Quantum electrodynamics and fundamental constants

This experimental development was matched by rapid theoretical progress, and the comparison and interplay between theory and experiment has been important in the field of metrology, leading to higher precision in the determination of the fundamental constants. We feel that now is a good time to review modern bound state theory. The theory of hydrogenic bound states is widely described in the literature. The basics of nonrelativistic theory are contained in any textbook on quantum mechanics, and the relativistic Dirac equation and the Lamb shift are discussed in any textbook on quantum electrodynamics and quantum field theory. An excellent source for the early results is the classic book by Bethe and Salpeter [6]. A number of excellent reviews contain more recent theoretical results, and a representative, but far from exhaustive, list of these reviews includes [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. 

The Schrodinger equation (more precisely the refined version incorporating both relativity and quantum electrodynamics), and those obtained from it, describe the physical and chemical features of the hydrogen atom with an accuracy limited only by the precision to which the fundamental constants required are known. Unfortunately, the hydrogen atom is the only chemical structure for which the Schrodinger equation can be solved exactly everything else requires approximation. For small atoms and very small molecules the approximations can be very good, but for any... 

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. 

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. 

For almost three decades, the S-2S two-photon transition in atomic hydrogen with its natural linewidth of only 1.3 Hz has inspired advances in high-resolution spectroscopy and optical frequency metrology. This resonance [the 1S-2S transition] has become a de facto optical frequency standard. More importantly, it is providing a cornerstone for the determination of fundamental constants and for stringent tests of quantum electrodynamic theory. In the future, it may unveil... 

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 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. 

Constantly comparing predictions to observations contributes to testing quantum electrodynamics (QED)—and, beyond QED, the Standard Model of fundamental interactions and the quantum field theories that it uses. Comparing the predicted hydrogen and deuterium transition frequencies with new ab initio QED results would contribute to testing QED. 

The possibilities of Doppler-free two-photon spectroscopy for metrology and fundamental physics has been impressively demonstrated by precision measurements of the 1S-2S transition in atomic hydrogen [260-263]. Precise measurements of this one-photon forbidden transition with a very narrow natural linewidth of 1.3 Hz yield accurate values of fundamental constants and can provide stringent tests of quantum electrodynamic theory (Sect. 9.7). A comparison of the 1S-2S transition frequency with the 2S-3P frequency allows the precise determination of the Lamb shift of the 15 ground state [261], whereas the 2S Lamb shift was already measured long ago by the famous Lamb-Rutherford experiments where the RF transition between 25 1/2 and 2P /2 were observed. Because of the isotope shift the 15-25 transitions of and differ by... 

Quantum electrodynamics is believed to provide a very good theory for the hydrogen atom, although the predictions of calculations 5 are limited by the uncertainties of fundamental constants, by unknown nuclear size and structure effects, and by computational approximations. Fortunately... 

Cold, trapped HD+-ions are ideal objects for direct spectroscopic tests of quantum-electrodynamics, relativistic corrections in molecules, or for determining fundamental constants such as the electron-proton mass ratio. It is also of interest for many applications since it has a dipole moment. The potential of localizing trapped ions in Coulomb crystals has been demonstrated recently with spectroscopic studies on HD+ ions with sub-MHz accuracy. The experiment has been performed with 150 HD+ ions which have been stored in a linear rf quadrupole trap and sympathetically cooled by 2000 laser-cooled Be+ ions. IR excitation of several rovibrational infrared transitions has been detected via selective photodissociation of the vibra-tionally excited ions. The resonant absorption of a 1.4/itm photon induces an overtone transition into the vibrational state v = A. The population of the V = A state so formed is probed via dissociation of the ion with a 266 nm photon leading to a loss of the ions from the trap. Due to different Franck-Condon factors, the absorption of the UV photon from the v = A level is orders of magnitude larger than that from v = 0. 

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. 

It is remarkable that a fundamental quantum mechanical constant is best measured with an apparatus whose operation is based on classical mechanics and classical electrodynamics. 

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