2016年国际物理学常量推荐使用值（一）.pdf
CODATA Recommended Values of the Fundamental Physical Constants:2014*Peter J.Mohr,David B.Newell,and Barry N.Taylor Citation:Journal of Physical and Chemical Reference Data 45,043102(2016);doi:10.1063/1.4954402 View online:http:/dx.doi.org/10.1063/1.4954402 View Table of Contents:http:/scitation.aip.org/content/aip/journal/jpcrd/45/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in CODATA Recommended Values of the Fundamental Physical Constants:2010a)J.Phys.Chem.Ref.Data 41,043109(2012);10.1063/1.4724320 CODATA recommended values of the fundamental physical constants:2006a)J.Phys.Chem.Ref.Data 37,1187(2008);10.1063/1.2844785 CODATA recommended values of the fundamental constants AIP Conf.Proc.543,3(2000);10.1063/1.1336265 CODATA Recommended Values of the Fundamental Physical Constants:1998 J.Phys.Chem.Ref.Data 28,1713(1999);10.1063/1.556049 The 1986 CODATA Recommended Values of the Fundamental Physical Constants J.Phys.Chem.Ref.Data 17,1795(1988);10.1063/1.555817 Reuse of AIP Publishing content is subject to the terms at:https:/publishing.aip.org/authors/rights-and-permissions.Download to IP:71.191.68.116 On:Sun,27 Nov2016 03:37:44CODATA Recommended Values of the Fundamental PhysicalConstants:2014*Peter J.Mohr,a)David B.Newell,b)and Barry N.Taylorc)National Institute of Standards and Technology,Gaithersburg,Maryland 20899-8420,USA(Received 28 April 2016;accepted 6 September 2016;published online 22 November 2016)This paper gives the 2014 self-consistent set of values of the constants and conversionfactors of physics and chemistry recommended by the Committee on Data for Science andTechnology(CODATA).These values are based on a least-squares adjustment that takesinto account all data available up to 31 December 2014.Details of the data selection andmethodology of the adjustment are described.The recommended values may also be foundathttp:/physics.nist.gov/constants.2016AIPPublishingLLCfortheNationalInstituteofStandards and Technology.http:/dx.doi.org/10.1063/1.4954402CONTENTSI.Introduction.4A.Background.4B.Highlights of the CODATA 2014adjustment.51.Planck constant h,elementary charge e,Boltzmann constant k,Avogadroconstant NA,and the redefinition of theSI.52.Relative atomic mass of the electronAre .53.Proton magnetic moment in units of thenuclear magneton p=N.54.Fine-structure constant.55.Relative atomic masses.66.Newtonian constant of gravitation G.67.Proton radius rpand theory of the muonmagnetic-moment anomaly a.6C.Outline of the paper.6II.Special Quantities and Units.6III.Relative Atomic Masses.7A.Relative atomic masses of atoms.7B.Relative atomic masses of ions and nuclei.7C.Relative atomic mass of the deuteron,triton,and helion.8IV.Atomic Transition Frequencies.10A.Hydrogen and deuterium transitionfrequencies,theRydbergconstantR,andtheproton and deuteron charge radii rp,rd.101.Theory of hydrogen and deuteriumenergy levels.10a.Dirac eigenvalue.10b.Relativistic recoil.10c.Nuclear polarizability.11d.Self energy.11e.Vacuum polarization.11f.Two-photon corrections.12g.Three-photon corrections.13h.Finite nuclear size.13i.Nuclear-size correction to selfenergy and vacuum polarization.13j.Radiative-recoil corrections.14k.Nucleus self energy.14l.Total energy and uncertainty.14m.Transition frequencies betweenlevels with n=2 and the fine-structure constant .142.Experiments on hydrogen and deuterium143.Nuclear radii.15a.Electron scattering.15b.Isotope shift and the deuteron-proton radius difference.16c.Muonic hydrogen.16B.Hyperfine structure and fine structure.17V.Magnetic Moments and g-factors.17A.Electron magnetic-moment anomaly aeandthe fine-structure constant .181.Theory of ae.182.Measurements of ae.19B.Muon magnetic-moment anomaly a.191.Theory of a.192.Measurement of a:Brookhaven.20*This review is being published simultaneously by Reviews of ModernPhysics.ThisreportwaspreparedbytheauthorsundertheauspicesoftheCODATATask Group on Fundamental Constants.The members of the task group areF.Cabiati,Istituto Nazionale di Ricerca Metrologica,Italy;J.Fischer,Physikalisch-Technische Bundesanstalt,Germany;J.Flowers(deceased),National Physical Laboratory,United Kingdom;K.Fujii,National MetrologyInstitute of Japan,Japan;S.G.Karshenboim,Pulkovo Observatory,RussianFederationandMax-Planck-Institutf urQuantenoptik,Germany;E.deMirand es,Bureau international des poids et mesures;P.J.Mohr,National Institute ofStandards and Technology,United States of America;D.B.Newell,NationalInstitute of Standards and Technology,United States of America;F.Nez,Laboratoire Kastler-Brossel,France;K.Pachucki,University of Warsaw,Poland;T.J.Quinn,Bureau international des poids et mesures;C.Thomas,Bureau international des poids et mesures;B.N.Taylor,National Institute ofStandards and Technology,United States of America;B.M.Wood,NationalResearch Council,Canada;and Z.Zhang,National Institute of Metrology,Peoples Republic of China.a)mohrnist.govb)dnewellnist.govc)barry.taylornist.gov0047-2689/2016/45(4)/043102/74/$47.00043102-1J.Phys.Chem.Ref.Data,Vol.45,No.4,2016 Reuse of AIP Publishing content is subject to the terms at:https:/publishing.aip.org/authors/rights-and-permissions.Download to IP:71.191.68.116 On:Sun,27 Nov2016 03:37:443.Comparison of theory and experimentfor a.20C.Proton magnetic moment in nuclearmagnetons p=N.21D.Atomic g-factors in hydrogenic12C and28Siand Are .221.Theory of the bound-electron g-factor.222.Measurements of g(12C5+)andg(28Si13+).24VI.Magnetic-MomentRatiosandtheMuon-Electron Mass Ratio.26A.Theoretical ratios of atomic bound-particleto free-particle g-factors.261.Ratio measurements.27B.Muonium transition frequencies,the muon-proton magnetic-moment ratio=p,andmuon-electron mass ratio m=me.281.Theory of the muonium ground-statehyperfine splitting.282.Measurements of muonium transitionfrequencies and values of=pandm=me.30VII.Quotient of Planck Constant and Particle Massh=m X and.30VIII.Electrical Measurements.31A.NPL watt balance.31B.METAS watt balance.32C.LNE watt balance.32D.NIST watt balance.32E.NRC watt balance.33IX.Measurements Involving Silicon Crystals.34A.Measurements with natural silicon.34B.Determination of NAwith enriched silicon34X.Thermal Physical Quantities.35A.Molar gas constant R,acoustic gasthermometry.351.New values.36a.NIM 2013.36b.NPL 2013.36c.LNE 2015.362.Updated values.37a.Molar mass of argon.37b.Molar mass of helium.37c.Thermal conductivity of argon.37B.Quotient k=h,Johnson noise thermometry.37C.Quotient Ae=R,dielectric-constant gasthermometry.38D.Other data.38E.Stefan-Boltzmann constant .38XI.Newtonian Constant of Gravitation G.39A.Updated values.391.Huazhong University of Science andTechnology.39B.New values.401.International Bureau of Weights andMeasures.402.European Laboratory for Non-LinearSpectroscopy,University of Florence.403.University of California,Irvine.40XII.Electroweak Quantities.41XIII.Analysis of Data.41A.Comparison of data through inferred valuesof,h,and k.41B.Multivariate analysis of data.461.Data related to the Newtonian constantof gravitation G.482.Data related to all other constants.523.Test ofthe Josephson and quantum-Hall-effect relations.55XIV.The 2014 CODATA Recommended Values.56A.Calculational details.56B.Tables of values.57XV.Summary and Conclusion.57A.Comparison of 2014 and 2010 CODATArecommended values.63B.Some implications of the 2014 CODATArecommended values and adjustment formetrology and physics.671.Conventional electrical units.672.Josephson and quantum-Hall effects.673.The new SI.674.Proton radius.675.Muon magnetic-moment anomaly.676.Electron magnetic-moment anomaly,fine-structure constant,and QED.67C.Suggestions for future work.68List of Symbols and Abbreviations.68Acknowledgments.71XVI.References.71List of TablesI.Some exact quantities relevant to the 2014adjustment.7II.Relative atomic masses used in the least-squares adjustment as given in the 2012atomic mass evaluation and the definedvalue for12C.7III.Ionization energies for1H,3H,3He,4He,12C,and28Si.8IV.Relevant values of the Bethe logarithmslnk0n,.11V.Values of the function GSE.11VI.Values of the function G1 VP .12VII.Values of B61used in the 2014adjustment.12VIII.Values of N used in the 2014adjustment.13IX.Values of B60,B60,or B71used in the2014 adjustment.13X.Summaryofmeasuredtransitionfrequencies considered in the present work for thedetermination of the Rydberg constant R.15043102-2MOHR,NEWELL,AND TAYLORJ.Phys.Chem.Ref.Data,Vol.45,No.4,2016 Reuse of AIP Publishing content is subject to the terms at:https:/publishing.aip.org/authors/rights-and-permissions.Download to IP:71.191.68.116 On:Sun,27 Nov2016 03:37:44XI.Theoretical contributions and total valuefor the g-factor of hydrogenic carbon 12based on the 2014 recommended values ofthe constants.22XII.Theoretical contributions and total valuefor the g-factor of hydrogenic silicon 28based on the 2014 recommended values ofthe constants.22XIII.Theoretical values for various bound-particle to free-particle g-factor ratiosrelevant to the 2014 adjustment based onthe 2014 recommended values of theconstants.27XIV.Summary of thermal physical measurementsrelevant to the 2014 adjustment.36XV.Summaryoftheresultsofmeasurementsofthe Newtonian constant of gravitationrelevant to the 2014 adjustment.39XVI.Summary of principal input data for thedetermination of the 2014 recommendedvalue of the Rydberg constant R.42XVII.Correlation coefficients r xi;xj?0:0001oftheinputdatarelatedtoRinTableXVI43XVIII.Summary of principal input data for thedetermination of the 2014 recommendedvalues of the fundamental constants(Rand G excepted).44XIX.Correlation coefficients r xi;xj?0:001 ofthe input data in Table XVIII.46XX.Inferredvaluesofthefine-structureconstant in order of increasing standarduncertainty obtained from the indicatedexperimental data in Table XVIII.46XXI.Inferred values of the Planck constant h inorder of increasing standard uncertaintyobtained from the indicated experimentaldata in Table XVIII.47XXII.Inferred values of the Boltzmann constantk in order of increasing standarduncertainty obtained from the indicatedexperimental data in Table XVIII.48XXIII.Observational equations that express theinput data related to Rin Table XVI asfunctionsoftheadjusted constantsinTableXXV.49XXIV.Observational equations that express theinput data in Table XVIII as functions ofthe adjusted constants in Table XXVI.50XXV.The 28 adjusted constants(variables)usedin the least-squares multivariate analysis ofthe Rydberg-constant data given in TableXVI.52XXVI.Variablesusedintheleast-squaresadjustment of the constants.52XXVII.Summary of values of G used to determinethe 2014 recommended value(see alsoTable XV,Sec.XI).53XXVIII.Summary of the results of some of theleast-squares adjustments used to analyzethe input data given in Tables XVI,XVII,XVIII,and XIX.54XXIX.Summary of the results of some of theleast-squares adjustments used to analyzethe input data related to R.54XXX.Generalized observational equations thatexpress input data B32B38 in TableXVIII as functions of the adjustedconstants in Tables XXV and XXVI withthe additional adjusted constants eJand eKas given in Eqs.(271)and(272).55XXXI.Summary of the results of several least-squares adjustments to investigate therelations KJ=2e=h 1+eJ andRK=h=e2 1+eK.56XXXII.An abbreviated list of the CODATArecommended values of the fundamentalconstants of physics and chemistry basedon the 2014 adjustment.57XXXIII.The CODATA recommendedvalues of thefundamental constants of physics andchemistry based on the 2014 adjustment.58XXXIV.Thevariances,covariances,andcorrelationcoefficients of the values of a selectedgroup of constants based on the 2014CODATA adjustment.63XXXV.Internationally adopted values of variousquantities.63XXXVI.Values of some x-ray-related quantitiesbased on the 2014 CODATA adjustmentof the values of the constants.63XXXVII.The values in SI units of some non-SI unitsbasedonthe2014CODATAadjustmentofthe values of the constants.64XXXVIII.The values of some energy equivalentsderived from the relationsE=mc2=hc=h=kT,and based onthe 2014 CODATA adjustment of thevalues of the constants.65XXXIX.The values of some energy equivalentsderived from the relationsE=mc2=hc=h=kT and based on the2014 CODATA adjustment of the valuesof the constants.65XL.Comparisonofthe2014and2010CODATA recommended values ofa representative group of constants.66List of Figures1.Values of the fine-structure constant withur107inferred from the input data in TableXVIIIinorderofdecreasinguncertaintyfromtoptobottom(see Table XX).47CODATA RECOMMENDED VALUES:2014043102-3J.Phys.Chem.Ref.Data,Vol.45,No.4,2016 Reuse of AIP Publishing content is subject to the terms at:https:/publishing.aip.org/authors/rights-and-permissions.Download to IP:71.191.68.116 On:Sun,27 Nov2016 03:37:442.Comparison of input data B22:2(HarvU-08)andB48(LKB-11)through their inferred values of .473.Values of the Planck constant h with ur106inferred from the input data in Table XVIII and the2014 CODATA recommended value inchronological order from top to bottom(see TableXXI).484.Values of the Planck constant h with ur:Z2+Z43?1+ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1Z2q?2Z5PZ9=;memN+1+ZZ2?memN?2=0:00000008770.for Z=6=0:00000020604.for Z=14,(169)where mNis the mass of the nucleus.Mass ratios,based on thecurrent adjustment values of the constants,are me=m12C6+=0:0000457275.and me=m28Si14+=0:0000196136.see Eqs.(10)and(3).For silicon,we use the interpolatedvalue P14=7:162231.For g2rec,we haveg2rec=Z23memN+=0:00000000006.for Z=6=0:00000000015.for Z=14.(170)Theuncertaintying2recisnegligiblecomparedtothatofg2rad.The nuclear-size correction is given to lowest order in Z2by(Karshenboim,2000)gns=83Z4?RNC?2,(171)where RNis the bound-state nuclear rms charge radius andCis the Compton wavelength of the electron divided by 2.Glazov and Shabaev(2002)have calculated additional cor-rections within perturbation theory.Scaling their results withthe squares of updated values for the nuclear radii RN=2:470322 fm and RN=3:122324 fm from the compilationof Angeli(2004)for12C and28Si respectively yieldsgns=0:0000000004081for12C,gns=0:000000020533for16Si.(172)Tables XI and XII list the contributions discussed above andtotals given byg12C5+=2:00104159018326,g28Si13+=1:995348958117.(173)Forthepurposeoftheleast-squaresadjustment,wewrite thetheoretical expressions for the g-factors asg12C5+=gC+C,g28Si13+=gSi+Si,(174)where the first term on the right-hand side of each expressiongivesthecalculatedvaluealongwithitsfunctionaldependenceon.The second term contains the theoretical uncertainty inthe calculated value,except for the component due to un-certainty in,which is taken into account by the least-squaresalgorithm through the first term.We thus haveC=0:02:61011,(175)Si=0:01:7109.(176)Ineachcase,theuncertaintyisdominatedbyuncalculatedtwo-loop higher-order terms,which are expected to be mainlyproportional to Z5.For the one-loop self energy,approx-imately85%oftheremainderscalesasZ5betweenCandSiseeEqs.(155)and(156).Asaconservativees
