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3 pages, 5769 KiB

Open AccessEditorial

Editorial of the Special Issue “General Relativistic Atomic Structure Program—GRASP”

by Jacek Bieroń, Charlotte Froese Fischer and Per Jönsson

Atoms 2023, 11(6), 93; https://doi.org/10.3390/atoms11060093 - 6 Jun 2023

Cited by 2 | Viewed by 1647

Abstract

The year 2022 marked the 10th anniversary not only of the

A T O M S

journal but also of the international collaboration on Computational Atomic Structure [...] Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

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Research

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21 pages, 397 KiB

Open AccessArticle

Fine-Tuning of Atomic Energies in Relativistic Multiconfiguration Calculations

by Yanting Li, Gediminas Gaigalas, Wenxian Li, Chongyang Chen and Per Jönsson

Atoms 2023, 11(4), 70; https://doi.org/10.3390/atoms11040070 - 8 Apr 2023

Cited by 2 | Viewed by 1825

Abstract

Ab initio calculations sometimes do not reproduce the experimentally observed energy separations at a high enough accuracy. Fine-tuning of diagonal elements of the Hamiltonian matrix is a process which seeks to ensure that calculated energy separations of the states that mix are in [...] Read more.

Ab initio calculations sometimes do not reproduce the experimentally observed energy separations at a high enough accuracy. Fine-tuning of diagonal elements of the Hamiltonian matrix is a process which seeks to ensure that calculated energy separations of the states that mix are in agreement with experiment. The process gives more accurate measures of the mixing than can be obtained in ab initio calculations. Fine-tuning requires the Hamiltonian matrix to be diagonally dominant, which is generally not the case for calculations based on

j j

-coupled configuration state functions. We show that this problem can be circumvented by a method that transforms the Hamiltonian in

j j

-coupling to a Hamiltonian in

L S J

-coupling for which fine-tuning applies. The fine-tuned matrix is then transformed back to a Hamiltonian in

j j

-coupling. The implementation of the method into the General Relativistic Atomic Structure Package is described and test runs to validate the program operations are reported. The new method is applied to the computation of the

2 s^{2}^{1} S_{0} - 2 s 2 p^{1, 3} P_{1}

transitions in C III and to the computation of Rydberg transitions in B I, for which the

2 s 2 p^{2}^{2} S_{1 / 2}

perturber enters the

2 s^{2} n s^{2} S_{1 / 2}

series. Improved convergence patterns and results are found compared with ab initio calculations. Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

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369 pages, 1459 KiB

Open AccessEditor’s ChoiceArticle

GRASP Manual for Users

by Per Jönsson, Gediminas Gaigalas, Charlotte Froese Fischer, Jacek Bieroń, Ian P. Grant, Tomas Brage, Jörgen Ekman, Michel Godefroid, Jon Grumer, Jiguang Li and Wenxian Li

Atoms 2023, 11(4), 68; https://doi.org/10.3390/atoms11040068 - 5 Apr 2023

Cited by 27 | Viewed by 4524

Abstract

grasp is a software package in Fortran 95, adapted to run in parallel under MPI, for research in atomic physics. The basic premise is that, given a wave function, any observed atomic property can be computed. Thus, the first step is always to [...] Read more.

grasp is a software package in Fortran 95, adapted to run in parallel under MPI, for research in atomic physics. The basic premise is that, given a wave function, any observed atomic property can be computed. Thus, the first step is always to determine a wave function. Different properties challenge the accuracy of the wave function in different ways. This software is distributed under the MIT Licence. Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

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25 pages, 761 KiB

Open AccessEditor’s ChoiceArticle

Performance Tests and Improvements on the rmcdhf and rci Programs of GRASP

by Yanting Li, Jinqing Li, Changxian Song, Chunyu Zhang, Ran Si, Kai Wang, Michel Godefroid, Gediminas Gaigalas, Per Jönsson and Chongyang Chen

Atoms 2023, 11(1), 12; https://doi.org/10.3390/atoms11010012 - 13 Jan 2023

Cited by 7 | Viewed by 2281

Abstract

The latest published version of GRASP (General-purpose Relativistic Atomic Structure Package), i.e., GRASP2018, retains a few suboptimal subroutines/algorithms, which reflect the limited memory and file storage of computers available in the 1980s. Here we show how the efficiency of the relativistic self-consistent-field (SCF) [...] Read more.

The latest published version of GRASP (General-purpose Relativistic Atomic Structure Package), i.e., GRASP2018, retains a few suboptimal subroutines/algorithms, which reflect the limited memory and file storage of computers available in the 1980s. Here we show how the efficiency of the relativistic self-consistent-field (SCF) procedure of the multiconfiguration-Dirac–Hartree–Fock (MCDHF) method and the relativistic configuration-interaction (RCI) calculations can be improved significantly. Compared with the original GRASP codes, the present modified version reduces the CPU times by factors of a few tens or more. The MPI performances for all the original and modified codes are carefully analyzed. Except for diagonalization, all computational processes show good MPI scaling. Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

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44 pages, 978 KiB

Open AccessEditor’s ChoiceArticle

An Introduction to Relativistic Theory as Implemented in GRASP

by Per Jönsson, Michel Godefroid, Gediminas Gaigalas, Jörgen Ekman, Jon Grumer, Wenxian Li, Jiguang Li , Tomas Brage, Ian P. Grant, Jacek Bieroń and Charlotte Froese Fischer

Atoms 2023, 11(1), 7; https://doi.org/10.3390/atoms11010007 - 31 Dec 2022

Cited by 31 | Viewed by 5052

Abstract

Computational atomic physics continues to play a crucial role in both increasing the understanding of fundamental physics (e.g., quantum electrodynamics and correlation) and producing atomic data for interpreting observations from large-scale research facilities ranging from fusion reactors to high-power laser systems, space-based telescopes [...] Read more.

Computational atomic physics continues to play a crucial role in both increasing the understanding of fundamental physics (e.g., quantum electrodynamics and correlation) and producing atomic data for interpreting observations from large-scale research facilities ranging from fusion reactors to high-power laser systems, space-based telescopes and isotope separators. A number of different computational methods, each with their own strengths and weaknesses, is available to meet these tasks. Here, we review the relativistic multiconfiguration method as it applies to the General Relativistic Atomic Structure Package [grasp2018, C. Froese Fischer, G. Gaigalas, P. Jönsson, J. Bieroń, Comput. Phys. Commun. (2018). DOI: 10.1016/j.cpc.2018.10.032]. To illustrate the capacity of the package, examples of calculations of relevance for nuclear physics and astrophysics are presented. Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

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12 pages, 452 KiB

Open AccessArticle

Independently Optimized Orbital Sets in GRASP—The Case of Hyperfine Structure in Li I

by Yanting Li, Per Jönsson, Michel Godefroid, Gediminas Gaigalas, Jacek Bieroń, José Pires Marques, Paul Indelicato and Chongyang Chen

Atoms 2023, 11(1), 4; https://doi.org/10.3390/atoms11010004 - 30 Dec 2022

Cited by 5 | Viewed by 2126

Abstract

In multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations, there is a strong coupling between the localization of the orbital set and the configuration state function (CSF) expansion used to determine it. Furthermore, it is well known that an orbital set resulting from calculations, including CSFs describing [...] Read more.

In multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations, there is a strong coupling between the localization of the orbital set and the configuration state function (CSF) expansion used to determine it. Furthermore, it is well known that an orbital set resulting from calculations, including CSFs describing core–core correlation and other effects, which aims to lower the weighted energies of a number of targeted states as much as possible, may be inadequate for building CSFs that account for correlation effects that are energetically unimportant but decisive for computed properties, e.g., hyperfine structures or transition rates. This inadequacy can be traced in irregular or oscillating convergence patterns of the computed properties as functions of the increasing orbital set. In order to alleviate the above problems, we propose a procedure in which the orbital set is obtained by merging several separately optimized, and mutually non-orthogonal, orbital sets. This computational strategy preserves the advantages of capturing electron correlation on the total energy through the variational MCDHF method and allows to target efficiently the correlation effects on the considered property. The orbital sets that are merged are successively orthogonalized against each other to retain orthonormality. The merged orbital set is used to build CSFs that efficiently lower the energy and also adequately account for the correlation effects that are important for the property. We apply the procedure to compute the hyperfine structure constants for the

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

and

1 s^{2} 2 p^{2} P_{1 / 2, 3 / 2}^{o}

states in

^{7}

Li and show that it leads to considerably improved convergence patterns with respect to the increasing orbital set compared to standard calculations based on a single orbital set, energy-optimized in the variational procedure. The perspectives of the new procedure are discussed in a broader context in the summary. Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

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6 pages, 272 KiB

Open AccessArticle

Re-Evaluation of the Nuclear Magnetic Octupole Moment of ²⁰⁹Bi

by Jiguang Li, Gediminas Gaigalas, Jacek Bieroń, Jörgen Ekman, Per Jönsson, Michel Godefroid and Charlotte Froese Fischer

Atoms 2022, 10(4), 132; https://doi.org/10.3390/atoms10040132 - 4 Nov 2022

Cited by 5 | Viewed by 1758

Abstract

We modified the Hfs92 code of the GRASP package in order to describe the magnetic octupole hyperfine interaction. To illustrate the utility of the modified code, we carried out state-of-the-art calculations of the electronic factors of the magnetic octupole hyperfine interaction constants [...] Read more.

We modified the Hfs92 code of the GRASP package in order to describe the magnetic octupole hyperfine interaction. To illustrate the utility of the modified code, we carried out state-of-the-art calculations of the electronic factors of the magnetic octupole hyperfine interaction constants for levels in the ground configuration of the Bi atom. The nuclear magnetic octupole moment of the

^{209}

Bi isotope was extracted by combining old measurements of the hyperfine structures of

6 p^{3}^{4} S_{3 / 2}^{o}

[Hull, R.; Brink, G. Phys. Rev. A 1970, 1, 685] and

^{2} P_{3 / 2}^{o}

[Landman, D.A.; Lurio, A. Phys. Rev. A 1970, 1, 1330] using the atomic-beam magnetic-resonance technique with our theoretical electronic factors. The present extracted octupole moment was consistent with all the available values but the one obtained in the single-particle nuclear shell model approximation. This observation supports the previous finding that nuclear many-body effects, such as the core polarization, significantly contribute to the nuclear magnetic octupole moment in the case of

^{209}

Bi. Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

36 pages, 565 KiB

Open AccessArticle

A Program Library for Computing Pure Spin–Angular Coefficients for One- and Two-Particle Operators in Relativistic Atomic Theory

by Gediminas Gaigalas

Atoms 2022, 10(4), 129; https://doi.org/10.3390/atoms10040129 - 1 Nov 2022

Cited by 9 | Viewed by 3888

Abstract

A program library for computing pure spin-angular coefficients for any one- and scalar two-particle operators is presented. The method used is based on the combination of the second quantization and quasi-spin techniques with the angular momentum theory and the method of irreducible tensorial [...] Read more.

A program library for computing pure spin-angular coefficients for any one- and scalar two-particle operators is presented. The method used is based on the combination of the second quantization and quasi-spin techniques with the angular momentum theory and the method of irreducible tensorial sets. A relativistic approach is assumed. This program library is integrated in the General Relativistic Atomic Structure Package but it can be implemented in other program packages, too. Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

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17 pages, 595 KiB

Open AccessArticle

Application of Symmetry-Adapted Atomic Amplitudes

by Stephan Fritzsche

Atoms 2022, 10(4), 127; https://doi.org/10.3390/atoms10040127 - 1 Nov 2022

Cited by 4 | Viewed by 1530

Abstract

Following the work of Giulio Racah and others from the 1940s onward, the rotational symmetry of atoms and ions, e.g., the conservation of angular momentum, has been utilized in order to efficiently predict atomic behavior, from their level structure to the interaction with [...] Read more.

Following the work of Giulio Racah and others from the 1940s onward, the rotational symmetry of atoms and ions, e.g., the conservation of angular momentum, has been utilized in order to efficiently predict atomic behavior, from their level structure to the interaction with external fields, and up to the angular distribution and polarization of either emitted or scattered photons and electrons, while this rotational symmetry becomes apparent first of all in the block-diagonal structure of the Hamiltonian matrix, it also suggests a straight and consequent use of symmetry-adapted interaction amplitudes in expressing the observables of most atomic properties and processes. We here emphasize and discuss how atomic structure theory benefits from exploiting this symmetry, especially if open-shell atoms and ions in different charge states need to be combined with electrons in the continuum. By making use of symmetry-adapted amplitudes, a large number of excitation, ionization, recombination or even cascade processes can be formulated rather independently of the atomic shell structure and in a language close to the formal theory. The consequent use of these amplitudes in existing codes such as Grasp will therefore qualify them to deal with the recently emerging demands for developing general-purpose tools for atomic computations. Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

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15 pages, 361 KiB

Open AccessArticle

Variational Methods for Atoms and the Virial Theorem

by Charlotte Froese Fischer and Michel Godefroid

Atoms 2022, 10(4), 110; https://doi.org/10.3390/atoms10040110 - 8 Oct 2022

Cited by 3 | Viewed by 1733

Abstract

In the case of the one-electron Dirac equation with a point nucleus, the virial theorem (VT) states that the ratio of the kinetic energy to potential energy is exactly

- 1

, a ratio that can be an independent test of the accuracy [...] Read more.

In the case of the one-electron Dirac equation with a point nucleus, the virial theorem (VT) states that the ratio of the kinetic energy to potential energy is exactly

- 1

, a ratio that can be an independent test of the accuracy of a computed solution. This paper studies the virial theorem for subshells of equivalent electrons and their interactions in many-electron atoms. This shows that the linear scaling of the dilation is achieved through the balancing of the contributions to the potential of an electron from inner and outer regions that some Slater integrals impose conditions on a single subshell, but others impose conditions between subshells. The latter slows the rate of convergence of the self-consistent field process in which radial functions are updated one at a time. Several cases are considered. Results are also extended to the nonrelativistic case. Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

17 pages, 419 KiB

Open AccessArticle

GRASP: The Future?

by Ian Grant and Harry Quiney

Atoms 2022, 10(4), 108; https://doi.org/10.3390/atoms10040108 - 2 Oct 2022

Cited by 10 | Viewed by 2259

Abstract

The theoretical foundations of relativistic electronic structure theory within quantum electrodynamics (QED) and the computational basis of the atomic structure code GRASP are briefly surveyed. A class of four-component basis set is introduced, which we denote the CKG-spinor set, that enforces the charge-conjugation [...] Read more.

The theoretical foundations of relativistic electronic structure theory within quantum electrodynamics (QED) and the computational basis of the atomic structure code GRASP are briefly surveyed. A class of four-component basis set is introduced, which we denote the CKG-spinor set, that enforces the charge-conjugation symmetry of the Dirac equation. This formalism has been implemented using the Gaussian function technology that is routinely used in computational quantum chemistry, including in our relativistic molecular structure code, BERTHA. We demonstrate that, unlike the kinetically matched two-component basis sets that are widely employed in relativistic quantum chemistry, the CKG-spinor basis is able to reproduce the well-known eigenvalue spectrum of point-nuclear hydrogenic systems to high accuracy for all atomic symmetry types. Calculations are reported of third- and higher-order vacuum polarization effects in hydrogenic systems using the CKG-spinor set. These results reveal that Gaussian basis set expansions are able to calculate accurately these QED effects without recourse to the apparatus of regularization and in agreement with existing methods. An approach to the evaluation of the electron self-energy is outlined that extends our earlier work using partial-wave expansions in QED. Combined with the treatment of vacuum polarization effects described in this article, these basis set methods suggest the development of a comprehensive ab initio approach to the calculation of radiative and QED effects in future versions of the GRASP code. Full article

(This article belongs to the Special Issue The General Relativistic Atomic Structure Package—GRASP)

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