Values of some fundamental constants

For each constant the standard deviation uncertainty in the least significant digits is given in parentheses  

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Abbreviations and Reconunended Values of Some Fundamental Constants and... 

For reference, recent values of some fundamental constants are given in Table 20.2. 

Recommended Consistent Values of Some Fundamental Physical Constants (1986)... 

A list of some non-SI units, together with their SI values, and a table containing the best values of some fundamental physical constants are given in appendix A. 

Table 4.1. Recommended values of some fundamental physical 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 values of the fundamental constants and the theory of quantum electrodynamics (QED) are cl< ely coupled. This is evident from the fact that the constants appear as parameters in the theoreticjd expressions that describe the physical properties of particles and matter, and most of these theoretical expressions are derived from QED. In practice, values of the constants are determined by a consistent competrison of the relevant measurements and theoretical expressions involving those constants. Such a comparison is being carried out in order to provide CODATA recommended values of the constants for 1997. This review describes some of the advances that have been made since the last set of constants was recommended in 1986. As a result of these advances, there is a significant reduction in the uncertainty of a number of constants included in the set of 1997 recommended values. 

The International System of Units is a widely used system of measurement standards that provide the basis for expressing physical quantities, such as the kilogram for mass. This paper will describe a proposed modernization of some of the unit definitions that would provide a system that is more stable over time and more suitable for expressing the values of many fundamental constants. 

In these equations, the kinetic and potential terms are summed over all particles in the system (nuclei and electrons), and each particle is characterized by its Cartesian coordinates, its mass (m) and its electric charge (e). In addition, h is Planck s constant and Vy is the distance separating particles i andj. It can thus be seen that the only empirical information required to solve the Schrodinger equation are the masses and charges of the nucleus and the electrons, and the values of some fundamental physical constants. For this reason, quantum-chemical calculations are referred to as ab initio ( without assumptions ) procedures. 

There are several publications dealing with units and symbols of physical chemical quantities. Some also list the values of the fundamental physical constants, as recommended by the Committee on Data for Science and Technology (CODATA) in 2005 [1], The following tables contain the information that is relevant for molecular energetics [1,2]. 

An ab initio calculation uses the correct molecular electronic Hamiltonian (1.275) and does not introduce experimental data (other than the values of the fundamental physical constants) into the calculation. A semiempirical calculation uses a Hamiltonian simpler than the correct one, and takes some of the integrals as parameters whose values are determined using experimental data. The Hartree-Fock SCF MO method seeks the orbital wave function 0 that minimizes the variational integral <(4> //el initio method. Semiempirical methods were developed because of the difficulties involved in ab initio calculation of medium-sized and large molecules. We can... 

The accurate study of some atoms (hydrogen, deuterium, muonium, helium and hydrogen-like carbon) and some free particles (electron, proton, muon) provides us with new highly accurate values of the fundamental physical constants which are important far beyond the physics of simple atoms. 

Both microwave and optical frequency standards have benefited greatly from the development of the laser and the methods of laser spectroscopy in atomic physics. In particular, the ability to determine both the internal and external (that is, motion) atomic states with laser light - by laser cooling for example - has opened up the prospect of frequency standards with relative uncertainties below lO, for example, the Cs atomic fountain clock. The best atomic theories in some cases at starting to match in accuracy that of measurement, providing thereby refined values of the fundamental, so-called atomic constants. Even quite practical measurements (such as used in GPS navigation and primary standards of length) have advanced in recent years. 

As mentioned above, the principle behind the adjustment of the fundamental constants consists in adjusting some parameters (fundamental constants and 5 s) so that experiments and predictions are consistent. Mathematically, the best possible consistency is achieved by minimizing the "distance" between experimentally known values and functions of the parameters that are supposed to reproduce the known values [2, Eq. (E18)]. The minimized function can be expressed as a sum of squares, hence the term "weighted least squares" used for describing the adjustments presented here. The weights in question make a precise experimental measurement constrain the adjusted parameters more than a less precise measurement [20]. 

In this chapter, we describe the application of precision molecular spectroscopy to the study of a possible temporal and spatial variation of the fundamental constants. As we will show below, molecular spectra are mostly sensitive to two such dimensionless constants, namely the fine-structure constant a = e jhc and the electron-to-proton mass ratio p, = m jm (note that some authors define p as an inverse value, i.e., the proton-to-electron mass ratio). At present, NIST lists the following values of these constants [1] a = 137.035999679(94) and p- = 1836.15267247(80). 

With the envisioned higher resolution, it should be possible to determine a better value of the electron/proton mass ratio from a precise measurement of the isotope shift. And a measurement of the absolute frequency or wavelength should provide a new value of the Rydberg constant with an accuracy up to 1 part in 10, as limited by uncertainties in the fine structure constant and the mean square radius of the proton charge distribution. A comparison with one of the Balmer transitions, or with a transition to or between Rydberg states could provide a value for the IS Lamb shift that exceeds the accuracy of the best radiofrequency measurements of the n=2 Lamb shift. Such experiments can clearly provide very stringent tests of quantum electrodynamic calculations, and when pushed to their limits, they may well lead to some surprising fundamental discovery. 

The system of atomic units was developed to simplify mathematical equations by setting many fundamental constants equal to 1. This is a means for theorists to save on pencil lead and thus possible errors. It also reduces the amount of computer time necessary to perform chemical computations, which can be considerable. The third advantage is that any changes in the measured values of physical constants do not affect the theoretical results. Some theorists work entirely in atomic units, but many researchers convert the theoretical results into more familiar unit systems. Table 2.1 gives some conversion factors for atomic units. 

The power law developed above uses the ratio of the two different shear rates as the variable in terms of which changes in 17 are expressed. Suppose that instead of some reference shear rate, values of 7 were expressed relative to some other rate, something characteristic of the flow process itself. In that case Eq. (2.14) or its equivalent would take on a more fundamental significance. In the model we shall examine, the rate of flow is compared to the rate of a chemical reaction. The latter is characterized by a specific rate constant we shall see that such a constant can also be visualized for the flow process. Accordingly, we anticipate that the molecular theory we develop will replace the variable 7/7. by a similar variable 7/kj, where kj is the rate constant for the flow process. 

Solid-surface room-temperature phosphorescence (RTF) is a relatively new technique which has been used for organic trace analysis in several fields. However, the fundamental interactions needed for RTF are only partly understood. To clarify some of the interactions required for strong RTF, organic compounds adsorbed on several surfaces are being studied. Fluorescence quantum yield values, phosphorescence quantum yield values, and phosphorescence lifetime values were obtained for model compounds adsorbed on sodiiun acetate-sodium chloride mixtures and on a-cyclodextrin-sodium chloride mixtures. With the data obtained, the triplet formation efficiency and some of the rate constants related to the luminescence processes were calculated. This information clarified several of the interactions responsible for RTF from organic compounds adsorbed on sodium acetate-sodium chloride and a-cyclodextrin-sodium chloride mixtures. Work with silica gel chromatoplates has involved studying the effects of moisture, gases, and various solvents on the fluorescence and phosphorescence intensities. The net result of the study has been to improve the experimental conditions for enhanced sensitivity and selectivity in solid-surface luminescence analysis. 

Over the last 20-30 years not too much effort has been made concerning the determination of standard potentials. It is mostly due to the funding policy all over the world, which directs the sources to new and fashionable research and practically neglects support for the quest for accurate fundamental data. A notable recent exception is the work described in Ref. 1, in which the standard potential of the cell Zn(Hg)jc (two phase) I ZnS O4 (aq) PbS O4 (s) Pb(Hg)jc (two phase) has been determined. Besides the measurements of electromotive force, determinations of the solubility, solubiKty products, osmotic coefficients, water activities, and mean activity coefficients have been carried out and compared with the previous data. The detailed analysis reveals that the uncertainties in some fundamental data such as the mean activity coefficient of ZnS04, the solubility product of Hg2S04, or even the dissociation constant of HS04 can cause uncertainties in the f " " values as high as 3-4 mV. The author recommends this comprehensive treatise to anybody who wants to go deeply into the correct determination of f " " values. 

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