| 1. |
- Jönsson, Per, et al.
(författare)
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An Introduction to Relativistic Theory as Implemented in GRASP
- 2023
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Ingår i: Atoms. - : MDPI. - 2218-2004. ; 11:1
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Tidskriftsartikel (refereegranskat)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 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. Jonsson, J. Bieron, 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.
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| 2. |
- Jönsson, Per, et al.
(författare)
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GRASP Manual for Users
- 2023
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Ingår i: Atoms. - : MDPI. - 2218-2004. ; 11:4
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Tidskriftsartikel (refereegranskat)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 determine a wave function. Different properties challenge the accuracy of the wave function in different ways. This software is distributed under the MIT Licence.
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| 3. |
- Papoulia, Asimina, et al.
(författare)
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Coulomb (Velocity) Gauge Recommended in Multiconfiguration Calculations of Transition Data Involving Rydberg Series
- 2019
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Ingår i: Atoms. - : MDPI. - 2218-2004. ; 7:4
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Tidskriftsartikel (refereegranskat)abstract
- Astronomical spectroscopy has recently expanded into the near-infrared (nIR) wavelength region, raising the demands on atomic transition data. The interpretation of the observed spectra largely relies on theoretical results, and progress towards the production of accurate theoretical data must continuously be made. Spectrum calculations that target multiple atomic states at the same time are by no means trivial. Further, numerous atomic systems involve Rydberg series, which are associated with additional difficulties. In this work, we demonstrate how the challenges in the computations of Rydberg series can be handled in large-scale multiconfiguration Dirac-Hartree-Fock (MCDHF) and relativistic configuration interaction (RCI) calculations. By paying special attention to the construction of the radial orbital basis that builds the atomic state functions, transition data that are weakly sensitive to the choice of gauge can be obtained. Additionally, we show that the Babushkin gauge should not always be considered as the preferred gauge, and that, in the computations of transition data involving Rydberg series, the Coulomb gauge could be more appropriate for the analysis of astrophysical spectra. To illustrate the above, results from computations of transitions involving Rydberg series in the astrophysically important C IV and C III ions are presented and analyzed.
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| 4. |
- Yordanov, Deyan T., et al.
(författare)
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Structural trends in atomic nuclei from laser spectroscopy of tin
- 2020
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Ingår i: Communications Physics. - : Springer Nature. - 2399-3650. ; 3:1
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Tidskriftsartikel (refereegranskat)abstract
- Tin is the chemical element with the largest number of stable isotopes. Its complete proton shell, comparable with the closed electron shells in the chemically inert noble gases, is not a mere precursor to extended stability; since the protons carry the nuclear charge, their spatial arrangement also drives the nuclear electromagnetism. We report high-precision measurements of the electromagnetic moments and isomeric differences in charge radii between the lowest 1/2(+), 3/2(+), and 11/2(-) states in Sn117-131, obtained by collinear laser spectroscopy. Supported by state-of-the-art atomic-structure calculations, the data accurately show a considerable attenuation of the quadrupole moments in the closed-shell tin isotopes relative to those of cadmium, with two protons less. Linear and quadratic mass-dependent trends are observed. While microscopic density functional theory explains the global behaviour of the measured quantities, interpretation of the local patterns demands higher-fidelity modelling. Measurements of the hyperfine structure of chemical elements isotopes provide unique insight into the atomic nucleus in a nuclear model-independent way. The authors present collinear laser spectroscopy data obtained at the CERN ISOLDE and measure hyperfine splitting along a long chain of odd-mass tin isotopes.
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| 5. |
- Fischer, Charlotte Froese, et al.
(författare)
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Advanced multiconfiguration methods for complex atoms : I. Energies and wave functions
- 2016
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Ingår i: Journal of Physics B: Atomic, Molecular and Optical Physics. - : IOP Publishing. - 0953-4075 .- 1361-6455. ; 49:18
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Forskningsöversikt (refereegranskat)abstract
- Multiconfiguration wave function expansions combined with configuration interaction methods are a method of choice for complex atoms where atomic state functions are expanded in a basis of configuration state functions. Combined with a variational method such as the multiconfiguration Hartree-Fock (MCHF) or multiconfiguration Dirac-Hartree-Fock (MCDHF), the associated set of radial functions can be optimized for the levels of interest. The present review updates the variational MCHF theory to include MCDHF, describes the multireference single and double process for generating expansions and the systematic procedure of a computational scheme for monitoring convergence. It focuses on the calculations of energies and wave functions from which other atomic properties can be predicted such as transition rates, hyperfine structures and isotope shifts, for example.
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| 6. |
- Li, Yanting, et al.
(författare)
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Independently Optimized Orbital Sets in GRASP : The Case of Hyperfine Structure in Li I
- 2023
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Ingår i: Atoms. - : MDPI. - 2218-2004. ; 11:1
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Tidskriftsartikel (refereegranskat)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 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 1s(2)2s (2)S1/2 and 1s(2)2p (2Po)(1/2, 3/2) states in Li-7 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.
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| 7. |
- Li, Yanting, et al.
(författare)
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Performance Tests and Improvements on the rmcdhf and rci Programs of GRASP
- 2023
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Ingår i: Atoms. - : MDPI. - 2218-2004. ; 11:1
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Tidskriftsartikel (refereegranskat)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) 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.
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| 8. |
- Ma, Mingxuan, et al.
(författare)
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Natural Orbitals and Targeted Non-Orthogonal Orbital Sets for Atomic Hyperfine Structure Multiconfiguration Calculations
- 2024
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Ingår i: Atoms. - : MDPI. - 2218-2004. ; 12:6
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Tidskriftsartikel (refereegranskat)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 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 {2s22p3,2s22p23p,2s22p24p} odd and {2s22p23s,2s2p4,2s22p24s,2s22p23d} 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 1s and 2s 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 2s22p23s 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.
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| 9. |
- Bieron, Jacek, et al.
(författare)
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Multiconfiguration Dirac-Hartree-Fock calculations of the electric dipole moment of radium induced by the nuclear Schiff moment
- 2009
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - : American Physical Society. - 1050-2947 .- 1094-1622. ; 80:1
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Tidskriftsartikel (refereegranskat)abstract
- The multiconfiguration Dirac-Hartree-Fock theory has been employed to calculate the electric dipole moment of the 7s6d 3D2 state of radium induced by the nuclear Schiff moment. The results are dominated by valence and core-valence electron correlation effects. We show that the correlation effects can be evaluated in a converged series of multiconfiguration expansions.
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| 10. |
- Froese Fischer, Charlotte, et al.
(författare)
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Configuration interaction with separately optimized pair correlation functions
- 2010
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Variational methods produce one-electron radial functions that minimize the total energy of the system. Independent pair correlation functions (PCFs) designed to represent a specific correlation effect – valence, core-valence, or core-core – can be obtained from multiconfiguration Hartree-Fock (MCHF) or Dirac-Hartree-Fock (MCDHF) calculations [1,2]. These separately optimized and nonorthogonal PCFs may then be coupled by solving the associated generalized eigenproblem. In the present study, the Hamiltonian and overlap matrix elements are evaluated through biorthonormal orbital transformations and efficient counter-transformation of the configuration interaction eigenvectors [3]. The ground state of Be atom has been thoroughly tested by this method for various computational strategies and correlation models. It has been shown that the energy convergence is faster than with the usual SD-MCHF method of optimizing a single, orthonormal, one-electron orbital basis spanning the complete configuration space. Beryllium is a small system for which basis saturation can be achieved through complete active space MCHF expansions. But for larger systems describing electron correlation in all space by optimizing a common orthonormal set becomes hopeless whereas the calculation of additional PCFs is straight forward. Our independent optimization scheme, raises many questions related in the choice of the zero-order model to be used when building the interaction matrix. The present study is the first step in the current development of the extension of the atsp2K and grasp2K packages [1,2] that will adopt the biorthonormal treatment for energies, isotope shifts, hyperfine structures and transition probabilities.
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