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CODATA Recommended Values of the Fundamental Physical Constants: 2014*

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CODATA Recommended Values of the Fundamental Physical Constants: 2014* REVIEWS OF MODERN PHYSICS, VOLUME 88, JULY–SEPTEMBER 2016 CODATA recommended values of the fundamental physical constants: 2014* Peter J. Mohr,† David B. Newell,‡ and Barry N. Taylor§ National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8420, USA (published 26 September 2016) This paper gives the 2014 self-consistent set of values of the constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA). These values are based on a least-squares adjustment that takes into account all data available up to 31 December 2014. Details of the data selection and methodology of the adjustment are described. The recommended values may also be found at physics.nist.gov/ constants. DOI: 10.1103/RevModPhys.88.035009 CONTENTS A. Relative atomic masses of atoms 5 B. Relative atomic masses of ions and nuclei 6 I. Introduction 2 C. Relative atomic mass of the deuteron, triton, A. Background 2 and helion 7 B. Highlights of the CODATA 2014 adjustment 3 IV. Atomic Transition Frequencies 8 1. Planck constant h, elementary charge e, A. Hydrogen and deuterium transition frequencies, the Boltzmann constant k, Avogadro constant NA, Rydberg constant R∞, and the proton and deuteron and the redefinition of the SI 3 charge radii r , r 8 2. Relative atomic mass of the electron A e 4 p d r 1. Theory of hydrogen and deuterium energy 3. Proton magnetic moment in units of theð nuclearÞ levels 9 magneton μ =μ 4 p N a. Dirac eigenvalue 9 4. Fine-structure constant α 4 b. Relativistic recoil 9 5. Relative atomic masses 4 c. Nuclear polarizability 10 6. Newtonian constant of gravitation G 4 d. Self energy 10 7. Proton radius r and theory of the muon p e. Vacuum polarization 10 magnetic-moment anomaly a 4 μ f. Two-photon corrections 11 C. Outline of the paper 5 g. Three-photon corrections 12 II. Special Quantities and Units 5 h. Finite nuclear size 12 III. Relative Atomic Masses 5 i. Nuclear-size correction to self energy and vacuum polarization 13 * j. Radiative-recoil corrections 13 This review is being published simultaneously by the Journal of k. Nucleus self energy 13 Physical and Chemical Reference Data. l. Total energy and uncertainty 13 This report was prepared by the authors under the auspices of the m. Transition frequencies between levels with CODATA Task Group on Fundamental Constants. The members of n 2 and the fine-structure constant α 13 the task group are F. Cabiati, Istituto Nazionale di Ricerca Metro- 2. Experiments¼ on hydrogen and deuterium 14 logica, Italy; J. Fischer, Physikalisch-Technische Bundesanstalt, 3. Nuclear radii 14 Germany; J. Flowers (deceased), National Physical Laboratory, a. Electron scattering 15 United Kingdom; K. Fujii, National Metrology Institute of Japan, b. Isotope shift and the deuteron-proton radius Japan; S. G. Karshenboim, Pulkovo Observatory, Russian Federation difference 15 and Max-Planck-Institut für Quantenoptik, Germany; E. de Mirandés, c. Muonic hydrogen 15 Bureau international des poids et mesures; P. J. Mohr, National B. Hyperfine structure and fine structure 16 Institute of Standards and Technology, United States of America; V. Magnetic Moments and g-factors 16 D. B. Newell, National Institute of Standards and Technology, United A. Electron magnetic-moment anomaly a and the States of America; F. Nez, Laboratoire Kastler-Brossel, France; e fine-structure constant α 17 K. Pachucki, University of Warsaw, Poland; T. J. Quinn, Bureau 1. Theory of a 17 international des poids et mesures; C. Thomas, Bureau international e 2. Measurements of a 18 des poids et mesures; B. N. Taylor, National Institute of Standards and e B. Muon magnetic-moment anomaly a 18 Technology, United States of America; B. M. Wood, National μ 1. Theory of a 18 Research Council, Canada; and Z. Zhang, National Institute of μ Metrology, People’s Republic of China. 2. Measurement of aμ: Brookhaven 19 †[email protected] 3. Comparison of theory and experiment for aμ 20 ‡[email protected] C. Proton magnetic moment in nuclear magnetons §[email protected] μp=μN 20 0034-6861=2016=88(3)=035009(73) 035009-1 Published by the American Physical Society Peter J. Mohr, David B. Newell, and Barry N. Taylor: CODATA recommended values of the fundamental ... D. Atomic g-factors in hydrogenic 12C and 28Si A. Comparison of 2014 and 2010 CODATA and Ar e 21 recommended values 64 1. Theoryð Þ of the bound-electron g-factor 22 B. Some implications of the 2014 CODATA 12 5 28 13 2. Measurements of g C þ and g Si þ 24 recommended values and adjustment for VI. Magnetic-moment Ratios andð the Muon-electronÞ ð Þ metrology and physics 65 Mass Ratio 25 1. Conventional electrical units 65 A. Theoretical ratios of atomic bound-particle to 2. Josephson and quantum-Hall effects 66 free-particle g-factors 26 3. The new SI 66 1. Ratio measurements 26 4. Proton radius 66 B. Muonium transition frequencies, the muon-proton 5. Muon magnetic-moment anomaly 66 magnetic-moment ratio μμ=μp, and muon-electron 6. Electron magnetic-moment anomaly, mass ratio mμ=me 27 fine-structure constant, and QED 66 1. Theory of the muonium ground-state C. Suggestions for future work 66 hyperfine splitting 28 List of Symbols and Abbreviations 67 2. Measurements of muonium transition frequencies Acknowledgments 69 and values of μμ=μp and mμ=me 29 References 69 VII. Quotient of Planck Constant and Particle Mass h=m X and α 30 I. INTRODUCTION VIII. Electricalð MeasurementsÞ 31 A. NPL watt balance 31 This report describes work carried out under the auspices of B. METAS watt balance 32 the Task Group on Fundamental Constants, one of several task C. LNE watt balance 32 groups of the Committee on Data for Science and Technology D. NIST watt balance 32 (CODATA) founded in 1966 as an interdisciplinary committee E. NRC watt balance 33 of the International Council for Science (ICSU). It gives a IX. Measurements Involving Silicon Crystals 33 detailed account of the 2014 CODATA multivariate least- A. Measurements with natural silicon 33 squares adjustment of the values of the constants as well as the B. Determination of NA with enriched silicon 34 X. Thermal Physical Quantities 35 resulting 2014 set of over 300 self-consistent recommended A. Molar gas constant R, acoustic gas thermometry 35 values. The cutoff date for new data to be considered for 1. New values 35 possible inclusion in the 2014 adjustment was at the close of a. NIM 2013 35 31 December 2014, and the new set of values first became b. NPL 2013 36 available on 25 June 2015 at physics.nist.gov/constants, part c. LNE 2015 36 of the website of the Fundamental Constants Data Center of 2. Updated values 36 the National Institute of Standards and Technology (NIST), a. Molar mass of argon 36 Gaithersburg, Maryland, USA. b. Molar mass of helium 37 c. Thermal conductivity of argon 37 A. Background B. Quotient k=h, Johnson noise thermometry 37 C. Quotient Aϵ=R, dielectric-constant gas thermometry 37 The compilation of a carefully reviewed set of values of the D. Other data 38 fundamental constants of physics and chemistry arguably E. Stefan-Boltzmann constant σ 38 began over 85 years ago with the paper of Birge (1929). In XI. Newtonian Constant of Gravitation G 38 1969, 40 years after the publication of Birge’s paper, the A. Updated values 38 CODATA Task Group on Fundamental Constants was estab- 1. Huazhong University of Science and Technology 38 lished for the following purpose: to periodically provide B. New values 39 the scientific and technological communities with a self- 1. International Bureau of Weights and Measures 39 consistent set of internationally recommended values of the 2. European Laboratory for Non-Linear basic constants and conversion factors of physics and chem- Spectroscopy, University of Florence 39 istry based on all the data available at a given point in time. 3. University of California, Irvine 40 The Task Group first met this responsibility with its 1973 XII. Electroweak Quantities 41 multivariate least-squares adjustment of the values of the XIII. Analysis of Data 41 A. Comparison of data through inferred values of constants (Cohen and Taylor, 1973), which was followed α, h, and k 41 13 years later by the 1986 adjustment (Cohen and Taylor, B. Multivariate analysis of data 43 1987). Starting with its third adjustment in 1998 the Task 1. Data related to the Newtonian constant of Group has carried them out every 4 years; if the 1998 gravitation G 46 adjustment is counted as the first of the new 4-year cycle, 2. Data related to all other constants 48 the 2014 adjustment described in this report is the 5th of the 3. Test of the Josephson and quantum-Hall-effect cycle. Throughout this article we refer to the detailed relations 53 reports describing the 1998, 2002, 2006, 2010, and 2014 XIV. The 2014 CODATA Recommended Values 55 adjustments, or sometimes the adjustments themselves, as A. Calculational details 55 CODATA-XX, where XX is 98, 02, 06, 10, or 14 (Mohr and B. Tables of values 63 Taylor, 2000, 2005; Mohr, Taylor, and Newell, 2008a, 2008b, XV. Summary and Conclusion 64 2012a, 2012b). Rev. Mod. Phys., Vol. 88, No. 3, July–September 2016 035009-2 Peter J. Mohr, David B. Newell, and Barry N. Taylor: CODATA recommended values of the fundamental ... To help keep this report to a reasonable length, our data B. Highlights of the CODATA 2014 adjustment review focuses on the new results that became available We summarize here the most significant advances made, or between the 31 December 2010 and 31 December 2014 lack thereof, in our knowledge of the values of the funda- closing dates of the 2010 and 2014 adjustments (in this paper the term “past 4 years” means this time interval); our previous mental constants in the past 4 years and, where appropriate, reports should be consulted for discussions of the older data.
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