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Nonn Á, Margócsy Á, Mátyus E. Bound-State Relativistic Quantum Electrodynamics: A Perspective for Precision Physics with Atoms and Molecules. J Chem Theory Comput 2024. [PMID: 38789399 DOI: 10.1021/acs.jctc.4c00128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
Precision physics aims to use atoms and molecules to test and develop the fundamental theory of matter, possibly beyond the Standard Model. Most of the atomic and molecular phenomena are described by the quantum electrodynamics (QED) sector of the Standard Model. Do we have the computational tools, algorithms, and practical equations for the most possible complete computation of atoms and molecules within the QED sector? What is the fundamental equation to start with? Is it still Schrödinger's wave equation for molecular matter, or is there anything beyond that? This paper provides a concise overview of the relativistic QED framework and recent numerical developments targeting precision physics and spectroscopy applications with common features of the robust and successful relativistic quantum chemistry methodology.
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Affiliation(s)
- Ádám Nonn
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Ádám Margócsy
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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Loetzsch R, Beyer HF, Duval L, Spillmann U, Banaś D, Dergham P, Kröger FM, Glorius J, Grisenti RE, Guerra M, Gumberidze A, Heß R, Hillenbrand PM, Indelicato P, Jagodzinski P, Lamour E, Lorentz B, Litvinov S, Litvinov YA, Machado J, Paul N, Paulus GG, Petridis N, Santos JP, Scheidel M, Sidhu RS, Steck M, Steydli S, Szary K, Trotsenko S, Uschmann I, Weber G, Stöhlker T, Trassinelli M. Testing quantum electrodynamics in extreme fields using helium-like uranium. Nature 2024; 625:673-678. [PMID: 38267680 PMCID: PMC10808054 DOI: 10.1038/s41586-023-06910-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Accepted: 11/28/2023] [Indexed: 01/26/2024]
Abstract
Quantum electrodynamics (QED), the quantum field theory that describes the interaction between light and matter, is commonly regarded as the best-tested quantum theory in modern physics. However, this claim is mostly based on extremely precise studies performed in the domain of relatively low field strengths and light atoms and ions1-6. In the realm of very strong electromagnetic fields such as in the heaviest highly charged ions (with nuclear charge Z ≫ 1), QED calculations enter a qualitatively different, non-perturbative regime. Yet, the corresponding experimental studies are very challenging, and theoretical predictions are only partially tested. Here we present an experiment sensitive to higher-order QED effects and electron-electron interactions in the high-Z regime. This is achieved by using a multi-reference method based on Doppler-tuned X-ray emission from stored relativistic uranium ions with different charge states. The energy of the 1s1/22p3/2 J = 2 → 1s1/22s1/2 J = 1 intrashell transition in the heaviest two-electron ion (U90+) is obtained with an accuracy of 37 ppm. Furthermore, a comparison of uranium ions with different numbers of bound electrons enables us to disentangle and to test separately the one-electron higher-order QED effects and the bound electron-electron interaction terms without the uncertainty related to the nuclear radius. Moreover, our experimental result can discriminate between several state-of-the-art theoretical approaches and provides an important benchmark for calculations in the strong-field domain.
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Affiliation(s)
- R Loetzsch
- Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, Jena, Germany.
| | - H F Beyer
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - L Duval
- Laboratoire Kastler Brossel, Sorbonne Université, ENS-PSL Research University, Collège de France, CNRS, Paris, France
| | - U Spillmann
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - D Banaś
- Institute of Physics, Jan Kochanowski University, Kielce, Poland
| | - P Dergham
- Institut des NanoSciences de Paris, CNRS, Sorbonne Université, Paris, France
| | - F M Kröger
- Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, Jena, Germany
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
- Helmholtz-Institut Jena, Jena, Germany
| | - J Glorius
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - R E Grisenti
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - M Guerra
- Laboratory of Instrumentation, Biomedical Engineering and Radiation Physics (LIBPhys-UNL), Department of Physics, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal
| | - A Gumberidze
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - R Heß
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - P-M Hillenbrand
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
- I. Physikalisches Institut, Justus-Liebig-Universität, Giessen, Germany
| | - P Indelicato
- Laboratoire Kastler Brossel, Sorbonne Université, ENS-PSL Research University, Collège de France, CNRS, Paris, France
| | - P Jagodzinski
- Institute of Physics, Jan Kochanowski University, Kielce, Poland
| | - E Lamour
- Institut des NanoSciences de Paris, CNRS, Sorbonne Université, Paris, France
| | - B Lorentz
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - S Litvinov
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - Yu A Litvinov
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - J Machado
- Laboratory of Instrumentation, Biomedical Engineering and Radiation Physics (LIBPhys-UNL), Department of Physics, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal
| | - N Paul
- Laboratoire Kastler Brossel, Sorbonne Université, ENS-PSL Research University, Collège de France, CNRS, Paris, France
| | - G G Paulus
- Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, Jena, Germany
- Helmholtz-Institut Jena, Jena, Germany
| | - N Petridis
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
- Institut für Kernphysik, Goethe-Universität, Frankfurt am Main, Germany
| | - J P Santos
- Laboratory of Instrumentation, Biomedical Engineering and Radiation Physics (LIBPhys-UNL), Department of Physics, NOVA School of Science and Technology, NOVA University Lisbon, Caparica, Portugal
| | - M Scheidel
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - R S Sidhu
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
- School of Physics and Astronomy, The University of Edinburgh, Edinburgh, UK
| | - M Steck
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
| | - S Steydli
- Institut des NanoSciences de Paris, CNRS, Sorbonne Université, Paris, France
| | - K Szary
- Institute of Physics, Jan Kochanowski University, Kielce, Poland
| | - S Trotsenko
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
- Helmholtz-Institut Jena, Jena, Germany
| | - I Uschmann
- Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, Jena, Germany
| | - G Weber
- Helmholtz-Institut Jena, Jena, Germany
| | - Th Stöhlker
- Institut für Optik und Quantenelektronik, Friedrich-Schiller-Universität, Jena, Germany
- GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
- Helmholtz-Institut Jena, Jena, Germany
| | - M Trassinelli
- Institut des NanoSciences de Paris, CNRS, Sorbonne Université, Paris, France.
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Experimental and theoretical approaches for determining the K-shell fluorescence yield of carbon. Radiat Phys Chem Oxf Engl 1993 2023. [DOI: 10.1016/j.radphyschem.2022.110501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Paul N, Bian G, Azuma T, Okada S, Indelicato P. Testing Quantum Electrodynamics with Exotic Atoms. PHYSICAL REVIEW LETTERS 2021; 126:173001. [PMID: 33988393 DOI: 10.1103/physrevlett.126.173001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2020] [Revised: 12/17/2020] [Accepted: 03/29/2021] [Indexed: 06/12/2023]
Abstract
Precision study of few-electron, high-Z ions is a privileged field for probing high-field, bound-state quantum electrodynamics (BSQED). However, the accuracy of such tests is plagued by nuclear uncertainties, which are often larger than the BSQED effects under investigation. We propose an alternative method with exotic atoms and show that transitions may be found between circular Rydberg states where nuclear contributions are vanishing while BSQED effects remain large. When probed with newly available quantum sensing detectors, these systems offer gains in sensitivity of 1 to 2 orders of magnitude, while the mean electric field largely exceeds the Schwinger limit.
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Affiliation(s)
- Nancy Paul
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, Case 74; 4, place Jussieu, F-75005 Paris, France
| | - Guojie Bian
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, Case 74; 4, place Jussieu, F-75005 Paris, France
- Key Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, 100088 Beijing, China
| | - Toshiyuki Azuma
- Atomic, Molecular and Optical Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan
| | - Shinji Okada
- Chubu University, Kasugai, Aichi 487-8501, Japan
| | - Paul Indelicato
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, Case 74; 4, place Jussieu, F-75005 Paris, France
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Kozioł K, Aucar IA, Aucar GA. Relativistic and QED effects on NMR magnetic shielding constant of neutral and ionized atoms and diatomic molecules. J Chem Phys 2019; 150:184301. [PMID: 31091909 DOI: 10.1063/1.5095476] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We show here results of four-component calculations of nuclear magnetic resonance σ for atoms with 10 ≤ Z ≤ 86 and their ions, within the polarization propagator formalism at its random phase level of approach, and the first estimation of quantum electrodynamic (QED) effects and Breit interactions of those atomic systems by using two theoretical effective models. We also show QED corrections to σ(X) in simple diatomic HX and X2 (X = Br, I, At) molecules. We found that the Z dependence of QED corrections in bound-state many-electron systems is proportional to Z5, which is higher than its dependence in H-like systems. The analysis of relativistic ee (or paramagneticlike) and pp (or diamagneticlike) terms of σ exposes two different patterns: the pp contribution arises from virtual electron-positron pair creation/annihilation and the ee contribution is mainly given by 1s → ns and 2s → ns excitations. The QED effects on shieldings have a negative sign, and their magnitude is larger than 1% of the relativistic effects for high-Z atoms such as Hg and Rn, and up to 0.6% of its total four-component value for neutral Rn. Furthermore, percentual contributions of QED effects to the total shielding are larger for ionized than for neutral atoms. In a molecule, the contribution of QED effects to σ(X) is determined by its highest-Z atoms, being up to -0.6% of its total σ value for astatine compounds. It is found that QED effects grow faster than relativistic effects with Z.
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Affiliation(s)
- Karol Kozioł
- Institute for Modelling and Innovative Technology, IMIT, Corrientes, Argentina
| | - I Agustín Aucar
- Institute for Modelling and Innovative Technology, IMIT, Corrientes, Argentina
| | - Gustavo A Aucar
- Institute for Modelling and Innovative Technology, IMIT, Corrientes, Argentina
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Abstract
Several issues, concerning QED corrections, that are important in precise atomic calculations are presented. The leading QED corrections, self-energy and vacuum polarization, to the orbital energy for selected atoms with 30 ≤ Z ≤ 118 have been calculated. The sum of QED and Breit contributions to the orbital energy is analyzed. It has been found that for ns subshells the Breit and QED contributions are of comparative size, but for np and nd subshells the Breit contribution takes a major part of the QED+Breit sum. It has also, been found that the Breit to leading QED contributions ratio for ns subshells is almost independent of Z. The Z-dependence of QED and Breit+QED contributions per subshell is shown. The fitting coefficients may be used to estimate QED effects on inner molecular orbitals. We present results of our calculations for QED contributions to orbital energy of valence ns-subshell for group 1 and 11 atoms and discuss about the reliability of these numbers by comparing them with experimental first ionization potential data.
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Affiliation(s)
- Karol Kozioł
- Institute for Modelling and Innovative Technology, IMIT, Corrientes, Argentina
| | - Gustavo A Aucar
- Institute for Modelling and Innovative Technology, IMIT, Corrientes, Argentina
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Kozioł K, Giménez CA, Aucar GA. Breit corrections to individual atomic and molecular orbital energies. J Chem Phys 2018; 148:044113. [DOI: 10.1063/1.5017986] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Karol Kozioł
- Institute for Modelling and Innovative Technology, IMIT, Corrientes, Argentina
| | - Carlos A. Giménez
- Institute for Modelling and Innovative Technology, IMIT, Corrientes, Argentina
- Physics Department, Natural and Exact Science Faculty, Northeastern University of Argentina, Corrientes, Argentina
| | - Gustavo A. Aucar
- Institute for Modelling and Innovative Technology, IMIT, Corrientes, Argentina
- Physics Department, Natural and Exact Science Faculty, Northeastern University of Argentina, Corrientes, Argentina
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Affiliation(s)
- Pekka Pyykkö
- Department of Chemistry, University of Helsinki, POB 55 (A. I. Virtasen aukio 1), 00014 Helsinki, Finland
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Indelicato P, Gorveix O, Desclaux JP. Multiconfigurational Dirac-Fock studies of two-electron ions. II. Radiative corrections and comparison with experiment. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0022-3700/20/4/007] [Citation(s) in RCA: 216] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Indelicato P. Correlation and Negative Continuum Effects for the Relativistic M1 Transition in Two-Electron Ions using the Multiconfiguration Dirac-Fock Method. PHYSICAL REVIEW LETTERS 1996; 77:3323-3326. [PMID: 10062191 DOI: 10.1103/physrevlett.77.3323] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Serpa FG, Meyer ES, Morgan CA, Gillaspy JD, Sugar J, Roberts JR, Brown CM, Feldman U. Anomalous Z dependence of a magnetic dipole transition in the Ti. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 53:2220-2224. [PMID: 9913130 DOI: 10.1103/physreva.53.2220] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Marrs RE, Elliott SR, Stöhlker T. Measurement of two-electron contributions to the ground-state energy of heliumlike ions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 52:3577-3585. [PMID: 9912659 DOI: 10.1103/physreva.52.3577] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Ludziejewski T, Rymuza P, Sujkowski Z, Boschung B, Dousse J, Galley B, Halabuka Z, Herren C, Hoszowska J, Kern J, Rhême C, Polasik M. High-resolution study of the K beta 2 x-ray spectra induced by proton and photon impact on Zr, Mo, and Pd targets. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 52:2791-2803. [PMID: 9912561 DOI: 10.1103/physreva.52.2791] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Lindgren I, Persson H, Salomonson S, Labzowsky L. Full QED calculations of two-photon exchange for heliumlike systems: Analysis in the Coulomb and Feynman gauges. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 51:1167-1195. [PMID: 9911698 DOI: 10.1103/physreva.51.1167] [Citation(s) in RCA: 116] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Indelicato P. Projection operators in multiconfiguration Dirac-Fock calculations: Application to the ground state of heliumlike ions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 51:1132-1145. [PMID: 9911693 DOI: 10.1103/physreva.51.1132] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Ishikawa Y, Koc K. Relativistic many-body perturbation theory based on the no-pair Dirac-Coulomb-Breit Hamiltonian: Relativistic correlation energies for the noble-gas sequence through Rn (Z=86), the group-IIB atoms through Hg, and the ions of Ne isoelectronic sequence. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:4733-4742. [PMID: 9911470 DOI: 10.1103/physreva.50.4733] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Papp T, Campbell JL, Maxwell JA. Deviation from the single-particle model in the angular distribution of thorium L3 x rays in proton-impact ionization. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 48:3062-3071. [PMID: 9909959 DOI: 10.1103/physreva.48.3062] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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Birkett BB, Briand JP, Charles P, Dietrich DD, Finlayson K, Indelicato P, Liesen D, Marrus R, Simionovici A. Hyperfine quenching and measurement of the 2 (3)P0-2 (3)P1 fine-structure splitting in heliumlike silver (Ag45+). PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:R2454-R2457. [PMID: 9909345 DOI: 10.1103/physreva.47.r2454] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Ishikawa Y, Quiney HM. Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:1732-1739. [PMID: 9909124 DOI: 10.1103/physreva.47.1732] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Hallett WA, Dietrich DD, Silver JD. Measurement of 1s2s 3S1-1s2p 3P2,0 wavelengths in heliumlike neon. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:1130-1135. [PMID: 9909037 DOI: 10.1103/physreva.47.1130] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Marques JP, Parente F, Indelicato P. Hyperfine quenching of the 1s22s2p 3P0 level in berylliumlike ions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 47:929-935. [PMID: 9909013 DOI: 10.1103/physreva.47.929] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Indelicato P, Lindroth E. Relativistic effects, correlation, and QED corrections on K alpha transitions in medium to very heavy atoms. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:2426-2436. [PMID: 9908399 DOI: 10.1103/physreva.46.2426] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Indelicato P, Birkett BB, Briand JP, Charles P, Dietrich DD, Marrus R, Simionovici A. Hyperfine quenching and precision measurement of the 2 (3)P0-2 3P1 fine-structure splitting in heliumlike gadolinium (Gd62+). PHYSICAL REVIEW LETTERS 1992; 68:1307-1310. [PMID: 10046133 DOI: 10.1103/physrevlett.68.1307] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Lindroth E, Hvarfner J. Relativistic calculation of the 2 (1)S0-2 (1),3P1 transitions in berylliumlike molybdenum and berylliumlike iron. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:2771-2776. [PMID: 9907307 DOI: 10.1103/physreva.45.2771] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Ishikawa Y, Quiney HM, Malli GL. Dirac-Fock-Breit self-consistent-field method: Gaussian basis-set calculations on many-electron atoms. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 43:3270-3278. [PMID: 9905409 DOI: 10.1103/physreva.43.3270] [Citation(s) in RCA: 26] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Indelicato P, Desclaux JP. Multiconfiguration Dirac-Fock calculations of transition energies with QED corrections in three-electron ions. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 42:5139-5149. [PMID: 9904640 DOI: 10.1103/physreva.42.5139] [Citation(s) in RCA: 49] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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30
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Okada S, Shinada M, Matsuoka O. Relativistic well‐tempered Gaussian basis sets for helium through mercury. Breit interaction included. J Chem Phys 1990. [DOI: 10.1063/1.458638] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Lindroth E, Salomonson S. Relativistic calculation of the 2 (3)S1-1 (1)S0 magnetic dipole transition rate and transition energy for heliumlike argon. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1990; 41:4659-4669. [PMID: 9903684 DOI: 10.1103/physreva.41.4659] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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32
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Schäfer A, Soff G, Indelicato P, Müller B, Greiner W. Prospects for an atomic parity-violation experiment in U90+. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 40:7362-7365. [PMID: 9902154 DOI: 10.1103/physreva.40.7362] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Indelicato P, Parente F, Marrus R. Effect of hyperfine structure on the 2 3P1 and the 2 3P0 lifetime in heliumlike ions. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 40:3505-3514. [PMID: 9902564 DOI: 10.1103/physreva.40.3505] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Blundell SA, Johnson WR, Liu ZW, Sapirstein J. Relativistic all-order equations for helium. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:3768-3775. [PMID: 9901697 DOI: 10.1103/physreva.39.3768] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Lindroth E, Mårtensson-Pendrill AM. Further analysis of the complete Breit interaction. PHYSICAL REVIEW. A, GENERAL PHYSICS 1989; 39:3794-3802. [PMID: 9901699 DOI: 10.1103/physreva.39.3794] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Gorceix O, Indelicato P. Effect of the complete Breit interaction on two-electron ion energy levels. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 37:1087-1094. [PMID: 9899769 DOI: 10.1103/physreva.37.1087] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Lindroth E. Numerical solution of the relativistic pair equation. PHYSICAL REVIEW. A, GENERAL PHYSICS 1988; 37:316-328. [PMID: 9899659 DOI: 10.1103/physreva.37.316] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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