Quantum fine structure constant

An atomic unit of length used in quantum mechanical calculations of electronic wavefunctions. It is symbolized by o and is equivalent to the Bohr radius, the radius of the smallest orbit of the least energetic electron in a Bohr hydrogen atom. The bohr is equal to where a is the fine-structure constant, n is the ratio of the circumference of a circle to its diameter, and is the Rydberg constant. The parameter a includes h, as well as the electron s rest mass and elementary charge, and the permittivity of a vacuum. One bohr equals 5.29177249 x 10 meter (or, about 0.529 angstroms). 

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]. 

A weakly bound state is necessarily nonrelativistic, v Za (see discussion of the electron in the field of a Coulomb center above). Hence, there are two small parameters in a weakly bound state, namely, the fine structure constant a. and nonrelativistic velocity v Za. In the leading approximation weakly bound states are essentially quantum mechanical systems, and do not require quantum field theory for their description. But a nonrelativistic quantum mechanical description does not provide an unambiguous way for calculation of higher order corrections, when recoil and many particle effects become important. On the other hand the Bethe-Salpeter equation provides an explicit quantum field theory framework for discussion of bound states, both weakly and strongly bound. Just due to generality of the Bethe-Salpeter formalism separation of the basic nonrelativistic dynamics for weakly bound states becomes difficult, and systematic extraction of high order corrections over a and V Za becomes prohibitively complicated. 

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.) ... 

In this way the three quantities (both the electric and the magnetic fine-structure constants at infinite momentum transfer and cxgut) would be equal. Furhermore, there would be a complete symmetry between electricity, magnetism, and strong force at the level of bare particles (i.e., at Q2 = oo) this symmetry would be broken by the effect of the quantum vacuum. 

In Chapter 1, the first order contributions to the annihilation rates from the dominant modes of decay of the S-states of both ortho- and para-positronium (for arbitrary principal quantum number nPs) were given as equations (1.5) and (1.6). These contributions are included in the following equations for the rates for the two ground states, which also contain terms of higher order in the fine structure constant, a ... 

The fine-structure constant a indicates that first-order perturbation theory has been applied the linear dependence on the photon energy Eph is due to the length form of the dipole operator used in equ. (2.1), and the wavenumber k compensates the 1 /k which appears if the absolute squared value of the continuum wavefunction is used (see equ. (7.29)). The summations over the magnetic quantum numbers M, of the photoion and ms of the photoelectron s spin are necessary because no observation is made with respect to these substates. Due to the closed-shell structure of the initial state with f — 0 and M = 0, the averaging over the magnetic quantum numbers M simply yields unity and is omitted. 

In order finally to derive the differential cross section of photoionization one inserts equ. (8.26) in equ. (8.24) and replaces the number nph of incident photons by nPh = ce0Alo)/2ti (see equs. (8.4b) and (8.8a) and (8.8b)) and the interaction operator by equ. (8.21). Then one removes the factor h2/m0 resulting from the normalization of the continuum function from the matrix element and incorporates it in the final prefactor (see footnote concerning equ. (7.28d)), and one introduces the fine structure constant a using a = el/4ne0hc. This leads to (for the summations over magnetic quantum numbers see below)... 

A comparison between theory and experiment for the fine structure intervals in helium holds the promise of providing a measurement of the fine structure constant a that would provide a significant test of other methods such as the ac Josephson effect the and quantum Hall effect. The latter two differ by 15 parts in 108 and are not in good agreement with each other [59]. 

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. 

Here, ag = h2/(m e2) is the reduced Bohr radius (m = M), n is a principal quantum number of the hydrogenic state i), and a = e2/(hc) 1/137 is the fine structure constant. In the following discussion, (2) will be the only restriction imposed on values of physical parameters. In particular, no distinction will be made as to whether the photon energy ho is less or greater than the ionization potential Jj of the state i). Note that = ftwi holds true only in the nonrelativistic approximation, whereas in general I) tkui. 

It may surprise you to know that, right up into the nineteen fifties, experimental determinations of the fine structure constant were based upon measurements of spin doublet intervals in X-ray spectra, that is to say, effectively the 2P,/2 - 2P 3/2 interval belonging to the hole in the L-shell. But the interpretation at this time rested upon the new form of quantum mechanics, and perhaps more important than the new mathematics, a piece of physics which had first to be discovered the spin and magnetic properties of the electron. 

This constant explains far more than the appearance of the hydrogen atom s spectrum, however. The fine-structure constant is recognized as one of the most important constants in physics. We know, for example, that the fine-strucmre constant is a measure of the strength of the interaction between photons and electrons. Thus, this constant will appear in all simations that reveal quantum and relativistic properties of electrically charged particles. If electrons and light did not interact, the fine-structure constant would be zero. 

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... 

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