The CODATA 2017 values of h , e , k , and N A for the revision of the SI

Sufficient progress towards redefining the International System of Units (SI) in terms of exact values of fundamental constants has been achieved. Exact values of the Planck constant h , elementary charge e , Boltzmann constant k , and Avogadro constant N A from the CODATA 2017 Special Adjustment of the Fundamental Constants are presented here. These values are recommended to the 26th General Conference on Weights and Measures to form the foundation of the revised SI.


The CODATA 2017 special adjustment
The input data for the CODATA 2017 Special Adjustment includes the input data used in the final CODATA 2014 regular adjustment on which the 2014 recommended values are based. Of these data, which are given in tables XV-XIX of Mohr et al (2016a), the following were omitted: the four cyclotron frequency ratios, items B8, B9, B11, and B12 that have been superseded by the 2016 atomic mass evaluation , and all measurements of the Newtonian constant of gravitation G. Key data that were published or accepted for publication before the 1 July 2017 closing date of the CODATA 2017 Special Adjustment and have a significant impact on the determination of h, e, k, and N A are listed in table 1. The full list of data considered for the CODATA 2017 Special Adjustment is given in tables 2-5 in Mohr et al (2018). Of note are data that are not included for the same reasons they were omitted from the 2014 adjustment. In particular, the measurements in muonic hydrogen and deuterium that have led to the proton radius 'puzzle' were not included. These data would have no effect on the 2017 values of h, e, k, and N A , but will be reconsidered for the next CODATA periodic adjustment.
The CODATA 2017 Special Adjustment follows the same procedures as the previous periodic CODATA adjustments of the fundamental constants (Mohr and Taylor 2000, 2005, Mohr et al 2008a, 2008b, Mohr et al 2012a, 2012b, Mohr et al 2016a, 2016b. Details of the Special Adjustment analysis are given in Mohr et al (2018). In general, the measure the CODATA TGFC uses for consistency of an input datum is the normalized (or reduced) residual of that datum given by the LSA, that is, the difference between an input datum and its adjusted value divided by the input datum uncertainty. If a residual for an input datum is larger than two, the TGFC identifies the fundamental constant primarily influenced by that datum as well as other input data that influence the same constant. The uncertainties of this subset of input data are multiplied by a factor that is large enough that the relevant residuals are two or less. To achieve consistency, multiplicative expansion factors were applied to the uncertainties of two subsets of input data corresponding to two adjusted constants for the 2017 Special Adjustment.
The first subset consists of the eight input data for the Planck and Avogadro constants listed in table 1, relevant to the adjusted value of the Planck constant. The uncertainties of these input data are multiplied by a factor of 1.7. With this expansion of the uncertainties of the eight data, five have relative standard uncertainties u r at or below 50 × 10 −9 , with two at or below 20 × 10 −9 , where the latter includes results from both the Kibble balance and the x-ray crystal density (XRCD) methods.
The second subset of expanded data consists of the input data that determine the relative atomic mass of the proton: the 2016 atomic mass evaluation value of 1 H and the cyclotron frequency ratio of hydrogenic carbon to the proton, items B2 and B12, respectively, of table 4 in Mohr et al (2018). Coincidentally, an expansion factor of 1.7 was also appropriate in this case, although its application has no effect on the 2017 values of h, e, k, and N A .  (2011) is that the revised SI be consistent with the present SI. In the SI prior to redefinition, the following quantities have exactly defined values: the international prototype of the kilogram m(K) = 1 kg, the vacuum magnetic permeability µ 0 = 4π × 10 −7 H m −1 , the triple point of water T TPW = 273.16 K, and the molar mass of carbon-12, M( 12 C) = 0.012 kg mol −1 . In the revised SI, these quantities are determined experimentally with associated uncertainties. As stated in the agreed upon CCU recommendation (CIPM 2016), the number of digits for the exact numerical values of h, e, and N A to define the revised SI are determined by requiring that the numerical values of m(K), µ 0 , and M( 12 C) remain consistent with their previous exact values within their relative standard uncertainties given by the CODATA 2017 Special Adjustment. The number of digits for k is chosen such that T TPW is equal to 273.16 K within a relative standard uncertainty at the level which T TPW can be realized (CCT 2017). The recommended exact numerical values of h, e, k, and N A to establish the revised SI are given in table 3.

Summary
Sufficient progress has been achieved towards meeting the recommendations for redefining the SI in terms of exact values of fundamental constants. The recommended exact numerical values of h, e, k, and N A to establish the revised SI based on fundamental constants are given. A detailed description of the unique 2017 CODATA special adjustment is given by Mohr et al (2017). The next regular CODATA periodic adjustment of the fundamental constants, CODATA 2018, will also be unique as it will be the first one based on the exact fundamental constants of the revised SI.