REVIEWS OF MODERN PHYSICS, VOLUME 77, JANUARY 2005 CODATA recommended values of the fundamental physical constants: 2002* Peter J. Mohr† and Barry N. Taylor‡ National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8401, USA ͑Published 18 March 2005͒ This paper gives the 2002 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 ͑CODATA͒ for international use. Further, it describes in detail the adjustment of the values of the subset of constants on which the complete 2002 set of recommended values is based. Two noteworthy additions in the 2002 adjustment are recommended values for the bound-state rms charge radii of the proton and deuteron and tests of the exactness of the Josephson and quantum-Hall-effect relations 2 KJ =2e/h and RK =h/e , where KJ and RK are the Josephson and von Klitzing constants, respectively, e is the elementary charge, and h is the Planck constant. The 2002 set replaces the previously recommended 1998 CODATA set. The 2002 adjustment takes into account the data considered in the 1998 adjustment as well as the data that became available between 31 December 1998, the closing date of that adjustment, and 31 December 2002, the closing date of the new adjustment. The differences between the 2002 and 1998 recommended values compared to the uncertainties of the latter are generally not unreasonable. The new CODATA set of recommended values may also be found on the World Wide Web at physics.nist.gov/constants. CONTENTS procedures 6 D. Time variation of the constants 6 E. Outline of paper 7 Glossary 3 I. Introduction 5 II. Special Quantities and Units 7 A. Background 5 A. Speed of light in vacuum c and realization of the B. Uncertainties 5 meter 8 ␮ ⑀ C. Data categorization, selection, and evaluation B. Magnetic constant 0 and electric constant 0 8 C. Electron volt eV, unified atomic mass unit u, and related quantities 8 *This report was prepared by the authors under the auspices D. Josephson effect and Josephson constant KJ 8 of the CODATA Task Group on Fundamental Constants. The E. Quantum Hall effect and von Klitzing constant RK 9 members of the task group are: F. Conventional Josephson and von Klitzing constants F. Cabiati, Istituto Elettrotecnico Nazionale “Galileo Fer- K and R and conventional electric units 9 raris,” Italy J−90 K−90 G. Acceleration of free fall g 10 E. R. Cohen, Science Center, Rockwell International ͑retired͒, United States of America III. Review of Data 10 K. Fujii, National Metrology Institute of Japan, Japan A. Relative atomic masses 10 S. G. Karshenboim, D. I. Mendeleyev All-Russian Research 1. Atomic mass evaluation 11 ͑3 ͒ Institute for Metrology, Russian Federation a. Ar He 11 ͑4 ͒ I. Lindgren, Chalmers University of Technology and Göteborg b. Ar He 12 University, Sweden ͑16 ͒ c. Ar O 12 B. A. Mamyrin, A. F. Ioffe Physical-Technical Institute, Rus- d. A ͑36Ar͒ 13 sian Federation r e. A ͑133Cs͒ 13 W. Martienssen, Johann Wolfgang Goethe-Universität, Ger- r many 2. Observational equations for neutral atoms 13 P. J. Mohr, National Institute of Standards and Technology, 3. Binding energies 13 United States of America 4. Electron and proton relative atomic masses ͑ ͒ ͑ ͒ F. Nez, Laboratoire Kastler-Brossel, France Ar e and Ar p 14 ͑ ͒ B. W. Petley, National Physical Laboratory, United Kingdom a. Ar e 14 T. J. Quinn, Bureau international des poids et mesures ͑ ͒ b. Ar p 14 B. N. Taylor, National Institute of Standards and Technology, ͑ ͒ 5. Neutron relative atomic mass Ar n 14 United States of America B. Hydrogenic transition frequencies and the Rydberg W. Wöger, Physikalisch-Technische Bundesanstalt, Germany constant Rϱ 15 B. M. Wood, National Research Council, Canada Z. Zhang, National Institute of Metrology, People’s Republic 1. Max Planck Institut für Quantenoptik 15 of China 2. Laboratoire Kastler-Brossel and Systèmes †Electronic address: [email protected] de réfèrence Temps Espace 16 ‡Electronic address: [email protected] 3. Other data 17 0034-6861/2005/77͑1͒/1͑107͒/$50.00 1 ©2005 The American Physical Society 2 P. J. Mohr and B. N. Taylor: CODATA values of the fundamental constants 2002 ͑ ͒ 4. Nuclear radii 17 J. Molar volume of silicon Vm Si 34 ͑ ͒ C. Magnetic moments and g-factors 18 1. NMIJ result for Vm Si 35 ͑ ͒ 1. Electron magnetic moment anomaly ae 18 2. PTB result for Vm Si 36 ͑ ͒ a. University of Washington 18 3. WGAC value of Vm Si 36 b. Theory 18 K. Quotient of Planck constant and particle mass 2. Muon magnetic moment anomaly a␮ 19 h/m͑X͒ 36 a. Brookhaven 20 1. Quotient h/mn 37 b. Theory 21 2. Quotient h/m͑133Cs͒ 37 ͑ ͒ 3. Electron g-factor in hydrogenic ions ge X 21 L. Hyperfine structure 39 ͑12 5+͒ a. ge C 21 M. Fine structure 39 ͑16 7+͒ b. ge O 22 N. Molar gas constant R 40 ͑12 5+͒ ͑16 7+͒ c. Relations between ge C and ge O 23 1. NIST: Speed of sound in argon 40 4. Magnetic moment ratios 23 2. NPL: Speed of sound in argon 40 a. Electron to proton magnetic moment ratio 3. Other values 41 ␮ ␮ e / p 23 O. Boltzmann constant k 41 b. Deuteron to electron magnetic moment ratio P. Stefan-Boltzmann constant ␴ 42 ␮ ␮ d / e 23 Q. Newtonian constant of gravitation G 42 c. Electron to shielded proton magnetic R. X-ray units 47 ␮ ␮Ј moment ratio e / p 23 S. Other quantities 48 d. Shielded helion to shielded proton magnetic IV. Analysis of Data 48 ␮Ј ␮Ј moment ratio h / p 24 A. Comparison of data 48 e. Neutron to shielded proton magnetic B. Multivariate analysis of data 55 ␮ ␮Ј moment ratio n / p 24 V. The 2002 CODATA Recommended Values 61 ␮ ␮ 5. Muon-proton magnetic moment ratio ␮/ p A. Calculation details 61 and muon-electron mass ratio m␮/me from B. Tables of values 61 muonium 24 VI. Summary and Conclusion 70 a. LAMPF 1982 24 A. Comparison of 2002 and 1998 CODATA b. LAMPF 1999 25 recommended values 70 c. Combined LAMPF results 25 B. Some implications for physics and metrology of the d. Other values 25 2002 CODATA recommended values and D. Shielded gyromagnetic ratios ␥Ј 26 adjustment 74 1. Proton p 27 C. Outlook and suggestions for future work 76 a. NIST: Low field 27 Acknowledgments 77 b. NIM: Low field and high field 27 Appendix A: Theory Relevant to the Rydberg Constant 77 c. NPL: High field 27 1. Dirac eigenvalue 77 2. Helion h 27 2. Relativistic recoil 78 a. KRISS/VNIIM: Low field 27 3. Nuclear polarization 78 b. VNIIM: Low field 28 4. Self-energy 78 E. Josephson constant KJ 28 5. Vacuum polarization 79 1. NML: Hg electrometer 29 6. Two-photon corrections 80 2. PTB: Capacitor voltage balance 29 7. Three-photon corrections 81 F. von Klitzing constant RK 29 8. Finite nuclear size 82 1. NIST: Calculable capacitor 29 9. Nuclear-size correction to self-energy and vacuum 2. NML: Calculable capacitor 29 polarization 83 3. NPL: Calculable capacitor 30 10. Radiative-recoil corrections 83 4. NIM: Calculable capacitor 30 11. Nucleus self-energy 83 5. BNM: Calculable capacitor 30 12. Total energy and uncertainty 83 6. Other values 31 13. Transition frequencies between levels with n=2 84 2 G. Product KJRK 31 Appendix B: Theory of Electron Magnetic Moment Anomaly 84 1. NPL: Watt balance 31 Appendix C: Theory of Muon Magnetic Moment Anomaly 86 2. NIST: Watt balance 32 Appendix D: Theory of Bound-State g-Factors 89 3. Other values 32 1. Bound electron in 12C5+ and in 16O7+ 89 H. Faraday constant F 32 2. Ratio of bound-particle to free-particle g-factors 93 1. NIST: Ag coulometer 32 3. Comparison of theory and experiment 93 2. Other values 33 Appendix E: Theory of Muonium Ground-State Hyperfine ͕ ͖ I. 220 lattice spacing of silicon d220 33 Splitting 94 1. d220 difference measurements 33 Appendix F: Test of the Josephson and Quantum Hall Effect 2. X-ray/optical interferometer measurements Relations 96 ͑ ͒ of d220 X 33 References 99 Rev. Mod. Phys., Vol. 77, No. 1, January 2005 P. J. Mohr and B. N. Taylor: CODATA values of the fundamental constants 2002 3 GLOSSARY GSI Gesellschaft für Schweironenforschung, AMDC Atomic Mass Data Center, Centre de Spec- Darmstadt, Germany trométrie Nucléaire et de Spectrométrie de Harvard Harvard University, Cambridge, Massachu- setts, USA Masse ͑CSNSM͒, Orsay, France h helion ͑nucleus of 3He͒ A ͑X͒ relative atomic mass of X: A ͑X͒ r r h Planck constant; ប=h/2␲ =m͑X͒/m u HUST Huazhong University of Science and Tech- A90 conventional unit of electric current: A90 nology, Wuhan, People’s Republic of China =V90/Ω90 ILL Institut Max von Laue-Paul Langevin, ͑ ␣ ͒ Å* Ångström-star: λ WK 1 =0.209 010 0 Å* Grenoble, France ae electron magnetic moment anomaly: ae IMGC Istituto di Metrologia “G. Colonnetti,” ͉͑ ͉ ͒ Torino, Italy = ge −2 /2 IUPAC International Union of Pure and Applied a␮ muon magnetic moment anomaly: a␮=͉͑g␮͉ Chemistry −2͒/2 IRMM Institute for Reference Materials and Mea- BIPM International Bureau of Weights and Mea- surements, Geel, Belgium sures, Sèvres, France KRISS Korea Research Institute of Standards and BNL Brookhaven National Laboratory, Upton, Science, Taedok Science Town, Republic of New York, USA Korea BNM Bureau national de métrologie, France KR/VN KRISS-VNIIM collaboration CCM Consultative Committee for Mass and Re- KJ Josephson constant: KJ =2e/h lated Quantities of the CIPM KJ−90 conventional value of the Josephson con- CERN European Laboratory for Particle Physics, −1 stant KJ : KJ−90=483 597.9 GHz V Geneva, Switzerland k Boltzmann constant: k=R/NA CIPM International Committee for Weights and LAMPF Clinton P.