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CODATA Recommended Values of the Fundamental Physical Constants: 2010∗

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CODATA Recommended Values of the Fundamental Physical Constants: 2010∗ CODATA Recommended Values of the Fundamental Physical Constants: 2010∗ Peter J. Mohr†, Barry N. Taylor‡, and David B. Newell§, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8420, USA (Dated: March 15, 2012) This paper gives the 2010 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. The 2010 adjustment takes into account the data considered in the 2006 adjustment as well as the data that became available from 1 January 2007, after the closing date of that adjustment, until 31 December 2010, the closing date of the new adjustment. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2010 set replaces the previously recommended 2006 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants. Contents D. Cyclotron resonance measurement of the electron relative atomic mass 8 I. Introduction 2 A. Background 2 IV. Atomic transition frequencies 8 B. Brief overview of CODATA 2010 adjustment 3 A. Hydrogen and deuterium transition frequencies, the Rydberg constant R∞, and the proton and deuteron 1. Fine-structure constant α 3 charge radii rp,rd 8 2. Planck constant h 3 1. Theory of hydrogen and deuterium energy levels 8 3. Molar gas constant R 4 2. Experiments on hydrogen and deuterium 16 4. Newtonian constant of gravitation G 4 3. Nuclear radii 17 5. Rydberg constant R∞ and proton radius rp 4 B. Antiprotonic helium transition frequencies and C. Outline of the paper 4 Ar(e) 19 1. Theory relevant to antiprotonic helium 19 II. Special quantities and units 4 2. Experiments on antiprotonic helium 20 3. Inferred value of Ar(e) from antiprotonic helium 20 III. Relative atomic masses 5 C. Hyperfine structure and fine structure 20 A. Relative atomic masses of atoms 5 B. Relative atomic masses of ions and nuclei 6 V. Magnetic moment anomalies and g-factors 22 C. Relative atomic masses of the proton, triton, and A. Electron magnetic moment anomaly ae and the helion 7 fine-structure constant α 22 1. Theory of ae 22 2. Measurements of ae 24 3. Values of α inferred from ae 24 ∗This report was prepared by the authors under the auspices of the B. Muon magnetic moment anomaly aµ 24 CODATA Task Group on Fundamental Constants. The members 1. Theory of aµ 24 of the task group are: 2. Measurement of aµ: Brookhaven 25 F. Cabiati, Istituto Nazionale di Ricerca Metrologica, Italy C. Bound electron g-factor in 12C5+ and in 16O7+ J. Fischer, Physikalisch-Technische Bundesanstalt, Germany and Ar(e) 26 J. Flowers, National Physical Laboratory, United Kingdom 1. Theory of the bound electron g-factor 26 K. Fujii, National Metrology Institute of Japan, Japan 2. Measurements of g (12C5+) and g (16O7+) 29 S. G. Karshenboim, Pulkovo Observatory, Russian Federation e e P. J. Mohr, National Institute of Standards and Technology, United VI. Magnetic moment ratios and the muon-electron States of America mass ratio 30 D. B. Newell, National Institute of Standards and Technology, United States of America A. Magnetic moment ratios 30 F. Nez, Laboratoire Kastler-Brossel, France 1. Theoretical ratios of atomic bound-particle to K. Pachucki, University of Warsaw, Poland free-particle g-factors 30 T. J. Quinn, Bureau international des poids et mesures 2. Bound helion to free helion magnetic moment ′ B. N. Taylor, National Institute of Standards and Technology, ratio µh/µh 31 United States of America 3. Ratio measurements 31 B. M. Wood, National Research Council, Canada B. Muonium transition frequencies, the muon-proton Z. Zhang, National Institute of Metrology, China (People’s Repub- magnetic moment ratio µµ/µp, and muon-electron lic of) mass ratio mµ/me 32 1. Theory of the muonium ground-state hyperfine †Electronic address: [email protected] splitting 32 ‡Electronic address: [email protected] 2. Measurements of muonium transition frequencies § Electronic address: [email protected] and values of µµ/µp and mµ/me 33 2 VII. Quotient of Planck constant and particle mass Nomenclature 86 h/m(X) and α 34 A. Quotient h/m(133Cs) 34 References 88 B. Quotient h/m(87Rb) 34 C. Other data 35 VIII. Electrical measurements 35 A. Types of electrical quantities 36 B. Electrical data 36 2 1. KJ RK and h: NPL watt balance 37 2 2. KJ RK and h: METAS watt balance 37 3. Inferred value of KJ 38 C. Josephson and quantum Hall effect relations 38 IX. Measurements involving silicon crystals 39 A. Measurements of d220(X) of natural silicon 39 I. INTRODUCTION B. d220 difference measurements of natural silicon crystals 40 A. Background C. Gamma-ray determination of the neutron relative atomic mass Ar(n) 40 D. Historic X-ray units 40 This article reports work carried out under the aus- E. Other data involving natural silicon crystals 41 pices of the Committee on Data for Science and Tech- F. Determination of NA with enriched silicon 41 nology (CODATA) Task Group on Fundamental Con- 1 X. Thermal physical quantities 42 stants. It describes in detail the CODATA 2010 least- A. Acoustic gas thermometry 42 squares adjustment of the values of the constants, for 1. NPL 1979 and NIST 1988 values of R 43 which the closing date for new data was 31 December 2. LNE 2009 and 2011 values of R 43 2010. Equally important, it gives the 2010 self-consistent 3. NPL 2010 value of R 43 set of over 300 CODATA recommended values of the fun- 4. INRIM 2010 value of R 44 B. Boltzmann constant k and quotient k/h 44 damental physical constants based on the 2010 adjust- 1. NIST 2007 value of k 44 ment. The 2010 set, which replaces its immediate pre- 2. NIST 2011 value of k/h 45 decessor resulting from the CODATA 2006 adjustment C. Other data 45 (Mohr et al., 2008), first became available on 2 June 2011 D. Stefan-Boltzmann constant σ 45 at physics.nist.gov/constants, a Web site of the NIST Fundamental Constants Data Center (FCDC). XI. Newtonian constant of gravitation G 46 A. Updated values 46 The World Wide Web has engendered a sea change in 1. National Institute of Standards and Technology expectations regarding the availability of timely informa- and University of Virginia 46 tion. Further, in recent years new data that influence our 2. Los Alamos National Laboratory 47 knowledge of the values of the constants seem to appear B. New values 47 1. Huazhong University of Science and Technology 47 almost continuously. As a consequence, the Task Group 2. JILA 48 decided at the time of the 1998 CODATA adjustment to take advantage of the extensive computerization that XII. Electroweak quantities 49 had been incorporated in that effort to issue a new set of recommended values every 4 years; in the era of the XIII. Analysis of Data 49 A. Comparison of data through inferred values of α, h, Web, the 12-13 years between the first CODATA set of k and Ar(e) 53 1973 (Cohen and Taylor, 1973) and the second CODATA B. Multivariate analysis of data 55 set of 1986 (Cohen and Taylor, 1987), and between this 1. Data related to the Newtonian constant of second set and the third set of 1998 (Mohr and Taylor, gravitation G 59 2000), could no longer be tolerated. Thus, if the 1998 set 2. Data related to all other constants 60 3. Test of the Josephson and quantum Hall effect is counted as the first of the new 4-year cycle, the 2010 relations 62 set is the 4th of that cycle. Throughout this article we refer to the detailed re- XIV. The 2010 CODATA recommended values 64 ports describing the 1998, 2002, and 2006 adjustments A. Calculational details 64 B. Tables of values 65 as CODATA-98, CODATA-02, and CODATA-06, respec- tively (Mohr and Taylor, 2000, 2005; Mohr et al., 2008). XV. Summary and Conclusion 82 To keep the paper to a reasonable length, our data re- A. Comparison of 2010 and 2006 CODATA view focuses on the new results that became available be- recommended values 82 B. Some implications of the 2010 CODATA recommended values and adjustment for metrology and physics 83 C. Suggestions for future work 84 1 CODATA was established in 1966 as an interdisciplinary com- mittee of the International Council of Science. The Task Group XVI. Acknowledgments 85 was founded 3 years later. 3 tween the 31 December 2006 and 31 December 2010 clos- B. Brief overview of CODATA 2010 adjustment ing dates of the 2006 and 2010 adjustments; the reader should consult these past reports for detailed discussions The 2010 set of recommended values is the result of of the older data. These past reports should also be applying the same procedures as in previous adjustments consulted for discussions of motivation, philosophy, the and is based on a least-squares adjustment with, in this treatment of numerical calculations and uncertainties, case, N = 160 items of input data, M = 83 variables etc. A rather complete list of acronyms and symbols called adjusted constants, and ν = N M = 77 degrees may be found in the nomenclature section near the end of freedom. The statistic “chi-squared”− is χ2 = 59.1 with of the paper. probability p(χ2 ν)=0.94 and Birge ratio R =0.88. | B A significant number of new results became avail- To further achieve a reduction in the length of this able for consideration, both experimental and theoreti- report compared to the lengths of its three most recent cal, from 1 January 2007, after the closing date of the predecessors, it has been decided to omit extensive de- 2006 adjustment, to 31 December 2010, the closing date scriptions of new experiments and calculations and to of the current adjustment.
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