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9 pages, 274 KiB

Open AccessArticle

Generalizations of the R-Matrix Method to the Treatment of the Interaction of Short-Pulse Electromagnetic Radiation with Atoms

by Barry I. Schneider, Kathryn R. Hamilton and Klaus Bartschat

Atoms 2022, 10(1), 26; https://doi.org/10.3390/atoms10010026 - 22 Feb 2022

Cited by 2 | Viewed by 2334

Abstract

Since its initial development in the 1970s by Phil Burke and his collaborators, the R-matrix theory and associated computer codes have become the method of choice for the calculation of accurate data for general electron–atom/ion/molecule collision and photoionization processes. The use of a [...] Read more.

Since its initial development in the 1970s by Phil Burke and his collaborators, the R-matrix theory and associated computer codes have become the method of choice for the calculation of accurate data for general electron–atom/ion/molecule collision and photoionization processes. The use of a non-orthogonal set of orbitals based on B-splines, now called the B-spline R-matrix (BSR) approach, was pioneered by Zatsarinny. It has considerably extended the flexibility of the approach and improved particularly the treatment of complex many-electron atomic and ionic targets, for which accurate data are needed in many modelling applications for processes involving low-temperature plasmas. Both the original R-matrix approach and the BSR method have been extended to the interaction of short, intense electromagnetic (EM) radiation with atoms and molecules. Here, we provide an overview of the theoretical tools that were required to facilitate the extension of the theory to the time domain. As an example of a practical application, we show results for two-photon ionization of argon by intense short-pulse extreme ultraviolet radiation. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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10 pages, 310 KiB

Open AccessArticle

Double Photoionization of Atomic Carbon

by Frank L. Yip

Atoms 2022, 10(1), 23; https://doi.org/10.3390/atoms10010023 - 12 Feb 2022

Viewed by 2232

Abstract

Double photoionization events provide a direct evaluation of electron correlation. The recent focus on few-electron targets continues to reveal the consequences of electron correlation for targets that possess several electrons. We consider the double photoionization of the

2 p^{2}

valence electrons of [...] Read more.

Double photoionization events provide a direct evaluation of electron correlation. The recent focus on few-electron targets continues to reveal the consequences of electron correlation for targets that possess several electrons. We consider the double photoionization of the

2 p^{2}

valence electrons of atomic carbon and focus on the first energetically accessible final-state symmetries that originate from coupling the active electrons in

^{3} P

configurations, which are doubly ionized by a single photon. Comparison of this process in carbon with neon provides an analogous case for the resulting final-state symmetries within the framework where the ejected electrons are influenced by the remaining bound electrons in a frozen-core approximation. Choosing this symmetry allows for comparison with previous theoretical results for total and energy sharing cross-sections of carbon. Fully differential cross-sections for both carbon and neon are also compared. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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12 pages, 1169 KiB

Open AccessArticle

Mechanisms of 1s Double-Core-Hole Excitation and Decay in Neon

by Maksim D. Kiselev, Elena V. Gryzlova, Sergei M. Burkov, Oleg Zatsarinny and Alexei N. Grum-Grzhimailo

Atoms 2021, 9(4), 114; https://doi.org/10.3390/atoms9040114 - 19 Dec 2021

Cited by 4 | Viewed by 2692

Abstract

The formation and decay of double-core-hole (DCH) states of the neon ion irradiated by an intense electromagnetic x-ray field are studied theoretically. In the present research DCH formation is the result of sequential absorption of two photons with the creation of an intermediate [...] Read more.

The formation and decay of double-core-hole (DCH) states of the neon ion irradiated by an intense electromagnetic x-ray field are studied theoretically. In the present research DCH formation is the result of sequential absorption of two photons with the creation of an intermediate ion. Detailed calculations of the partial decays and probabilities of shake-ups at the atomic and ionic ionization stages are presented. The angular distribution of photoelectrons corresponding to various residual ionic states are calculated. Specifically, we predict the lack of any photoelectrons corresponding to the residual ionic state

1 s^{1} 2 s^{2} 2 p^{n} m p^{n^{'} 2 S_{f} + 1} D

in the direction of the electric field polarization. Dynamical competition between single-core-hole state decay and excitation is analyzed and pulse parameters corresponding to various dynamical regimes are found. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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30 pages, 10884 KiB

Open AccessArticle

Oleg Zatsarinny (1953–2021): Memories by His Colleagues

by Klaus Bartschat, Charlotte Froese Fischer and Alexei N. Grum-Grzhimailo

Atoms 2021, 9(4), 109; https://doi.org/10.3390/atoms9040109 - 7 Dec 2021

Cited by 2 | Viewed by 2661

Abstract

A collection of short stories about Oleg Ivanovich Zatsarinny (1953–2021) to whom this Special Issue of Atoms is dedicated. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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11 pages, 563 KiB

Open AccessArticle

Circular Dichroism in the Photoionization of Unpolarized Atoms by Two Crossing Photon Beams

by Alexei V. Meremianin and Nikolai L. Manakov

Atoms 2021, 9(4), 108; https://doi.org/10.3390/atoms9040108 - 3 Dec 2021

Viewed by 2010

Abstract

The polarization dependence of the photoionization probability was analyzed in the case when a randomly oriented atom is irradiated by two crossing polarized monochromatic photon beams with the same frequency. It was found that the angular distributions of photoelectrons exhibit the effect of [...] Read more.

The polarization dependence of the photoionization probability was analyzed in the case when a randomly oriented atom is irradiated by two crossing polarized monochromatic photon beams with the same frequency. It was found that the angular distributions of photoelectrons exhibit the effect of circular dichroism (CD), which consists of the dependence of the photoionization probability on the sign of the circular polarization degree of each beam. We demonstrate that the CD effect exists only for coherent crossing photon beams. It was shown that CD effects are strongly dependent on the phase difference between the electric field vectors of the photon beams and have a quite large magnitude. The possibilities of the experimental observation of CD effects are discussed. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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6 pages, 1803 KiB

Open AccessArticle

Oleg Zatsarinny: Expert Atomic Theorist, Kind Man

by Thomas W. Gorczyca

Atoms 2021, 9(4), 107; https://doi.org/10.3390/atoms9040107 - 3 Dec 2021

Viewed by 2159

Abstract

I met Oleg Zatsarinny in 2001, and he then worked with me at Western Michigan University for two years. From 2003 to 2013, we were coauthors of 15 papers on theoretical atomic physics, and maintained a friendly relationship over twenty years, meeting and [...] Read more.

I met Oleg Zatsarinny in 2001, and he then worked with me at Western Michigan University for two years. From 2003 to 2013, we were coauthors of 15 papers on theoretical atomic physics, and maintained a friendly relationship over twenty years, meeting and socializing often at conferences. Further elaboration follows below. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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13 pages, 500 KiB

Open AccessEditor’s ChoiceArticle

Electron Scattering Cross-Section Calculations for Atomic and Molecular Iodine

by Harindranath B. Ambalampitiya, Kathryn R. Hamilton, Oleg Zatsarinny, Klaus Bartschat, Matt A. P. Turner, Anna Dzarasova and Jonathan Tennyson

Atoms 2021, 9(4), 103; https://doi.org/10.3390/atoms9040103 - 30 Nov 2021

Cited by 12 | Viewed by 4382

Abstract

Cross sections for electron scattering from atomic and molecular iodine are calculated based on the R-matrix (close-coupling) method. Elastic and electronic excitation cross sections are presented for both I and I

_{2}

. The dissociative electron attachment and vibrational excitation cross sections [...] Read more.

Cross sections for electron scattering from atomic and molecular iodine are calculated based on the R-matrix (close-coupling) method. Elastic and electronic excitation cross sections are presented for both I and I

_{2}

. The dissociative electron attachment and vibrational excitation cross sections of the iodine molecule are obtained using the local complex potential approximation. Ionization cross sections are also computed for I

_{2}

using the BEB model. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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8 pages, 895 KiB

Open AccessArticle

Excitation of the 6d ²D → 6p ²P^o Radiative Transitions in the Pb⁺ Ion by Electron Impact

by Viktoriya Roman, Valdas Jonauskas, Sigitas Kučas, Anna Gomonai, Aleksandr Gomonai and Yuriy Hutych

Atoms 2021, 9(4), 102; https://doi.org/10.3390/atoms9040102 - 29 Nov 2021

Viewed by 2496

Abstract

Results of experimental and theoretical investigation of electron-impact excitation of the

6 s^{2} 6 d D_{2} \to 6 s^{2} 6 p P_{2}^{o}

spectral transitions from the ground [...] Read more.

Results of experimental and theoretical investigation of electron-impact excitation of the

6 s^{2} 6 d D_{2} \to 6 s^{2} 6 p P_{2}^{o}

spectral transitions from the ground

6 s^{2} 6 p P_{2}_{1 / 2}^{o}

level in the Pb⁺ ion are presented. The experimental excitation functions for the transitions, measured by a VUV spectroscopy method, using the crossed electron and ion beams technique, reveal a rather distinct resonance structure resulting mainly from the electron decay of both atomic and ionic autoionizing states. The absolute values of the emission cross-sections, obtained by normalizing the experimental data at the incident electron energy 100 eV by those calculated using the Flexible Atomic Code software package, were found to be (0.35 ± 0.17) × 10^–16 cm² for the

6 s^{2} 6 d D_{2}_{3 / 2}

→

6 s^{2} 6 p P_{2}_{1 / 2}^{o}

(λ143.4 nm) transition and (0.19 ± 0.09) × 10^–16 cm² for the

6 s^{2} 6 d D_{2}_{5 / 2}

→

6 s^{2} 6 p P_{2}_{3 / 2}^{o}

(λ182.2 nm) transition. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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11 pages, 1748 KiB

Open AccessArticle

Relativistic B-Spline R-Matrix Calculations for Electron Scattering from Thallium Atoms

by Yang Wang, Hai-Liang Du, Xi-Ming Zhu, Oleg Zatsarinny and Klaus Bartschat

Atoms 2021, 9(4), 94; https://doi.org/10.3390/atoms9040094 - 5 Nov 2021

Cited by 1 | Viewed by 2603

Abstract

The Dirac B-spline R-matrix (DBSR) method is employed to treat low-energy electron collisions with thallium atoms. Special emphasis is placed on spin polarization phenomena that are investigated through calculations of the differential cross-section and the spin asymmetry function. Overall, good agreement between the [...] Read more.

The Dirac B-spline R-matrix (DBSR) method is employed to treat low-energy electron collisions with thallium atoms. Special emphasis is placed on spin polarization phenomena that are investigated through calculations of the differential cross-section and the spin asymmetry function. Overall, good agreement between the present calculations and the available experimental measurements is found. The contributions of electron exchange to the spin asymmetry cannot be ignored at low impact energies, while the spin–orbit interaction plays an increasingly significant role as the impact energy rises. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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12 pages, 2726 KiB

Open AccessArticle

Benchmark PhotoIonization Cross-Sections of Neutral Scandium from the Ground and Excited States

by Swaraj S. Tayal and Oleg Zatsarinny

Atoms 2021, 9(4), 83; https://doi.org/10.3390/atoms9040083 - 19 Oct 2021

Cited by 1 | Viewed by 1929

Abstract

The B-spline R-matrix method has been used to investigate cross-sections for photoionization of neutral scandium from the ground and excited states in the energy region from the 3d and 4s valence electron ionization thresholds to 25 eV. The initial [...] Read more.

The B-spline R-matrix method has been used to investigate cross-sections for photoionization of neutral scandium from the ground and excited states in the energy region from the 3d and 4s valence electron ionization thresholds to 25 eV. The initial bound states of Sc and the final residual Sc

^{+}

ionic states have been accurately calculated by combining the multiconfiguration Hartree-Fock method with the frozen-core close-coupling approach. The lowest 20 bound states of Sc I belonging to the ground

3 d 4 s^{2}

and excited

3 d^{2} 4 s

,

3 d^{2} 4 p

,

3 d 4 s 4 p

,

4 s^{2} 4 p

, and

3 d^{3}

configurations have been considered as initial states. The 81

L S

final ionic states of Sc

^{+}

belonging to the terms of

3 p^{6} 3 d^{2}

,

3 p^{6} 3 d 4 l

(l = 0–3),

3 p^{6} 3 d 5 l

(l = 0–3),

3 p^{6} 3 d 6 s

,

3 p^{6} 4 s^{2}

,

3 p^{6} 4 s 4 l

(l = 0–3),

3 p^{6} 4 s 5 l

(l = 0–1), and

3 p^{6} 4 p^{2}

configurations have been included in the final-state close-coupling expansion. The cross-sections are dominated by complicated resonance structures in the low energy region converging to several Sc

^{+}

ionic thresholds. The inclusion of all these final ionic states has been noted to significantly impact the near-threshold resonance structures and background cross-sections. The important scattering channels for leaving the residual ion in various final states have been identified, and the

3 d

electron ionization channels have been noted to dominate the cross-sections at higher photon energies. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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9 pages, 296 KiB

Open AccessFeature PaperArticle

Low-Energy Elastic Electron Scattering from Helium Atoms

by Robert P. McEachran, Kathryn R. Hamilton and Klaus Bartschat

Atoms 2021, 9(4), 82; https://doi.org/10.3390/atoms9040082 - 18 Oct 2021

Cited by 2 | Viewed by 1728

Abstract

We reinvestigate a key process in electron-atom collision physics, the elastic scattering of electrons from helium atoms. Specifically, results from a special-purpose relativistic polarized-orbital method, which is designed to treat elastic scattering only, are compared with those from a very extensive, fully ab [...] Read more.

We reinvestigate a key process in electron-atom collision physics, the elastic scattering of electrons from helium atoms. Specifically, results from a special-purpose relativistic polarized-orbital method, which is designed to treat elastic scattering only, are compared with those from a very extensive, fully ab initio, general-purpose B-spline R-matrix (close-coupling) code. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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13 pages, 3404 KiB

Open AccessArticle

Three-Photon Ionization with One-Photon Resonance between Excited Levels

by Aleksandr Gomonai, Eugene Remeta and Anna Gomonai

Atoms 2021, 9(3), 68; https://doi.org/10.3390/atoms9030068 - 17 Sep 2021

Viewed by 1758

Abstract

Within the framework of a three-level model, the process of three-photon ionization with one-photon resonance between two excited levels (with the lower one being initially unpopulated) is considered using the density matrix method. It is shown that such resonance can result in the [...] Read more.

Within the framework of a three-level model, the process of three-photon ionization with one-photon resonance between two excited levels (with the lower one being initially unpopulated) is considered using the density matrix method. It is shown that such resonance can result in the appearance of a maximum in the three-photon ionization spectrum when detuning between the resonance wavenumber and the wavenumber of the transition responsible for the lower excited level being populated exceeds the laser radiation linewidth by more than three orders of magnitude. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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8 pages, 1738 KiB

Open AccessEditor’s ChoiceArticle

Revealing the Target Electronic Structure with Under-Threshold RABBITT

by Anatoli Kheifets

Atoms 2021, 9(3), 66; https://doi.org/10.3390/atoms9030066 - 13 Sep 2021

Cited by 13 | Viewed by 2366

Abstract

The process of reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) reveals the target atom electronic structure when one of the transitions proceeds from below the ionization threshold. Such an under-threshold RABBITT resonates with the target bound states and thus maps [...] Read more.

The process of reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) reveals the target atom electronic structure when one of the transitions proceeds from below the ionization threshold. Such an under-threshold RABBITT resonates with the target bound states and thus maps faithfully the discrete energy levels and the corresponding oscillator strengths. We demonstrate this sensitivity by considering the Ne atom driven by the combination of the XUV and IR pulses at the fundamental laser frequency in the 800 and 1000 nm ranges. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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14 pages, 725 KiB

Open AccessArticle

Benchmark Angle-Differential Cross-Section Ratios for Excitation of the 4p5s Configuration in Krypton

by Ahmad Sakaamini, Jean-Baptiste Faure, Murtadha A. Khakoo, Oleg I. Zatsarinny and Klaus Bartschat

Atoms 2021, 9(3), 61; https://doi.org/10.3390/atoms9030061 - 2 Sep 2021

Cited by 3 | Viewed by 2994

Abstract

Benchmark intensity ratio measurements of the energy loss lines of krypton for excitation of the

4 p^{6}^{1} S_{0}

→

4 p^{5} 5 s {[3 / 2]}_{2}

, [...] Read more.

Benchmark intensity ratio measurements of the energy loss lines of krypton for excitation of the

4 p^{6}^{1} S_{0}

→

4 p^{5} 5 s {[3 / 2]}_{2}

,

4 p^{5} 5 s {[3 / 2]}_{1}

,

4 p^{5} 5 s^{'} {[1 / 2]}_{0}

, and

4 p^{5} 5 s^{'} {[1 / 2]}_{1}

transitions are reported, these being the lowest electronic excitations for krypton. The importance of these ratios as stringent tests of theoretical electron scattering models for the noble gases is discussed, as well as the role of spin-exchange and direct processes regarding the angular dependence of these ratios. The experimental data are compared with predictions from fully-relativistic B-spline R-matrix (close-coupling) calculations. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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14 pages, 763 KiB

Open AccessEditor’s ChoiceArticle

Towards B-Spline Atomic Structure Calculations

by Charlotte Froese Fischer

Atoms 2021, 9(3), 50; https://doi.org/10.3390/atoms9030050 - 31 Jul 2021

Cited by 6 | Viewed by 2425

Abstract

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, [...] Read more.

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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8 pages, 286 KiB

Open AccessArticle

Relativistic B-Spline R-Matrix Calculations for Electron Collisions with Ytterbium

by Kathryn R. Hamilton, Klaus Bartschat and Oleg Zatsarinny

Atoms 2021, 9(3), 47; https://doi.org/10.3390/atoms9030047 - 23 Jul 2021

Cited by 2 | Viewed by 2340

Abstract

We have applied the full-relativistic Dirac B-Spline R-matrix method to obtain cross sections for electron scattering from ytterbium atoms. The results are compared with those obtained from a semi-relativistic (Breit-Pauli) model-potential approach and the few available experimental data. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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19 pages, 1208 KiB

Open AccessArticle

A Fully Relativistic Approach to Photon Scattering and Photoionization of Alkali Atoms

by Adam Singor, Dmitry Fursa, Igor Bray and Robert McEachran

Atoms 2021, 9(3), 42; https://doi.org/10.3390/atoms9030042 - 8 Jul 2021

Cited by 3 | Viewed by 2553

Abstract

A fully relativistic approach to calculating photoionization and photon-atom scattering cross sections for quasi one-electron atoms is presented. An extensive set of photoionization cross sections have been calculated for alkali atoms: lithium, sodium, potassium, rubidium and cesium. The importance of relativistic effects and [...] Read more.

A fully relativistic approach to calculating photoionization and photon-atom scattering cross sections for quasi one-electron atoms is presented. An extensive set of photoionization cross sections have been calculated for alkali atoms: lithium, sodium, potassium, rubidium and cesium. The importance of relativistic effects and core polarization on the depth and position of the Cooper minimum in the photoionization cross section is investigated. Good agreement was found with previous Dirac-based B-spline R-matrix calculations of Zatsarinny and Tayal and recent experimental results. Full article

(This article belongs to the Special Issue A Tribute to Oleg Zatsarinny (1953–2021) and His Science–Fees Are Waived)

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