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CODATA Recommended Values of the Fundamental Physical Constants: 2010Ã Peter J. Mohr, a) Barry N. Taylor, b) and David B. Newell c) National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8420, USA (Received 21 March 2012; accepted 17 May 2012; published online 28 December 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 Decem- ber 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. Ó 2012 by the U.S. Secretary of Commerce on behalf of the United States. All rights reserved. [http://dx.doi.org/10.1063/1.4724320] CONTENTS 3.4. Cyclotron resonance measurement of the electron relative atomic mass . 9 1. Introduction ............................. 4 4. Atomic Transition Frequencies .............. 9 1.1. Background . 4 4.1. Hydrogen and deuterium transition 1.2. Brief overview of CODATA 2010 adjustment 5 frequencies, the Rydberg constant R∞, and the 1.2.1. Fine-structure constant a............ 5 proton and deuteron charge radii rp, rd .... 9 1.2.2. Planck constant h................... 5 4.1.1. Theory of hydrogen and deuterium 1.2.3. Molar gas constant R ............... 5 energy levels . 9 1.2.4. Newtonian constant of gravitation G 5 4.1.1.1. Dirac eigenvalue. 10 1.2.5. Rydberg constant R∞ and proton radius 4.1.1.2. Relativistic recoil . 10 rp .................................. 5 4.1.1.3. Nuclear polarizability . 10 1.3. Outline of the paper . 5 4.1.1.4. Self energy . 11 2. Special Quantities and Units ................ 6 4.1.1.5. Vacuum polarization. 12 3. Relative Atomic Masses.................... 6 4.1.1.6. Two-photon corrections . 13 3.1. Relative atomic masses of atoms. 7 4.1.1.7. Three-photon corrections. 15 3.2. Relative atomic masses of ions and nuclei. 8 4.1.1.8. Finite nuclear size . 15 3.3. Relative atomic masses of the proton, triton, 4.1.1.9. Nuclear-size correction to and helion. 8 self energy and vacuum polarization. 16 Ã This report was prepared by the authors under the auspices of the CODATA 4.1.1.10. Radiative-recoil corrections 16 Task Group on Fundamental Constants. The members of the task group are F. 4.1.1.11. Nucleus self energy. 16 Cabiati, Istituto Nazionale di Ricerca Metrologica, Italy; J. Fischer, Physi- kalisch-Technische Bundesanstalt, Germany; J. Flowers, National Physical 4.1.1.12. Total energy and Laboratory, United Kingdom; K. Fujii, National Metrology Institute of Japan, uncertainty . 16 Japan; S. G. Karshenboim, Pulkovo Observatory, Russian Federation; P. J. 4.1.1.13. Transition frequencies Mohr, National Institute of Standards and Technology, United States of between levels with n ¼ 2 America; D. B. Newell, National Institute of Standards and Technology, United States of America; F. Nez, Laboratoire Kastler-Brossel, France; K. and the fine-structure Pachucki, University of Warsaw, Poland; T. J. Quinn, Bureau international des constant a................ 17 poids et mesures; B. N. Taylor, National Institute of Standards and Technol- 4.1.1.14. Isotope shift and the ogy, United States of America; B. M. Wood, National Research Council, deuteron-proton radius Canada; and Z. Zhang, National Institute of Metrology, People’s Republic of China. This review is being published simultaneously by Reviews of Modern difference . 17 Physics; see Rev. Mod. Phys. 84, 1527 (2012). 4.1.2. Experiments on hydrogen and a)[email protected] b) deuterium . 18 [email protected] 4.1.3. Nuclear radii . 18 c)[email protected] Ó 2012 by the U.S. Secretary of Commerce on behalf of the United States. All 4.1.3.1. Electron scattering . 19 rights reserved 4.1.3.2. Muonic hydrogen . 19 0047-2689/2012/41(4)/043109/84/$47.00 043109-1 J. Phys. Chem. Ref. Data, Vol. 41, No. 4, 2012 Downloaded 31 Dec 2012 to 129.6.13.245. Redistribution subject to AIP license or copyright; see http://jpcrd.aip.org/about/rights_and_permissions 043109-2 MOHR, TAYLOR, AND NEWELL 4.2. Antiprotonic helium transition frequencies 9.3. Gamma-ray determination of the neutron and Ar(e)................................. 20 relative atomic mass Ar(n)................ 40 4.2.1. Theory relevant to antiprotonic helium 20 9.4. Historic x-ray units . 41 4.2.2. Experiments on antiprotonic helium . 21 9.5. Other data involving natural silicon crystals 41 4.2.3. Inferred value of Ar(e) from 9.6. Determination of NA with enriched silicon 42 antiprotonic helium . 22 10. Thermal Physical Quantities ............... 42 4.3. Hyperfine structure and fine structure . 22 10.1. Acoustic gas thermometry . 43 5. Magnetic-Moment Anomalies and g-Factors ... 23 10.1.1. NPL 1979 and NIST 1988 values of R 43 5.1. Electron magnetic-moment anomaly ae and 10.1.2. LNE 2009 and 2011 values of R ... 43 the fine-structure constant a .............. 23 10.1.3. NPL 2010 value of R .............. 44 5.1.1. Theory of ae ....................... 23 10.1.4. INRIM 2010 value of R ........... 44 5.1.2. Measurements of ae ................ 25 10.2. Boltzmann constant k and quotient k=h .. 44 5.1.2.1. University of Washington . 25 10.2.1. NIST 2007 value of k ............. 44 5.1.2.2. Harvard University . 25 10.2.2. NIST 2011 value of k=h ........... 45 5.1.3. Values of a inferred from ae ........ 25 10.3. Other data . 45 5.2. Muon magnetic-moment anomaly am...... 25 10.4. Stefan-Boltzmann constant s ............ 46 5.2.1. Theory of am ....................... 25 11. Newtonian Constant of Gravitation G ........ 46 5.2.2. Measurement of am: Brookhaven. 26 11.1. Updated values. 47 5.3. Bound-electron g-factor in 12C5þ and in 11.1.1. National Institute of Standards and 16 7þ Technology and University of O and Ar(e).......................... 27 5.3.1. Theory of the bound electron g-factor 27 Virginia. 47 12 5þ 11.1.2. Los Alamos National Laboratory . 47 5.3.2. Measurements of geð C Þ and 16 7þ 11.2. New values . 47 geð O Þ .......................... 30 11.2.1. Huazhong University of Science and 6. Magnetic-moment Ratios and the Muon-electron Technology . 47 Mass Ratio .............................. 30 11.2.2. JILA. 48 6.1. Magnetic-moment ratios . 31 12. Electroweak Quantities ................... 48 6.1.1. Theoretical ratios of atomic bound- 13. Analysis of Data......................... 48 particle to free-particle g-factors . 31 13.1. Comparison of data through inferred values 6.1.2. Bound helion to free helion magnetic- of a, h, k, and A (e)..................... 48 0= r moment ratio mh mh ................ 32 13.2. Multivariate analysis of data. 52 6.1.3. Ratio measurements . 32 13.2.1. Data related to the Newtonian 6.2. Muonium transition frequencies, the muon- constant of gravitation G .......... 55 = proton magnetic-moment ratio mm mp, and 13.2.2. Data related to all other constants. 55 = muon-electron mass ratio mm me.......... 32 13.2.3. Test of the Josephson and quantum- 6.2.1. Theory of the muonium ground-state Hall-effect relations . 58 hyperfine splitting . 32 14. The 2010 CODATA Recommended Values ... 61 6.2.2. Measurements of muonium transition 14.1. Calculational details. 61 = frequencies and values of mm mp and 14.2. Tables of values. 64 mm=me ............................. 34 15. Summary and Conclusion ................. 66 7. Quotient of Planck Constant and Particle Mass 15.1. Comparison of 2010 and 2006 CODATA h=m(X) and a ............................ 35 recommended values . 67 7.1. Quotient h=mð133CsÞ ..................... 35 15.2. Some implications of the 2010 CODATA 7.2. Quotient h=mð87RbÞ ...................... 35 recommended values and adjustment for 7.3. Other data. 36 metrology and physics. 74 8. Electrical Measurements ................... 36 15.3. Suggestions for future work . 77 8.1. Types of electrical quantities . 36 List of Symbols and Abbreviations .......... 78 8.2. Electrical data. 37 Acknowledgments ....................... 80 2 16. References ............................. 80 8.2.1. Kj RK and h: NPL watt balance. 37 2 8.2.2. Kj RK and h: METAS watt balance . 38 8.2.3. Inferred value of KJ ................ 38 8.3. Josephson and quantum-Hall-effect relations 38 9. Measurements Involving Silicon Crystals ...... 39 List of Tables 9.1. Measurements of d220ðÞX of natural silicon 40 9.2. d220 difference measurements of natural 1. Some exact quantities relevant to the 2010 silicon crystals . 40 adjustment. 6 J. Phys. Chem. Ref. Data, Vol. 41, No. 4, 2012 Downloaded 31 Dec 2012 to 129.6.13.245. Redistribution subject to AIP license or copyright; see http://jpcrd.aip.org/about/rights_and_permissions CODATA RECOMMENDED VALUES: 2010 043109-3 2. Values of the relative atomic masses of the neutron 28. Inferred values of the electron relative atomic and various atoms as given in the 2003 atomic mass Ar(e).................................... 59 mass evaluation. 7 29. Summary of the results of several least-squares 3. Values of the relative atomic masses of various adjustments to investigate the relations 2 atoms that have become available since the 2003 KJ ¼ (2e=h)(1 þ J) and RK ¼ (h=e )(1 þ K).
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  • Arxiv:1707.07258V4 [Hep-Ph] 30 Mar 2020

    Arxiv:1707.07258V4 [Hep-Ph] 30 Mar 2020

    I. INTRODCUTION The existence of dark matter is overwhelmingly supported by numerous cosmological and astrophysical observations on a wide range of scales. However, the nature of dark matter has not been revealed for almost a century except for its gravitational interactions. The identification of the nature of dark matter is one of the most important challenges of modern particle physics (see [1{3] for review). Among various candidates for dark matter, the weakly interacting massive particles (WIMPs) are the most extensively studied category of dark matter. The WIMPs couple to the standard model particles via interactions similar in strength to the weak nuclear force. Through the weak interaction, the WIMPs are thermally produced in the early uni- verse, and the relic density is set as they freeze out from the thermal bath [4]. The WIMPs are particularly attractive since the dark matter density does not depend on the details of the initial condition of the universe. The WIMPs are also highly motivated as they are interrelated to physics beyond the standard model such as supersymmetry (see e.g. [5]). The ambient WIMPs can be directly detected by searching for its scattering with the atomic nuclei [6]. Given a circular speed at around the Sun of 239 ± 5 km/s [7], the WIMPs recoil the nuclei elastically with a typical momentum transfer of qA ∼ 100 MeV for the target 1 nucleus mass of mN ∼ 100 GeV. The recoil signatures are detected through ionization, scintillation, and the production of heat in the detectors (see [8{10] for review). To date, for example, liquid xenon detectors such as LUX [11], PandaX-II [12], and XENON1T [13] have put stringent exclusion limits on the spin-independent WIMP-nucleon recoil cross section.