Symmetry

Editorial

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3 pages, 165 KiB

Open AccessEditorial

Some Current Trends in Atomic Theory

by Mikhail G. Kozlov

Symmetry 2021, 13(8), 1486; https://doi.org/10.3390/sym13081486 - 13 Aug 2021

Viewed by 1618

Abstract

Atomic theory continues to develop even after a century of rapid progress [...] Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

Research

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24 pages, 553 KiB

Open AccessArticle

Many-Electron QED with Redefined Vacuum Approach

by Romain N. Soguel, Andrey V. Volotka, Dmitry A. Glazov and Stephan Fritzsche

Symmetry 2021, 13(6), 1014; https://doi.org/10.3390/sym13061014 - 5 Jun 2021

Cited by 6 | Viewed by 2636

Abstract

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example [...] Read more.

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions. Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

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13 pages, 516 KiB

Open AccessEditor’s ChoiceArticle

Scalable Codes for Precision Calculations of Properties of Complex Atomic Systems

by Charles Cheung, Marianna Safronova and Sergey Porsev

Symmetry 2021, 13(4), 621; https://doi.org/10.3390/sym13040621 - 8 Apr 2021

Cited by 19 | Viewed by 2957

Abstract

High precision atomic data are indispensable for studies of fundamental symmetries, tests of fundamental physics postulates, developments of atomic clocks, ultracold atom experiments, astrophysics, plasma science, and many other fields of research. We have developed a new parallel atomic structure code package that [...] Read more.

High precision atomic data are indispensable for studies of fundamental symmetries, tests of fundamental physics postulates, developments of atomic clocks, ultracold atom experiments, astrophysics, plasma science, and many other fields of research. We have developed a new parallel atomic structure code package that enables computations that were not previously possible due to system complexity. This code package also allows much quicker computations to be run with higher accuracy for simple systems. We explored different methods of load-balancing matrix element calculations for many-electron systems, which are very difficult due to the intrinsic nature of the computational methods used to calculate them. Furthermore, dynamic memory allocation and MPI parallelization have been implemented to optimize and accelerate the computations. We have achieved near-perfect linear scalability and efficiency with the number of processors used for calculation, paving the way towards the future where most open-shell systems will finally be able to be treated with good accuracy. We present several examples illustrating new capabilities of the newly developed codes, specifically correlating up to all 60 electrons in the highly charged Ir

^{17 +}

ion and predicting certain properties of Fe

^{16 +}

. Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

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18 pages, 584 KiB

Open AccessEditor’s ChoiceArticle

Atomic Cascade Computations

by Stephan Fritzsche, Patrick Palmeri and Stefan Schippers

Symmetry 2021, 13(3), 520; https://doi.org/10.3390/sym13030520 - 23 Mar 2021

Cited by 28 | Viewed by 4153

Abstract

Atomic cascades are ubiquitous in nature and they have been explored within very different scenarios, from precision measurements to the modeling of astrophysical spectra, and up to the radiation damage in biological matter. However, up to the present, a quantitative analysis of these [...] Read more.

Atomic cascades are ubiquitous in nature and they have been explored within very different scenarios, from precision measurements to the modeling of astrophysical spectra, and up to the radiation damage in biological matter. However, up to the present, a quantitative analysis of these cascades often failed because of their inherent complexity. Apart from utilizing the rotational symmetry of atoms and a proper distinction of different physical schemes, a hierarchy of useful approaches is therefore needed in order to keep cascade computations feasible. We here suggest a classification of atomic cascades and demonstrate how they can be modeled within the framework of the Jena Atomic Calculator. As an example, we shall compute within a configuration-average approach the stepwise decay cascade of atomic magnesium, following a

1 s

inner-shell ionization, and simulate the corresponding (final) ion distribution. Our classification of physical scenarios (schemes) and the hierarchy of computational approaches are both flexible to further refinements as well as to complex shell structures of the atoms and ions, for which the excitation and decay dynamics need to be modeled in good detail. Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

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8 pages, 240 KiB

Open AccessArticle

Calculation of Polarizabilities for Atoms with Open Shells

by Vladimir Dzuba

Symmetry 2020, 12(12), 1950; https://doi.org/10.3390/sym12121950 - 26 Nov 2020

Cited by 11 | Viewed by 1953

Abstract

A version of the configuration interaction method for atoms with open shells (the Configuration Interaction with Perturbation Theory—CIPT method, PRA 95, 012503 (2017)) is extended for calculation of static and dynamic polarizabilities. Its use is demonstrated by calculation of the polarizabilities for the [...] Read more.

A version of the configuration interaction method for atoms with open shells (the Configuration Interaction with Perturbation Theory—CIPT method, PRA 95, 012503 (2017)) is extended for calculation of static and dynamic polarizabilities. Its use is demonstrated by calculation of the polarizabilities for the ground and excited states of Er, Tm and Yb. It is proved to be an useful tool in designing a new generation of optical atomic clocks sensitive to new physics. Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

16 pages, 1661 KiB

Open AccessArticle

Significance of Non-Linear Terms in the Relativistic Coupled-Cluster Theory in the Determination of Molecular Properties

by V. Srinivasa Prasannaa, Bijaya K. Sahoo, Minori Abe and Bhanu P. Das

Symmetry 2020, 12(5), 811; https://doi.org/10.3390/sym12050811 - 13 May 2020

Cited by 5 | Viewed by 2630

Abstract

The relativistic coupled-cluster (RCC) theory has been applied recently to a number of heavy molecules to determine their properties very accurately. Since it demands large computational resources, the method is often approximated to single and double excitations (RCCSD method). The effective electric fields [...] Read more.

The relativistic coupled-cluster (RCC) theory has been applied recently to a number of heavy molecules to determine their properties very accurately. Since it demands large computational resources, the method is often approximated to single and double excitations (RCCSD method). The effective electric fields (

E_{e f f}

) and molecular permanent electric dipole moments (PDMs) of SrF, BaF, and mercury monohalides (HgX with X = F, Cl, Br, and I) molecules are of immense interest for probing fundamental physics. In our earlier calculations of

E_{e f f}

and PDMs for the above molecules, we neglected the non-linear terms in the property evaluation expression of the RCCSD method. In this work, we demonstrate the roles of these terms in determining the above quantities and their computational time scalability with the number of processors of a computer. We also compare our results with previous calculations that employed variants of RCC theory, as well as other many-body methods and available experimental values. Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

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10 pages, 299 KiB

Open AccessArticle

Nuclear Spin-Dependent Effects of Parity Nonconservation in Ortho-H₂

by Dmitry V. Chubukov, Leonid V. Skripnikov, Leonti N. Labzowsky and Günter Plunien

Symmetry 2020, 12(1), 141; https://doi.org/10.3390/sym12010141 - 10 Jan 2020

Cited by 2 | Viewed by 2123

Abstract

We report a theoretical treatment of the nuclear spin-dependent spatial parity nonconserving (NSD-PNC) electron–nuclear interaction effect in the diatomic homonuclear ortho-H

_{2}

molecule. The magnetic dipole transition between

v = 1

and

v = 0

vibrational sublevels of the ground [...] Read more.

We report a theoretical treatment of the nuclear spin-dependent spatial parity nonconserving (NSD-PNC) electron–nuclear interaction effect in the diatomic homonuclear ortho-H

_{2}

molecule. The magnetic dipole transition between

v = 1

and

v = 0

vibrational sublevels of the ground

^{1} Σ_{g}^{+}

state is examined. The orthohydrogen molecule is a unique molecular system where the parity nonconserving (PNC) nuclear spin-dependent interaction due to the neutral weak currents can be directly observed and the corresponding coupling constant can be extracted from the future experiments. The theoretical simulation shows that using the cavity-enhanced scheme in conjunction with the record achievement of the intracavity absorption spectroscopy, the experiment on the observation of the NSD-PNC effect due to the neutral weak current in ortho-H

_{2}

looks feasible. Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

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Review

Jump to: Editorial, Research

26 pages, 417 KiB

Open AccessFeature PaperReview

Atomic Structure Calculations of Helium with Correlated Exponential Functions

by Vladimir A. Yerokhin, Vojtěch Patkóš and Krzysztof Pachucki

Symmetry 2021, 13(7), 1246; https://doi.org/10.3390/sym13071246 - 11 Jul 2021

Cited by 16 | Viewed by 2941

Abstract

The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant

α

. [...] Read more.

The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant

α

. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances,

r_{1}

,

r_{2}

and

r = | {\vec{r}}_{1} - {\vec{r}}_{2} |

. The choice of the exponential basis functions of the form

exp (- α r_{1} - β r_{2} - γ r)

allows us to construct an accurate and compact representation of the nonrelativistic wave function and to efficiently compute matrix elements of numerous singular operators representing relativistic and QED effects. Calculations of the leading QED effects of order

α^{5} m

(where m is the electron mass) are complemented with the systematic treatment of higher-order

α^{6} m

and

α^{7} m

QED effects. Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

23 pages, 434 KiB

Open AccessReview

Calculations of QED Effects with the Dirac Green Function

by Vladimir A. Yerokhin and Anna V. Maiorova

Symmetry 2020, 12(5), 800; https://doi.org/10.3390/sym12050800 - 11 May 2020

Cited by 12 | Viewed by 3385

Abstract

Modern spectroscopic experiments in few-electron atoms reached the level of precision at which an accurate description of quantum electrodynamics (QED) effects is mandatory. In many cases, theoretical treatment of QED effects need to be performed without any expansion in the nuclear binding strength [...] Read more.

Modern spectroscopic experiments in few-electron atoms reached the level of precision at which an accurate description of quantum electrodynamics (QED) effects is mandatory. In many cases, theoretical treatment of QED effects need to be performed without any expansion in the nuclear binding strength parameter

Z α

(where Z is the nuclear charge number and

α

is the fine-structure constant). Such calculations involve multiple summations over the whole spectrum of the Dirac equation in the presence of the binding nuclear field, which can be evaluated in terms of the Dirac Green function. In this paper we describe the technique of numerical calculations of QED corrections with the Dirac Green function, developed in numerous investigations during the last two decades. Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

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