Adjustment of fundamental constants

The fine structure constant a can be determined with the help of several methods. The most accurate test of QED involves the anomalous magnetic moment of the electron [40] and provides the most accurate way to determine a value for the fine structure constant. Recent progress in calculations of the helium fine structure has allowed one to expect that the comparison of experiment [23,24] and ongoing theoretical prediction [23] will provide us with a precise value of a. Since the values of the fundamental constants and, in particular, of the fine structure constant, can be reached in a number of different ways it is necessary to compare them. Some experiments can be correlated and the comparison is not trivial. A procedure to find the most precise value is called the adjustment of fundamental constants [39]. A more important target of the adjustment is to check the consistency of different precision experiments and to check if e.g. the bound state QED agrees with the electrical standards and solid state physics. 

The adjustment of fundamental constants and other quantities—performed so that experiments match theoretical results—consists in a numerical procedure. It is to be noted, though that the energy levels obtained by such a method come from a mix of theory and experiments they are not pure ab initio results. For instance, the "prediction" of the 1S-2S transition in Ref. [1] comes mostly from its experimental measurement [7]. On the other hand, the classic Lamb shift prediction mentioned above, which is given [1] to a precision better than that of experiments, is obviously not a pure experimental result, but nonetheless relies on the information provided by experiments. 

The officially recommended values for a are plotted in Fig. 1 as a function of time. The last least -squares adjustment of fundamental constants was in 1973 with a value [3]... 

Even though the prediction of new energy levels and transition frequencies in [1] has no direct impact on the recommended values of the fundamental constants, compared to the adjustment on which the new predictions are based (CODATA 2002 [3]), they motivate new theoretical calculations, as mentioned above. In turn, such calculations can close the virtuous circle and contribute to an increased accuracy in the determination of fundamental constants. 

The quantities adjusted in CODATA [2,3] can be divided into two classes the group of fundamental constants chosen for the adjustment, and the group of outstanding, theoretically unknown contributions 5. These quantities are involved in equations such as equation (1) above, which gives the 1S-2S transition frequency as a function of constants such as the Rydberg constant Roo, the electron mass, etc., and also of quantities denoted by 5is and 52. ... 

Adjusting the fundamental constants requires to define both a list of parameters to be adjusted (fundamental constants and 5 s), and a system of equations that constrain them. 

It must be noted that even though some theory may have been used in determining the published final experimental results of the input data Q, this theory differs from the one expressed by the functions F. For example, experimentalists can theoretically take into account the contribution of some electromagnetic fields present in the apparatus, in order to deduce a specific frequency from raw data [22] such a use of theory relies on well-tested physics that has no direct connection with ab initio theoretical results F used in adjusting the fundamental constants. 

The method described above, which adjusts variables in order to make theory and experiments match best, was applied to the determination of fundamental constants [3]. However, fundamental constants only belong to one of the two types of adjusted variables Z non-calculated energy contributions S (Section 2.1.1) were also evaluated, as mentioned above in Section 2.2.2.3. It is thus possible to optimally predict the energy levels whose 5-contribution was adjusted in [3], by evaluating the right-hand side of formula Eq. (2), which is exact. Their are about two dozen levels whose energy can thus be optimally evaluated the list can be found on the web. ... 

One important result [1] is that the addition of new 5 s to be calculated (Section 2.3.2.1) has no influence on the best estimates for the variables Z initially adjusted (Section 2.2.2.1) the determinations (of fundamental constants and 5 s) obtained in CODATA 2002 are not influenced by the predictions of new energy levels. This is expected, as no new information pertaining to the already adjusted quantities Z (which includes 5is, for instance) is added by the extension of the CODATA adjustment to new levels—no new experiment or theoretical prediction of a level used in CODATA is added by the extension (Section 2.3.2.2). One important practical gain brought forth by this result is that the linearizations (Section 2.2.2.3) of system (3) around successive values of the adjusted variables Z, which were done for CODATA [3], do not have to be carried out again the linearization of system (3) around the final values Z of the CODATA variables thus directly contributes to the new predictions [1], and is readily available . 

Table 1.2-12 deals with the natural units, which are based directly on fundamental constants or combinations of fundamental constants. Like the CGS system, this system is based on mechanical quantities only. The numerical values in SI units are given here according to the 2002 CODATA adjustment... 

Cohen, E.R. and Taylor, B.N. (1986). The 1986 Adjustment of the Fundamental Physical Constants, report of the CODATA Task Group on Fundamental Constants, CODATA Bulletin 63, Pergamon, Elmsford, New York (1987). The 1986 adjustment of the fundamental constants, Rev. Mod. Phys., 59, 1121-1148 (1993). The fundamental physical constants, Phys. Today August, Part 2, 9-13. 

Abstract. A review is given of the latest adjustment of the values of the fundamental constants. The new values are recommended by the Committee on Data for Science and Technology (CODATA) for international use. Most of the fundamental constants are obtained by the comparison of the results of critical experiments and the corresponding theoretical expressions based on quantum electrodynamics (QED). An important case is the Rydberg constant which is determined primarily by precise frequency measurements in hydrogen and deuterium. 

The 1998 adjustment of the values of the fundamental physical constants has been carried out by the authors under the auspices of the CODATA Task Group on Fundamental Constants [1,2]. The purpose of the adjustment is to determine best values of various fundamental constants such as the fine-structure constant, Rydberg constant, Avogadro constant, Planck constant, electron mass, muon mass, as well as many others, that provide the greatest consistency among the most critical experiments based on relationships derived from condensed matter theory and quantum electrodynamics (QED) theory. The 1998 CODATA recommended values of the constants also may be found on the Web at physics.nist.gov/constants. 

We first recall the method of least squares as it is applied to the adjustment of values of the fundamental constants. The experimental results, or possibly theoretical results, form the observational data qi, qi,..., qn- A selected set of the fundamental constants z, Z2, , zm (M < N), are the unknowns or variables (also called adjusted constants) of the adjustment and are related to the data by observational equations of the form... 

Numerical results (in kHz) for hydrogen and deuterium atoms and the helium-3 ion are collected in Table 2. One can see that the new corrections essentially shift the theoretical predictions. A comparison of the QED predictions (in kHz) against the experiments is summarized in Table 1. We take the values of the fundamental constants (like e. g. the fine structure constant a) from the recent adjustment (see Ref. [25]). 

More accurate force constants for a number of transition metal complexes with ammine ligands have been derived by normal-coordinate analyses of infrared spectra[130, 31l The fundamental difference between spectroscopic and molecular mechanics force constants (see Section 3.4) leads to the expectation that some empirical adjustment of the force constants may be necessary even when these force constants have been derived by full normal-coordinate analyses of the infrared data. This is even more important for force constants associated with valence angle deformation (see below). It is unusual for bond-length deformation terms to be altered substantially from the spectroscopically derived values. 

Numerous new and revised thermochemical tables are included in this collection. However, this Third Edition is primarily a rewriting and a recalculation of all the tables no attempt has been made to reanalyze the data for all tables. The rewritten tables adhere more closely to the current lU-PAC recommendations on symbols and notation. The recalculated tables are all based on the current lUPAC and CODATA recommendations for relative molecular masses and fundamental constants. As a result, a comparison of a table in this Third Edition and its previously published form (i.e., same revision date) will reveal differences however, these result from the adjustments mentioned above rather than from a reanalysis of the data. 

The molecular constants which are given for NH in the JANAP Thermochemical Tables (3) were adjusted for the isotope effect. The National Bureau of Standards prepared this table (4) by critical analysis of data existing in 1972. Using molecular constants and A H selected by NBS (4), we recalculate the table in terras of 1973 fundamental constants ( ), 1975 atomic weights (6), and current JANAP reference states for the elements. 

An adjustment of the fundamental constants is underway to provide the CODATA 1997 recommended values. The results of this work will be described in a report of the CODATA Task Group on Fundamental Constants written by Barry Taylor (NIST), E. Richard Cohen (Rockwell Int, retired), and the present author. 

A pioneering evaluation of a set of fundamental physical constants was done by Raymond Birge in 1929 [1]. It is of interest to note that this is the first article (vol. 1, p. 1) in the journal that was to become the Reviews of Modern Physics. Adjustments done since 1950 include the following ... 

Beyond the 1997 adjustment of the fundamental constants, the possibility of more frequent adjustments is being considered. The World Wide Web as a... 

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