1
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Heydarizadmotlagh F, Skinner TDG, Kato K, George MC, Hessels EA. Precision Measurement of the n=2 Triplet P J=1 to J=0 Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields. PHYSICAL REVIEW LETTERS 2024; 132:163001. [PMID: 38701455 DOI: 10.1103/physrevlett.132.163001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 02/28/2024] [Indexed: 05/05/2024]
Abstract
Increasing accuracy of the theory and experiment of the n=2 ^{3}P fine structure of helium has allowed for increasingly precise tests of quantum electrodynamics (QED), determinations of the fine-structure constant α, and limitations on possible beyond the standard model physics. Here we present a 2 ppb measurement of the J=1 to J=0 interval. The measurement is performed using frequency-offset separated-oscillatory fields. Our result of 29 616 955 018(60) Hz represents a landmark for helium fine-structure measurements, and, for the first time, will allow for a 1-ppb determination of the fine-structure constant when QED theory for the interval is improved.
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Affiliation(s)
- F Heydarizadmotlagh
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - T D G Skinner
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - K Kato
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - M C George
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - E A Hessels
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
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2
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Imgram P, König K, Maaß B, Müller P, Nörtershäuser W. Collinear Laser Spectroscopy of 2 ^{3}S_{1}→2 ^{3}P_{J} Transitions in Helium-like ^{12}C^{4+}. PHYSICAL REVIEW LETTERS 2023; 131:243001. [PMID: 38181159 DOI: 10.1103/physrevlett.131.243001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Accepted: 09/21/2023] [Indexed: 01/07/2024]
Abstract
Transition frequencies and fine-structure splittings of the 2 ^{3}S_{1}→2 ^{3}P_{J} transitions in helium-like ^{12}C^{4+} were measured by collinear laser spectroscopy on a 1-ppb level. Accuracy is increased by more than 3 orders of magnitude with respect to previous measurements, enabling tests of recent nonrelativistic (NR) QED calculations including terms up to mα^{7}. Deviations between the theoretical and experimental values are within theoretical uncertainties and are ascribed to mα^{8} and higher-order contributions in the series expansion of the NR QED calculations. Finally, prospects for an all-optical charge radius determination of light isotopes are evaluated.
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Affiliation(s)
- P Imgram
- Institut für Kernphysik, Departement of Physics, Technische Universität Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt, Germany
| | - K König
- Institut für Kernphysik, Departement of Physics, Technische Universität Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt, Germany
- Helmholtz Research Academy Hesse for FAIR, Campus Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt, Germany
| | - B Maaß
- Institut für Kernphysik, Departement of Physics, Technische Universität Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt, Germany
| | - P Müller
- Institut für Kernphysik, Departement of Physics, Technische Universität Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt, Germany
| | - W Nörtershäuser
- Institut für Kernphysik, Departement of Physics, Technische Universität Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt, Germany
- Helmholtz Research Academy Hesse for FAIR, Campus Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt, Germany
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3
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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. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, r1, r2 and r = |r→1−r→2|. The choice of the exponential basis functions of the form exp(−αr1−βr2−γr) 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 α5m (where m is the electron mass) are complemented with the systematic treatment of higher-order α6m and α7m QED effects.
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4
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Sun YR, Hu SM. Precision spectroscopy of atomic helium. Natl Sci Rev 2020; 7:1818-1827. [PMID: 34691519 PMCID: PMC8288801 DOI: 10.1093/nsr/nwaa216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Revised: 12/15/2019] [Accepted: 03/13/2020] [Indexed: 11/13/2022] Open
Abstract
Helium is a prototype three-body system and has long been a model system for developing quantum mechanics theory and computational methods. The fine-structure splitting in the 23P state of helium is considered to be the most suitable for determining the fine-structure constant α in atoms. After more than 50 years of efforts by many theorists and experimentalists, we are now working toward a determination of α with an accuracy of a few parts per billion, which can be compared to the results obtained by entirely different methods to verify the self-consistency of quantum electrodynamics. Moreover, the precision spectroscopy of helium allows determination of the nuclear charge radius, and it is expected to help resolve the 'proton radius puzzle'. In this review, we introduce the latest developments in the precision spectroscopy of the helium atom, especially the discrepancies among theoretical and experimental results, and give an outlook on future progress.
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Affiliation(s)
- Yu R Sun
- Hefei National Laboratory for Physical Sciences at Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Shui-Ming Hu
- Hefei National Laboratory for Physical Sciences at Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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5
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Qi XQ, Zhang PP, Yan ZC, Drake GWF, Zhong ZX, Shi TY, Chen SL, Huang Y, Guan H, Gao KL. Precision Calculation of Hyperfine Structure and the Zemach Radii of ^{6,7}Li^{+} Ions. PHYSICAL REVIEW LETTERS 2020; 125:183002. [PMID: 33196244 DOI: 10.1103/physrevlett.125.183002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2020] [Accepted: 09/17/2020] [Indexed: 06/11/2023]
Abstract
The hyperfine structures of the 2^{3}S_{1} states of the ^{6}Li^{+} and ^{7}Li^{+} ions are investigated theoretically to extract the Zemach radii of the ^{6}Li and ^{7}Li nuclei by comparing with precision measurements. The obtained Zemach radii are larger than the previous values of Puchalski and Pachucki [Phys. Rev. Lett. 111, 243001 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.243001] and disagree with them by about 1.5 and 2.2 standard deviations for ^{6}Li and ^{7}Li, respectively. Furthermore, our Zemach radius of ^{6}Li differs significantly from the nuclear physics value, derived from the nuclear charge and magnetic radii [Phys. Rev. A 78, 012513 (2008)PLRAAN1050-294710.1103/PhysRevA.78.012513] by more than 6σ, indicating an anomalous nuclear structure for ^{6}Li. The conclusion that the Zemach radius of ^{7}Li is about 40% larger than that of ^{6}Li is confirmed. The obtained Zemach radii are used to calculate the hyperfine splittings of the 2^{3}P_{J} states of ^{6,7}Li^{+}, where an order of magnitude improvement over the previous theory has been achieved for ^{7}Li^{+}.
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Affiliation(s)
- Xiao-Qiu Qi
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Pei-Pei Zhang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- Department of Physics, University of Windsor, Windsor, Ontario, Canada N9B 3P4
| | - Zong-Chao Yan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- Department of Physics, University of New Brunswick, Fredericton, New Brunswick, Canada E3B 5A3
- Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China
| | - G W F Drake
- Department of Physics, University of Windsor, Windsor, Ontario, Canada N9B 3P4
| | - Zhen-Xiang Zhong
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Ting-Yun Shi
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Shao-Long Chen
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Yao Huang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Hua Guan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
| | - Ke-Lin Gao
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- Center for Cold Atom Physics, Chinese Academy of Sciences, Wuhan 430071, China
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6
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Atomic fine-structure calculations performed with a finite-nuclear-mass approach and with all-electron explicitly correlated Gaussian functions. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.137476] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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7
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8
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Chen S, Liang S, Sun W, Huang Y, Guan H, Gao K. Saturated fluorescence spectroscopy measurement apparatus based on metastable Li + beam with low energy. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:043112. [PMID: 31043027 DOI: 10.1063/1.5088187] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2019] [Accepted: 03/23/2019] [Indexed: 06/09/2023]
Abstract
The apparatus for fluorescence spectroscopy measurement is developed to determine the fine structure (FS)/hyperfine structure (HFS) splittings of 1s2p 3PJ(J=0,1,2) states of Li+. The instrument is composed of a low energy Li+ ion source and a saturated fluorescence spectroscopic probing system. A low energy Li+ ion source, containing 1.8(7)% of 1s2s 3S1 metastable ions with an energy of ∼500 eV, is obtained by an electron bombardment process. The ion current can stay more than 250 h with the variation of ∼0.3%, and the divergence of ion beam is ∼0.5 mrad. The symmetric profile of Lamb dip signals of 1s2s 3S1--1s2p 3PJ transitions with linewidths of ∼50 MHz are obtained after subtracting Doppler background from the saturated fluorescence signals. A back-and-forth scan method is adopted to determine the FS/HFS splittings of 1s2p 3PJ states. Under these conditions, as a preliminary test, several splittings of 7Li+ are measured. The statistical uncertainties of the FS/HFS splittings are estimated to be less than 50 kHz, and the results are one order of magnitude better than previous results. The apparatus is feasible to precisely determine the splittings of energy levels of alkali and alkaline earth ions.
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Affiliation(s)
- Shaolong Chen
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Shiyong Liang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Wei Sun
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Yao Huang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Hua Guan
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
| | - Kelin Gao
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
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9
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Kato K, Skinner TDG, Hessels EA. Ultrahigh-Precision Measurement of the n=2 Triplet P Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields. PHYSICAL REVIEW LETTERS 2018; 121:143002. [PMID: 30339449 DOI: 10.1103/physrevlett.121.143002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2018] [Indexed: 06/08/2023]
Abstract
For decades, improved theory and experiment of the n=2 ^{3}P fine structure of helium have allowed for increasingly precise tests of quantum electrodynamics, determinations of the fine-structure constant α, and limitations on possible beyond-the-standard-model physics. Here we use the new frequency-offset separated-oscillatory-fields technique to measure the 2^{3}P_{2}→2^{3}P_{1} interval. Our result of 2 291 176 590(25) Hz represents a major step forward in precision for helium fine-structure measurements.
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Affiliation(s)
- K Kato
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - T D G Skinner
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
| | - E A Hessels
- Department of Physics and Astronomy, York University, Toronto, Ontario M3J 1P3, Canada
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10
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Zheng X, Sun YR, Chen JJ, Jiang W, Pachucki K, Hu SM. Measurement of the Frequency of the 2 ^{3}S-2 ^{3}P Transition of ^{4}He. PHYSICAL REVIEW LETTERS 2017; 119:263002. [PMID: 29328711 DOI: 10.1103/physrevlett.119.263002] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2017] [Indexed: 06/07/2023]
Abstract
The 2 ^{3}S-2 ^{3}P transition of ^{4}He was measured by comb-linked laser spectroscopy using a transverse-cooled atomic beam. The centroid frequency was determined to be 276 736 495 600.0(1.4) kHz, with a fractional uncertainty of 5.1×10^{-12}. This value is not only more accurate but also differs by as much as -49.5 kHz (20σ) from the previous result given by [Cancio Pastor et al., Phys. Rev. Lett. 92, 023001 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.023001; Cancio Pastor et al.Phys. Rev. Lett.97, 139903(E) (2006)10.1103/PhysRevLett.97.139903; Cancio Pastor et al.Phys. Rev. Lett.108, 143001 (2012)10.1103/PhysRevLett.108.143001]. In combination with ongoing theoretical calculations, this work may allow the most accurate determination of the nuclear charge radius of helium.
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Affiliation(s)
- X Zheng
- Hefei National Laboratory for Physical Sciences and Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Y R Sun
- Hefei National Laboratory for Physical Sciences and Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - J-J Chen
- Hefei National Laboratory for Physical Sciences and Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
| | - W Jiang
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - K Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - S-M Hu
- Hefei National Laboratory for Physical Sciences and Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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11
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Li J, Holzmann M, Duchemin I, Blase X, Olevano V. Helium Atom Excitations by the GW and Bethe-Salpeter Many-Body Formalism. PHYSICAL REVIEW LETTERS 2017; 118:163001. [PMID: 28474954 DOI: 10.1103/physrevlett.118.163001] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2016] [Indexed: 06/07/2023]
Abstract
The helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schrödinger equation is known for helium ground and excited states, and it represents a benchmark for any many-body methodology. Here, we check the ab initio many-body GW approximation and the Bethe-Salpeter equation (BSE) against the exact solution for helium. Starting from the Hartree-Fock method, we show that the GW and the BSE yield impressively accurate results on excitation energies and oscillator strength, systematically improving the time-dependent Hartree-Fock method. These findings suggest that the accuracy of the BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.
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Affiliation(s)
- Jing Li
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, Institut Néel, 38042 Grenoble, France
| | - Markus Holzmann
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, LPMMC, 38042 Grenoble, France
- European Theoretical Spectroscopy Facility (ETSF), 38000 Grenoble, France
| | - Ivan Duchemin
- Université Grenoble Alpes, 38000 Grenoble, France
- CEA, INAC-MEM L_Sim, 38054 Grenoble, France
| | - Xavier Blase
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, Institut Néel, 38042 Grenoble, France
| | - Valerio Olevano
- Université Grenoble Alpes, 38000 Grenoble, France
- CNRS, Institut Néel, 38042 Grenoble, France
- European Theoretical Spectroscopy Facility (ETSF), 38000 Grenoble, France
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12
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Zheng X, Sun YR, Chen JJ, Jiang W, Pachucki K, Hu SM. Laser Spectroscopy of the Fine-Structure Splitting in the 2^{3}P_{J} Levels of ^{4}He. PHYSICAL REVIEW LETTERS 2017; 118:063001. [PMID: 28234532 DOI: 10.1103/physrevlett.118.063001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2016] [Indexed: 06/06/2023]
Abstract
The fine-structure splitting in the 2^{3}P_{J} (J=0, 1, 2) levels of ^{4}He is of great interest for tests of quantum electrodynamics and for the determination of the fine-structure constant α. The 2^{3}P_{0}-2^{3}P_{2} and 2^{3}P_{1}-2^{3}P_{2} intervals are measured by laser spectroscopy of the ^{3}P_{J}-2^{3}S_{1} transitions at 1083 nm in an atomic beam, and are determined to be 31 908 130.98±0.13 kHz and 2 291 177.56±0.19 kHz, respectively. Compared with calculations, which include terms up to α^{5}Ry, the deviation for the α-sensitive interval 2^{3}P_{0}-2^{3}P_{2} is only 0.22 kHz. It opens the window for further improvement of theoretical predictions and an independent determination of the fine-structure constant α with a precision of 2×10^{-9}.
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Affiliation(s)
- X Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
| | - Y R Sun
- Hefei National Laboratory for Physical Sciences at the Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - J-J Chen
- Hefei National Laboratory for Physical Sciences at the Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
| | - W Jiang
- School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China
| | - K Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - S-M Hu
- Hefei National Laboratory for Physical Sciences at the Microscale, iChem Center, University of Science and Technology of China, Hefei 230026, China
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13
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Nörtershäuser W, Geppert C, Krieger A, Pachucki K, Puchalski M, Blaum K, Bissell ML, Frömmgen N, Hammen M, Kowalska M, Krämer J, Kreim K, Neugart R, Neyens G, Sánchez R, Yordanov DT. Precision Test of Many-Body QED in the Be+ 2p Fine Structure Doublet Using Short-Lived Isotopes. PHYSICAL REVIEW LETTERS 2015; 115:033002. [PMID: 26230786 DOI: 10.1103/physrevlett.115.033002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2015] [Indexed: 06/04/2023]
Abstract
Absolute transition frequencies of the 2s 2S{1/2}→2p2P{1/2,3/2} transitions in Be^{+} were measured for the isotopes ^{7,9-12}Be. The fine structure splitting of the 2p state and its isotope dependence are extracted and compared to results of ab initio calculations using explicitly correlated basis functions, including relativistic and quantum electrodynamics effects at the order of mα(6) and mα(7) ln α. Accuracy has been improved in both the theory and experiment by 2 orders of magnitude, and good agreement is observed. This represents one of the most accurate tests of quantum electrodynamics for many-electron systems, being insensitive to nuclear uncertainties.
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Affiliation(s)
| | - Christopher Geppert
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
| | - Andreas Krieger
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Mariusz Puchalski
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Klaus Blaum
- Max-Planck-Institut für Kernphysik, D-69117 Heidelberg, Germany
| | - Mark L Bissell
- Instituut voor Kern- en Stralingsfysica, KU Leuven, B-3001 Leuven, Belgium
| | - Nadja Frömmgen
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
| | - Michael Hammen
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
| | | | - Jörg Krämer
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - Kim Kreim
- Max-Planck-Institut für Kernphysik, D-69117 Heidelberg, Germany
| | - Rainer Neugart
- Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz, Germany
| | - Gerda Neyens
- Instituut voor Kern- en Stralingsfysica, KU Leuven, B-3001 Leuven, Belgium
| | - Rodolfo Sánchez
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt, Germany
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14
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Puchalski M, Pachucki K. Quantum electrodynamics corrections to the 2P fine splitting in Li. PHYSICAL REVIEW LETTERS 2014; 113:073004. [PMID: 25170705 DOI: 10.1103/physrevlett.113.073004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2014] [Indexed: 06/03/2023]
Abstract
We consider quantum electrodynamics (QED) corrections to the fine splitting E(2P_{3/2})-E(2P_{1/2}) in the Li atom. We derive complete formulas for the mα^{6} and mα^{7}lnα contributions and calculate them numerically using highly optimized, explicitly correlated basis functions. The obtained results are in agreement with the most recent measurement, helping to resolve discrepancies between former ones and lay the foundation for the investigation of QED effects in light, many-electron atoms.
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Affiliation(s)
- Mariusz Puchalski
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Hoża 69, 00-681 Warsaw, Poland
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15
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Cancio P, Bartalini S, De Rosa M, Giusfredi G, Mazzotti D, Maddaloni P, Vitiello M, De Natale P. Atomic and molecular spectroscopy with optical-frequency-comb-referenced IR coherent sources. EPJ WEB OF CONFERENCES 2013. [DOI: 10.1051/epjconf/20135702003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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16
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Amaro P, Schlesser S, Guerra M, Le Bigot EO, Isac JM, Travers P, Santos JP, Szabo CI, Gumberidze A, Indelicato P. Absolute measurement of the relativistic magnetic dipole transition energy in heliumlike argon. PHYSICAL REVIEW LETTERS 2012; 109:043005. [PMID: 23006085 DOI: 10.1103/physrevlett.109.043005] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2011] [Indexed: 05/22/2023]
Abstract
The 1s2s (3)S(1)→1s(2) (1)S(0) relativistic magnetic dipole transition in heliumlike argon, emitted by the plasma of an electron-cyclotron resonance ion source, has been measured using a double-flat crystal x-ray spectrometer. Such a spectrometer, used for the first time on a highly charged ion transition, provides absolute (reference-free) measurements in the x-ray domain. We find a transition energy of 3104.1605(77) eV (2.5 ppm accuracy). This value is the most accurate, reference-free measurement done for such a transition and is in good agreement with recent QED predictions.
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Affiliation(s)
- Pedro Amaro
- Laboratoire Kastler Brossel, Ecole Normale Supérieure, CNRS, Université Pierre et Marie Curie-Paris 6, Case 74, 4 Place Jussieu, F-75005 Paris, France
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17
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Cancio Pastor P, Consolino L, Giusfredi G, De Natale P, Inguscio M, Yerokhin VA, Pachucki K. Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius. PHYSICAL REVIEW LETTERS 2012; 108:143001. [PMID: 22540790 DOI: 10.1103/physrevlett.108.143001] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2011] [Revised: 02/29/2012] [Indexed: 05/31/2023]
Abstract
We measure the absolute frequency of seven out of the nine allowed transitions between the 2 (3)S and 2 (3)P hyperfine manifolds in a metastable (3)He beam by using an optical frequency comb synthesizer-assisted spectrometer. The relative uncertainty of our measurements ranges from 1×10(-11) to 5×10(-12), which is, to our knowledge, the most precise result for any optical ^{3}He transition to date. The resulting 2 (3)P-2 (3)S centroid frequency is 276,702,827,204.8(2.4) kHz. Comparing this value with the known result for the (4)He centroid and performing ab initio QED calculations of the (4)He-(3)He isotope shift, we extract the difference of the squared nuclear charge radii δr(2) of (3)He and (4)He. Our result for δr(2)=1.074(3) fm(2) disagrees by about 4σ with the recent determination [R. van Rooij et al., Science 333, 196 (2011)].
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Affiliation(s)
- P Cancio Pastor
- Istituto Nazionale di Ottica-CNR (INO-CNR), Via Nello Carrara 1, I-50019 Sesto Fiorentino, Italy.
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van Rooij R, Borbely JS, Simonet J, Hoogerland MD, Eikema KSE, Rozendaal RA, Vassen W. Frequency Metrology in Quantum Degenerate Helium: Direct Measurement of the 2
3
S
1
→ 2
1
S
0
Transition. Science 2011; 333:196-8. [DOI: 10.1126/science.1205163] [Citation(s) in RCA: 99] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- R. van Rooij
- LaserLaB Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - J. S. Borbely
- LaserLaB Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - J. Simonet
- École Normale Supérieure, Laboratoire Kastler-Brossel, 24 rue Lhomond, 75005 Paris, France
| | - M. D. Hoogerland
- Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand
| | - K. S. E. Eikema
- LaserLaB Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - R. A. Rozendaal
- LaserLaB Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - W. Vassen
- LaserLaB Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
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Consolino L, Giusfredi G, De Natale P, Inguscio M, Cancio P. Optical frequency comb assisted laser system for multiplex precision spectroscopy. OPTICS EXPRESS 2011; 19:3155-3162. [PMID: 21369137 DOI: 10.1364/oe.19.003155] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
A laser system composed of two lasers phase-locked onto an Optical Frequency Comb Synthesizer (OFCS), operating around 1083 nm, was developed. An absolute frequency precision of 6x10(-13) at 1s, limited by the OFCS, was measured with a residual rms phase-noise of 71 mrad and 87 mrad for the two phase-locks, respectively. Multiplex spectroscopy on 1083 nm Helium transitions with this set-up is demonstrated. Generalization of this system to a larger number of OFCS assisted laser sources for wider frequency separations, even in other spectral regions, is discussed.
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Affiliation(s)
- L Consolino
- European Laboratory for Non-Linear Spectroscopy (LENS) and Dipartimento di Fisica,Universitá degli Studi di Firenze, Via N. Carrara 1, 50019-Sesto Fiorentino (FI), Italy.
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21
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Smiciklas M, Shiner D. Determination of the fine structure constant using helium fine structure. PHYSICAL REVIEW LETTERS 2010; 105:123001. [PMID: 20867632 DOI: 10.1103/physrevlett.105.123001] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2010] [Indexed: 05/29/2023]
Abstract
We measure 31,908,131.25(30) kHz for the 2(3)}P J=0 to 2 fine structure interval in helium. The difference between this and theory to order mα7 (20 Hz numerical uncertainty) implies 0.22(30) kHz for uncalculated terms. The measurement is performed by using atomic beam and electro-optic laser techniques. Various checks include a 3He 2{3}S hyperfine measurement. We can obtain an independent value for the fine structure constant α with a 5 ppb experimental uncertainty. However, dominant mα8 terms (potentially 1.2 kHz) limit the overall uncertainty to a less competitive 20 ppb in α.
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Affiliation(s)
- Marc Smiciklas
- Department of Physics, University of North Texas, Denton, Texas 76203, USA
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