Quantum electrodynamics fine-structure constant

DCB is correct to second order in the fine-structure constant a, and is expected to be highly accurate for all neutral and weakly-ionized atoms [8]. Higher quantum electrodynamic (QED) terms are required for strongly-ionized species these are outside the scope of this chapter. A comprehensive discussion of higher QED effects and other aspects of relativistic atomic physics may be found in the proceedings of the 1988 Santa Barbara program [9]. 

The degree of precision of the quantized Hall effect has amaz-cd even the experts. Measured values of the Hall resistance at various integer plateaus are accurate to about one part in six million. The effect can be used to construct a laboratory standard of electrical resistance that is much more accurate than Ihe standard resistors currently in use. Authorities also observe that, if the quantized Hall effect is combined with a new calibration ol an absolute resistance standard, it should he able lo yield an improved measurement of the fundamental dimensionless constant of quantum electrodynamics. Ihe fine-structure constant or. 

This is due to the comparative weakness of the electromagnetic interaction, the theory of which contains a small dimensionless parameter (fine structure constant), by the powers of which the corresponding quantities can be expanded. The electron transition probability of the radiation of one photon, characterized by a definite value of angular momentum, in the first order of quantum-electrodynamical perturbation theory mdy be described as follows [53] (a.u.) ... 

Abstract. Muonium is a hydrogen-like system which in many respects may be viewed as an ideal atom. Due to the close confinement of the bound state of the two pointlike leptons it can serve as a test object for Quantum Electrodynamics. The nature of the muon as a heavy copy of the electron can be verified. Furthermore, searches for additional, yet unknown interactions between leptons can be carried out. Recently completed experimental projects cover the ground state hyperfine structure, the ls-2s energy interval, a search for spontaneous conversion of muonium into antimuonium and a test of CPT and Lorentz invariance. Precision experiments allow the extraction of accurate values for the electromagnetic fine structure constant, the muon magnetic moment and the muon mass. Most stringent limits on speculative models beyond the standard theory have been set. 

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. 

Quantum-electrodynamics (QED) as the fundamental theory for electromagnetic interaction seems to be well understood. Numerous experiments in atomic physics as well as in high energy physics do not show any significant discrepancy between theoretical predictions and experimental results. The most striking example of agreement between theory and experiment represents the g factor of the free electron. The experimental value of g = 2.002 319 304 376 6 (87) [1] is confirmed by the calculated value of g = 2.002 319 304 307 0 (280) on the 10 11-level, where the fine structure constant as an input in the theoretical calculation was taken from the quantum Hall effect [2], Up to now uncalculated non-QED contributions play no important role. Indeed today experiment and theory of the free electron yield the most precise fine structure constant. 

Abstract. Using Doppler-tuned fast-beam laser spectroscopy the ls2p 3Po - 3Pi fine structure interval in 24Mg10+ has been measured to be 833.133(15) cm-1. The calibration procedure used the intercombination ls2s 1So - ls2p 3Pi transition in 14N5+. The result tests quantum-electrodynamic and relativistic corrections to high precision calculations, which will be used to obtain a new value for the fine structure constant from the fine structure of helium. 

Quantum electrodynamics (QED) is one of the most successful, unifying theories of physics.In fact, the theory of QED underlies all the experiments I have just Hsted. Eurthermore, with QED and the fine-structure constant, physicists can predict the values of many physical parameters to a high level of precision. For these reasons, QED is highly regarded by physicists. Nonetheless, QED, like all theories of physics, is always vulnerable. Since the theory of QED underlies all the various experiments shown above, the measured values of the fine-structure constant from these different experiments should be the same. If these experiments revealed different values of a, even slightly different values, questions as to the validity of QED would automatically follow. That s the way physics and other quantitative sciences work. 

The paper that reported these results ended with the recognition that there was a problem Whether the failure of theory and experiment to agree is because of some unknown factor in the theory of the hydrogen atom or simply an error in the estimate of one of the natural constants, such as [the fine structure constant], only further experiment can decide. This was the result that Rabi conveyed to the physicists at Shelter Island. Rabi s reputation as an experimentalist brought credibility to the measured results and issued a challenge to the theorists. As with the Lamb shift, it was quantum electrodynamics that was brought to bear on... 

Precision spectroscopy of two-electron atoms tests fundamental relativistic and quantum-electrodynamic atomic theory. Additional current interest in heliumlike ls2p P fine structure stems from the possibility of obtaining the fine structure constant, a, from comparison of theory [1,2,3] and experiment [4,5,6,7,8,9] for the fine structure of helium. Measurements in moderate Z ions, though less precise than those in helium, can be more sensitive to higher-order relativistic and QED corrections. Measurements have been carried out using laser techniques in Li+, see e.g. ref. [10], Be + [11], [12], N + [13,14], and F + [15,16]. For... 

The leading quantum electrodynamic effects to be accounted for in electronic structure calculations are the radiative corrections known as electron self-energy interaction and vacuum polarization. For the energy of electronic systems, the latter is usually small compared to the former, but only the latter can be expressed in terms of an effective additive potential to be included in the electronic structure calculations. The total vacuum polarization potential can be expanded into a double power series in the fine structure constant a and the external coupling constant Za. The lowest-order term, the Uehling potential, can be expressed as [110-112] ... 

The anomalous contribution to the magnetic moment of an electron has been explained by the quantum electrodynamic theory. The additional contribution—the radiative correction —arises from the interaction of the electron-positron virtual pair emitted and absorbed by the real electron. A theoretical expression in terms of the fine structure constant a is... 

Although the proper point of departure for relativistic atomic structure calculations is quantum electrodynamics (QED), very few atomic structure calculations have been carried out entirely within the QED framework. Indeed, almost all relativistic calculations of the structure of many-electron atoms are based on some variant of the Hamiltonian introduced a half century ago by Brown and Ravenhall [1] to understand the helium fine structure. By decoupling the electron and radiation fields in QED to order a (the fine-structure constant) using a contact transformation. Brown and Ravenhall obtained a relativistic momentum-space Hamiltonian in which the electron-electron Coulomb interaction was surrounded by positive-energy projection operators. Owing to the fact that contributions from virtual electron-positron pairs are automatically projected out of... 

Several classifications have been introduced. The earliest seems to have been according to estimates of overall uncertainty. This is particularly useful in reducing complexity in the adjustment process if one group of experiments is significantly more accurate than a second group whose members are of approximately equal (and lesser) estimated accuracy [5]. A second type of classification partitioned the input measurements into a class whose data reduction required use of quantum electrodynamics in a significant way and the remainder which did not. This separation was particularly informative when the Josephson 2e/h measurement allowed for a choice between values for the fine-structure constant as derived from fine-structure and hyperfine structure in hydrogen [6]. 

Fig. 2 Summary of values for the fine-structure constant without using quantum electrodynamic theory. The recommended value is characterized by the dotted lines, and the measured values of a (including one standard deviation) using the %-method and the h/e -method ( quantum Hall effect) are plotted as vertical lines. The national laboratories are NBS (National Bureau of Standards, U.S.), NIM (National Institute of Metrology, China), VlIIIM (Mendeleev Institute, USSR), and NPL (National Physics Laboratory, U.K.)...

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. 

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