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CODATA Recommended Values of the Fundamental Physical Constants: 2010a)
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10.1063/1.4724320
/content/aip/journal/jpcrd/41/4/10.1063/1.4724320
http://aip.metastore.ingenta.com/content/aip/journal/jpcrd/41/4/10.1063/1.4724320

Figures

Image of FIG. 1.
FIG. 1.

Values of the fine-structure constant α with implied by the input data in Table 20, in order of decreasing uncertainty from top to bottom (see Table 25).

Image of FIG. 2.
FIG. 2.

Values of the fine-structure constant α with implied by the input data in Table 20 and the 2006 and 2010 CODATA recommended values in chronological order from top to bottom (see Table 25).

Image of FIG. 3.
FIG. 3.

Values of the Planck constant h with implied by the input data in Table 20 and the 2006 and 2010 CODATA recommended values in chronological order from top to bottom (see Table 26).

Image of FIG. 4.
FIG. 4.

Values of the Boltzmann constant k implied by the input data in Table 20 and the 2006 and 2010 CODATA recommended values in chronological order from top to bottom (see Table 27). AGT: acoustic gas thermometry; RIGT: refractive index gas thermometry; JNT: Johnson noise thermometry.

Image of FIG. 5.
FIG. 5.

Values of the electron relative atomic mass implied by the input data in Tables 20 and 22 and the 2006 and 2010 CODATA recommended values in chronological order from top to bottom (see Table 28).

Image of FIG. 6.
FIG. 6.

Values of the Newtonian constant of gravitation G in Table 24 and the 2006 and 2010 CODATA recommended values in chronological order from top to bottom.

Image of FIG. 7.
FIG. 7.

Comparison of the five individual values of obtained from the five values of R K, data items B35.1–B35.5, and the combined value (open circle) from adjustment (ii) given in Table 29. The applicable observational equation in Table 39 is .

Image of FIG. 8.
FIG. 8.

Comparison of the three individual values of obtained from the three low-field gyromagnetic ratios, data items B32.1, B32.2, and B33, and the combined value (open circle) from adjustment (iii) given in Table 29. The applicable observational equations in Table 39 are and . Because of the form of these equations, the value of when is identical to the value of when , hence the label at the bottom of the figure.

Tables

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TABLE 1.

Some exact quantities relevant to the 2010 adjustment.

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TABLE 2.

Values of the relative atomic masses of the neutron and various atoms as given in the 2003 atomic mass evaluation together with the defined value for .

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TABLE 3.

Values of the relative atomic masses of various atoms that have become available since the 2003 atomic mass evaluation.

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TABLE 4.

The variances, covariances, and correlation coefficients of the University of Washington values of the relative atomic masses of deuterium, helium 4, and oxygen 16. The numbers in bold above the main diagonal are 1020 times the numerical values of the covariances; the numbers in bold on the main diagonal are 1020 times the numerical values of the variances; and the numbers in italics below the main diagonal are the correlation coefficients.

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TABLE 5.

Relevant values of the Bethe logarithms .

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TABLE 6.

Values of the function .

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TABLE 7.

Data from Jentschura et al. (2005) and the deduced values of for n = 12.

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TABLE 8.

Values of the function . (The minus signs on the zeros in the last two columns indicate that the values are nonzero negative numbers smaller than the digits shown.)

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TABLE 9.

Values of B 61 used in the 2010 adjustment.

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TABLE 10.

Values of B 60, , or used in the 2010 adjustment.

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TABLE 11.

Summary of measured transition frequencies ⟨ considered in the present work for the determination of the Rydberg constant R (H is hydrogen and D is deuterium).

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TABLE 12.

Summary of data related to the determination of from measurements of antiprotonic helium. The uncertainties of the 15 calculated values are the root sum square (rss) of the following 15 pairs of uncertainty components in MHz, where the first component reflects the possible size of uncalculated terms of order and higher, and the second component reflects the uncertainty of the numerical calculations: (0.8, 0.2); (1.0, 0.3); (1.1, 0.3); (1.1, 0.3); (1.1, 0.4); (1.0, 0.8); (1.8, 0.4); (1.6, 0.3); (2.1, 0.3); (0.9, 0.1); (1.1, 0.2); (1.1, 0.4); (1.1, 0.3); (1.8, 0.3); (2.2, 0.2).

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TABLE 13.

Theoretical contributions and total for the g -factor of the electron in hydrogenic carbon 12 based on the 2010 recommended values of the constants.

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TABLE 14.

Theoretical contributions and total for the g -factor of the electron in hydrogenic oxygen 16 based on the 2010 recommended values of the constants.

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TABLE 15.

Theoretical values for various bound-particle to free-particle g -factor ratios relevant to the 2010 adjustment based on the 2010 recommended values of the constants.

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TABLE 16.

Summary of thermal physical measurements relevant to the 2010 adjustment (see text for details). AGT: acoustisc gas thermometry; RIGT: refractive index gas thermometry; JNT: Johnson noise thermometry; cylindrical, spherical, quasispherical: shape of resonator used; JE and QHE: Josephson effect voltage and quantum-Hall-effect resistance standards.

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TABLE 17.

Summary of the results of measurements of the Newtonian constant of gravitation G relevant to the 2010 adjustment.

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TABLE 18.

Summary of principal input data for the determination of the 2010 recommended value of the Rydberg constant R .

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TABLE 19.

Correlation coefficients of the input data related to R in Table 18. For simplicity, the two items of data to which a particular correlation coefficient corresponds are identified by their item numbers in Table 18.

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TABLE 20.

Summary of principal input data for the determination of the 2010 recommended values of the fundamental constants (R and G excepted).

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TABLE 21.

Non-negligible correlation coefficients of the input data in Table 20. For simplicity, the two items of data to which a particular correlation coefficient corresponds are identified by their item numbers in Table 20.

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TABLE 22.

Summary of principal input data for the determination of the relative atomic mass of the electron from antiprotonic helium transitions. The numbers in parentheses denote the transition .

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TABLE 23.

Non-negligible correlation coefficients of the input data in Table 22. For simplicity, the two items of data to which a particular correlation coefficient corresponds are identified by their item numbers in Table 22.

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TABLE 24.

Summary of values of G used to determine the 2010 recommended value (see also Table 17, Sec. XI).

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TABLE 25.

Inferred values of the fine-structure constant α in order of increasing standard uncertainty obtained from the indicated experimental data in Table 20.

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TABLE 26.

Inferred values of the Planck constant h in order of increasing standard uncertainty obtained from the indicated experimental data in Table 20.

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TABLE 27.

Inferred values of the Boltzmann constant k in order of increasing standard uncertainty obtained from the indicated experimental data in Table 20.

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TABLE 28.

Inferred values of the electron relative atomic mass in order of increasing standard uncertainty obtained from the indicated experimental data in Tables 20 and 22.

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TABLE 29.

Summary of the results of several least-squares adjustments to investigate the relations and . See the text for an explanation and discussion of each adjustment, but in brief, adjustment (i) uses all the data, (ii) assumes (that is, ) and obtains from the five measured values of R K, (iii) is based on the same assumption and obtains from the two values of the proton gyromagnetic ratio and one value of the helion gyromagnetic ratio, (iv) is (iii) but assumes (that is, ) and obtains in place of , (v)–(vii) are based on the same assumption and obtain from all the measured values given in Table 20 for the quantities indicated.

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TABLE 30.

The 28 adjusted constants (variables) used in the least-squares multivariate analysis of the Rydberg-constant data given in Table 18. These adjusted constants appear as arguments of the functions on the right-hand side of the observational equations of Table 31.

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TABLE 31.

Observational equations that express the input data related to R in Table 18 as functions of the adjusted constants in Table 30. The numbers in the first column correspond to the numbers in the first column of Table 18. Energy levels of hydrogenic atoms are discussed in Sec. IV A. As pointed out at the beginning of that section, is in fact proportional to and independent of h , hence h is not an adjusted constant in these equations. See Sec. XIII B for an explanation of the symbol ≐.

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TABLE 32.

The 39 adjusted constants (variables) used in the least-squares multivariate analysis of the input data in Table 20. These adjusted constants appear as arguments of the functions on the right-hand side of the observational equations of Table 33.

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TABLE 33.

Observational equations that express the input data in Table 20 as functions of the adjusted constants in Table 32. The numbers in the first column correspond to the numbers in the first column of Table 20. For simplicity, the lengthier functions are not explicitly given. See Sec. XIII B for an explanation of the symbol ≐.

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TABLE 34.

The 15 adjusted constants relevant to the antiprotonic helium data given in Table 22. These adjusted constants appear as arguments of the theoretical expressions on the right-hand side of the observational equations of Table 35.

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TABLE 35.

Observational equations that express the input data related to antiprotonic helium in Table 22 as functions of adjusted constants in Tables 32 and 34. The numbers in the first column correspond to the numbers in the first column of Table 22. Definitions of the symbols and values of the parameters in these equations are given in Sec. IV B. See Sec. XIII B for an explanation of the symbol ≐.

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TABLE 36.

Summary of the results of some of the least-squares adjustments used to analyze the input data given in Tables 18–23. The values of α and h are those obtained in the adjustment, N is the number of input data, M is the number of adjusted constants, is the degrees of freedom, and is the Birge ratio. See the text for an explanation and discussion of each adjustment, but in brief, adjustment 1 is all the data; 2 is the same as 1 except with the uncertainties of the key data that determine h multiplied by 2; 3 is 2 with the low-weight input data deleted and is the adjustment on which the 2010 recommended values are based; 4 is 2 with the input data that provide the most accurate values of alpha deleted; and 5 is 1 with the input data that provide the most accurate values of h deleted as well as low-weight data for α.

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TABLE 37.

Normalized residuals r i and self-sensitivity coefficients S c that result from the five least-squares adjustments summarized in Table 36 for the three input data with the largest absolute values of r i in adjustment 1. S c is a measure of how the least-squares estimated value of a given type of input datum depends on a particular measured or calculated value of that type of datum; see Appendix E of CODATA-98. See the text for an explanation and discussion of each adjustment; brief explanations are given in the caption to Table 36.

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TABLE 38.

Summary of the results of some of the least-squares adjustments used to analyze the input data related to R . The values of R , r p, and r d are those obtained in the indicated adjustment, N is the number of input data, M is the number of adjusted constants, is the degrees of freedom, and is the Birge ratio. See the text for an explanation and discussion of each adjustment. In brief, adjustment 6 is 3 but the scattering data for the nuclear radii are omitted; 7 is 3, but with only the hydrogen data included (no isotope shift); 8 is 7 with the r p data deleted; 9 and 10 are similar to 7 and 8, but for the deuterium data; 11 is 3 with the muonic Lamb-shift value of r p included; and 12 is 11, but without the scattering values of r p and r d.

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TABLE 39.

Generalized observational equations that express input data B32–B38 in Table 20 as functions of the adjusted constants in Tables 30 and 32 with the additional adjusted constants and as given in Eqs. (285) and (286). The numbers in the first column correspond to the numbers in the first column of Table 20. For simplicity, the lengthier functions are not explicitly given. See Sec. XIII B for an explanation of the symbol .

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TABLE 40.

An abbreviated list of the CODATA recommended values of the fundamental constants of physics and chemistry based on the 2010 adjustment.

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TABLE 41.

The CODATA recommended values of the fundamental constants of physics and chemistry based on the 2010 adjustment.

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TABLE 42.

The variances, covariances, and correlation coefficients of the values of a selected group of constants based on the 2010 CODATA adjustment. The numbers in bold above the main diagonal are 1016 times the numerical values of the relative covariances; the numbers in bold on the main diagonal are 1016 times the numerical values of the relative variances; and the numbers in italics below the main diagonal are the correlation coefficients.a

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TABLE 43.

Internationally adopted values of various quantities.

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TABLE 44.

Values of some x-ray-related quantities based on the 2010 CODATA adjustment of the values of the constants.

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TABLE 45.

The values in SI units of some non-SI units based on the 2010 CODATA adjustment of the values of the constants.

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TABLE 46.

The values of some energy equivalents derived from the relations , and based on the 2010 CODATA adjustment of the values of the constants; , , and is the Hartree energy (hartree).

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TABLE 47.

The values of some energy equivalents derived from the relations , and based on the 2010 CODATA adjustment of the values of the constants; , , and is the Hartree energy (hartree).

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TABLE 48.

Comparison of the 2010 and 2006 CODATA adjustments of the values of the constants by the comparison of the corresponding recommended values of a representative group of constants. Here D r is the 2010 value minus the 2006 value divided by the standard uncertainty u of the 2006 value (i.e., D r is the change in the value of the constant from 2006 to 2010 relative to its 2006 standard uncertainty).

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2012-12-28
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: CODATA Recommended Values of the Fundamental Physical Constants: 2010a)
http://aip.metastore.ingenta.com/content/aip/journal/jpcrd/41/4/10.1063/1.4724320
10.1063/1.4724320
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