with neutral noble-gas atoms, namely, Ne, Ar, Kr, and Xe. We used a three-body classical-trajectory Monte Carlo (CTMC) method to calculate the total (TCS) and differential (DCS) [...] Read more.

We present a classical treatment of the ionization and electron-capture processes in the interaction of protons with neutral noble-gas atoms, namely, Ne, Ar, Kr, and Xe. We used a three-body classical-trajectory Monte Carlo (CTMC) method to calculate the total (TCS) and differential (DCS) cross sections of single-electron processes. The Garvey-type model potential was employed in the CTMC model to describe the collision between the projectile and the target, accounting for the screening effect of the inactive electrons. The TCSs are evaluated for impact energies in the energy range between 0.2 keV and 50 MeV for a number of sub-shells of the targets. The ionization DCS are evaluated for an impact energy of 35 keV, focusing on the outer sub-shells only. We found that our ionization and electron-capture TCSs are in very good agreement with the previous theoretical and experimental data for all targets. Moreover, we presented single (SDCS)- and double (DDCS)-differential cross sections as a function of the energy and ejection angle of the ionized electron for all collision systems. Full article

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

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8 pages, 1546 KiB

Open AccessArticle

External Radiation Assistance of Neutrinoless Double Electron Capture

by Vladimir N. Kondratyev and Feodor F. Karpeshin

Atoms 2024, 12(5), 27; https://doi.org/10.3390/atoms12050027 - 28 Apr 2024

Abstract

The influence of electromagnetic radiation on nuclear processes is applied to an example of a neutrinoless double electron capture (0ν2ec). For cases with X-ray free-electron lasers (X-ray FELs) and/or inverse Compton X-ray sources, it was shown that such a decay can [...] Read more.

The influence of electromagnetic radiation on nuclear processes is applied to an example of a neutrinoless double electron capture (0ν2ec). For cases with X-ray free-electron lasers (X-ray FELs) and/or inverse Compton X-ray sources, it was shown that such a decay can be significantly enhanced by tuning the system to the resonant conditions through the absorption and/or emission of a photon with the decay resonance defect energy Δ. In this case, the 0v2ec decay rate Γ_2e of nuclide Z grew linearly with field intensity (S/S_z) up to the X-ray flux power S_m~Z⁶, while S_z~Z⁶ (Γ/Δ)² with decay width Γ of a daughter atom. For the case of ⁷⁸Kr → ⁷⁸Se − 0ν2eL₁L₁ capture we find S_z~10⁹ W cm⁻² and S_m~10¹⁷ W cm⁻² which indicate a possibility of increasing decay rate to eight orders of magnitude or even larger. Full article

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

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