The 1986 adjustment of the fundamental physical constants' prepared by E. Richard Cohen Rockwell International Science Center, Thousand Oaks, California 91360 Barry N. Taylor National Sureau of Standards, Gaithersburg, Maryland 20899 One of the early projects established by CODATA was intended to provide a recommended set of the fun- damental physical constants, which are so important to the analysis and interpretation of experimental data in many scientific disciplines, The first "Recommended Consistent Values of the Fundamental Physical Constants" appeared in 1973 and was subsequently adopted by most international and national bodies in their own recommendations. This process has contributed to improved compatibility of scientific and tech- nical data in all fields of science. CODATA presents here a revised version of these recommendations which takes into account the significant advances in metrology that have occurred since the 1973 analysis. "The 1986 adjustment of the fundamental physical constants" represents a 5-year effort involving experts from the major metrological laboratories of the world. It is hoped that this recommended data set will re- ceive the acceptance of the scientific community which was achieved by its predecessor. CONTENTS 3. Type 3. Direct volt determinations 1129 Glossary 1122 4. Type 4. Faraday constant 1131 I. Introduction 1123 5. Type 5. Gyromagnetic ratio (low field) 1131 A. Background 1123 6. Type 6. Gyromagnetic ratio (high field) 1131 B. Data selection and evaluation procedures 1123 7. Type 7. Silicon lattice spacing 1131 II. Review of the Data 1125 8. Type 8. Molar volume of silicon 1132 A. Auxiliary constants 1126 9. Type 9. Quantized Hall resistance 1132 1 1. The speed of light and the definition of the meter 1126 10. Type 10. Fine-structure constant 1132 2. Proton-electron mass ratio 1126 11. Type 11. Muon magnetic moment 1132 3. Relative atomic masses and mass ratios 1126 12. Type 12. Muonium hyperfine splitting 1133 4. Rydberg constant 1127 C. Secondary stochastic data 1133 5. g factor for the free electron and muon 1127 1. Molar gas constant 1133 6. Electron and nuclear magnetic moment ratios 1127 2. Stefan-Boltzmann constant 1133 7. "As-maintained" volt and ohm standards 1128 3. Newtonian constant of gravitation 1134 8. Acceleration due to gravity 1128 III. Data Analysis 1134 B. Primary stochastic input data 1129 A. Relationships among data of different types 1134 1. Type 1. Direct ohm determinations 1129 B. Multivariate analysis of the data 1136 2. Type 2. Direct ampere determinations 1129 IV. Recommended Values and Discussion 1138 Originally appearing as CODATA Bulletin No. 63, November, 1986 (Pergamon, Oxford/New York). In view of the universal im- portance of the fundamental constants, the editors of Reuietas ofModern Physics believed that it would be of value to the physics com- munity to reprint this official report of the Committee on Data for Science and Technology (CODATA) of the International Council of Scientific Unions, which was previously available only to those with access to the CODATA Bulletins. The reprint contains a few minor modifications to the original that were made for clarity. RMP wishes to thank David R. Lide, President of CODATA, for making the article available to us. A report of the CODATA Task Group on Fundamental Constants; members of the Task Group: T. J. Quinn, Bureau International des Poids et Mesures (Chairman, 1985—) E. R. Cohen, Rockwell International Science Center (United States of America, Chairman, 1969—1985) B. Kramer, Physikalisch-Technische Bundesanstalt (Federal Republic of Germany) B. A. Mamyrin, A. F. Joffe Physical-Technical Institute (Union of Soviet Socialist Republics) M. Morimura, National Research Laboratory of Metrology (Japan) B.N. Oleinik, D. I. Mendeleev All Union Research Institute of Metrology (Union of Soviet Socialist Republics) B. %'. Petley, National Physical Laboratory (United Kingdom) H. Preston-Thomas, National Research Council (Canada) B.N. Taylor, National Bureau of Standards (United States of America) Reviews of Modern Physics, Vol. 59, No. 4, October 1987 Copyright 1987 The American Physical Society t 122 Cohen and Taylor: The 3986 adjustment of the fundamental physical constants A. 1986 recommended values of the fundamental physi- ground (1S) state of hydrogen cal constants 1139 gp 2p p /p B Q factor of the free proton re- B. Comparison with the 1973 adjustment 1145 -ferred to the Bohr magneton Acknowledgments 1146 2pp/pB, g factor of the proton in a References 1146 spherical sample of pure water at 25 C gp(H) effective g factor of the proton in the ground (1S) state of hydrogen GI OSSARY 2@~/(eh/2m„), g factor of the free muon ABIPM The time-dependent BIPM representa- 1971 International G-ravity Standardiza- tion of the an1pere prior to January 1, tion Net ABIPM VBIPM/+BIPM KA The ratio AB,s5/A A69—BI The time-dependent BIPM representa- v The ratio V76 Bt/V (483594 0 tion of the ampere from January 1, GHz/V)/(2e/h); Kv KA/——Kn 1969 to January 1, 1976: &n The ratio ABI85/Q A69—BI +69—BI/+69 —BI KhGIMIP Kharkov State Scientific Research Insti- A76—BI The time-dependent BIPM representa- tute of Metrology, USSR tion of the ampere since January 1, LCIE Laboratoire Central des Industries +76—BI +76—BI/+69—BI Electrique (Central Laboratory for the ABI85 The value of A76 BI on January 1, Electrical Industries), France 1985 number of variables in a least-squares ASMW Amt fur Standardisierung, Messwesen adjustment and Warenpriifung der DDR (Office molar mass of the proton for Standardization, Metrology and number of items of stochastic input Quality Control, German Democratic data in a least-squares adjustment Republic) NBS National Bureau of Standards, US BIPM Bureau International des Poids et Me- NIM Nationa1 Institute of Metrology, Peo- sures (International Bureau of Weights ples' Republic of China and Measures), Sevres, France National Measurement Laboratory CBI85 The BIPM representation of the (CSIRO Division of Applied Physics) coulomb on January 1, 1985: [formerly, National Standards Laborato- CBI85 ABI85 s ry (NSL)], Australia CCE Comite Consultatif d'Electricite (Consul- NPL National Physical Laboratory, UK tative Committee on Electricity of the NPLI National Physical Laboratory, India CIPM) ppm parts per million Organization Europeenne pour la Re- PTB Physikalisch- Technische Bundesantalt cherche Nucleaire (European Organiza- (Federal Physical- Technical Institute), tion for Nuclear Research), Switzerland Federal Republic of Germany Conference Generale des Poids et Me- Residual of an input datum in a least- sures (General Conference of Weights squares adjustment: r; =y; —y; where and Measures) y; is the input datum and y; is the ad- CIPM Comite International des Poids et Me- justed value sures (International Committee of E.B Birge ratio: RB —(g2/v)'~ Weights and Measures of the CGPM) RH Quantized Hall resistance: CODATA Committee on Data for Science and RH —h/e =poc/2a=25812. 8 0; Technology of the International Council poc =Zp =impedance of free space of Scientific Unions (ICSU) =377 Q CSIRO Commonwealth Scientific and Industrial 2 a priori assigned estimate of the vari- Research Organization, Australia ance of the ith stochastic datum 220 crystallographic (220) lattice spacing of Systeme International d'Unites (Interna- silicon at 22.5'C in vacuum tional System of Units), the official 483 594.0 GHz/V name of the system of units based on ELS1 extended least-squares algorithm 1 [Eq. the meter, kilogram, second, ampere, (1.3)] kelvin, mole, and candela ELS2 extended least-squares algorithm 2 [Eq. +BIPM The time-dependent BIPM representa- (1.4)] tion of the volt prior to January 1, ETL Electrotechnical -Laboratory, Japan 1969 ge 2p, /pB, g factor of the free electron +69—BI The time-dependent BIPM representa- gj.(H) effective g factor of the electron in the tion of the volt from January 1, 1969 Rev. Mod. Phys. , Vol. 59, No. 4, October 1987 Cohen and Taylor: The 1986 adjustment of the fundamental physical constants 1123 to January 1, 1976 report (CODATA, 1973) provided the first internationally V76—B The BIPM representation of the volt on adopted set of values for the fundamental constants of the basis of the defined Josephson physics and chemistry. Those values were almost im- frequency-voltage quotient: mediately challenged by several new measurements, and it 2e/h =483 594.0 GHz/V7$ has been clear for at least the past decade that a new ad- All-Union Scientific Research Institute justment was required. However, data that affect our of Metrology (Mendeleev Institute), knowledge of the physical constants are constantly ap- USSR pearing and it is always difficult to establish an optimal Van Swinden Laboratory, The Nether- time at which to make a change in the recommended lands values. January 1, 1986 was established as a cutoff date weight of the ith stochastic datum: for this review, recognizing that any additional changes to w; =1/o; the 1973 values that might be introduced by newer data fine-structure constant: poce /2h that are thereby excluded would almost certainly be much gyromagnetic ratio of the free proton: less than the changes already implied by the data that pp cop /B 2pp/A were available prior to that cutoff date. Vp effective gyromagneticequi/2mratio of the pro- During the past five years the present authors, with the ton in pure water (spherical sample at guidance of the other members of the Task Group, have 25 'C): y ~ =co~/B reviewed and analyzed a wealth of material. This report PB Bohr magneton: eA/2m, summarizes that effort and gives the new set of "best" PN nuclear magneton: ~ values derived from the 1986 adjustment. This review is Pp effective magnetic moment of the pro- similar in concept to its predecessors (Taylor, Parker, and ton in pure water (spherical sample at Langenberg, 1969; Cohen and Taylor, 1973).