Determination the fine structure constant

The parameters X, X, X2,X are determined hy four especially chosen reference points. The energies of the states of Li-like ions were calculated twice with the real value of the fine structure constant a = 1/137 and with the smaller value a = a/lOOO. The results of these latter calculations were considered as non-relativistic. This helped the isolation of Ej and. A detailed evaluation of their accuracy may be made only after a complete calculation of Z,nlj). It may be stated that the above extrapolation... 

The absolute frequency of the fundamental IS — 2S transition in atomic hydrogen has now been measured to 1.8 parts in 1014, an improvement by a factor of 104 in the past twelve years. This improvement was made possible by a revolutionary new approach to optical frequency metrology with the regularly spaced frequency comb of a mode locked femto-second multiple pulsed laser broadened in a non-linear optical fiber. Optical frequency measurement and coherent mixing experiments have now superseded microwave determination of the 2S Lamb shift and have led to improved values of the fundamental constants, tests of the time variation of the fine structure constant, tests of cosmological variability of the electron-to-proton mass ratio and tests of QED by measurement of g — 2 for the electron and muon. 

Another metrological application of simple atoms is the determination of values of the fundamental physical constants. In particular, the use of the new frequency chain for the hydrogen and deuterium lines [6] provided an improvement of a value of the Rydberg constant (Roc)- But that is not the only the constant determined with help of simple atoms. A recent experiment on g factor of a bound electron [27,11] has given a value of the proton-to-electron mass ratio. This value now becomes very important because of the use of photon-recoil spectroscopy for the determination of the fine structure constant [41] (see also [8])-... 

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. 

Fig. 4. The fine structure constant a has been determined with various methods [25-28]. most precise is the determination from the magnetic anomaly of the electron. The muonium atom offers two different routes which uses independent sets of fundamental constants. The disagreement (the error bars are mostly statistical) seem to indicate that the value h/me from neutron de Broglie wavelength measurements may be quoted with too high accuracy...

At present the good agreement within two standard deviations between the fine structure constant determined from muonium hyperfine structure and the one from the electron magnetic anomaly is generally considered the best test of internal consistency of QED, as one case involves bound state QED and the other one QED of free particles. 

Abstract. A suitable femtosecond (fs) laser system can provide a broad band comb of stable optical frequencies and thus can serve as an rf/optical coherent link. In this way we have performed a direct comparison of the IS — 2S transition in atomic hydrogen at 121 nm with a cesium fountain clock, built at the LPTF/Paris, to reach an accuracy of 1.9 x 10-14. The same comb-line counting technique was exploited to determine and recalibrate several important optical frequency standards. In particular, the improved measurement of the Cesium Di line is necessary for a more precise determination of the fine structure constant. In addition, several of the best-known optical frequency standards have been recalibrated via the fs method. By creating an octave-spanning frequency comb a single-laser frequency chain has been realized and tested. 

Recently we have used the femtosecond technology to measure the transition frequency of the cesium Di line [45]. This line provides an important link for a new determination of the fine structure constant a. Because a scales all electromagnetic interactions, it can be determined by a variety of independent physical methods. Different values measured with comparable accuracy disagree with each other by up to 3.5 standard deviations and the derivation of the currently most accurate value of a from the electron g — 2 experiment relies on extensive QED calculations [46], The 1999 CODATA value [47] or1 = 137.035 999 76(50) (3.7 x 10-9) follows from the g — 2 results. To resolve this unsatisfactory situation it is most desirable to determine a value for the fine structure constant that is comparable in accuracy with the value from the g — 2 experiment but does not depend heavily on QED calculations. A promising way is to use the accurately known Rydberg constant i oc according to ... 

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. 

One of the most important constants is the fine-structure constant a. It is determined primarily by comparison of measurement and theory for the electron magnetic moment anomaly ae defined by... 

Abstract. We present a review of the helium spectroscopy, related to transitions between 23S and 23P states around 1083 nm. A detailed description of our measurements, that have produced the most accurate value of the 23Po — 23Pi fine structure interval, is given. It could produce an accurate determination (34 ppb) of the fine structure constant a. Improvements in the experimental set up are presented. In particular, a new frequency reference of the laser system has been developed by frequency lock of a 1083 nm diode laser to iodine hyperfine transitions around its double of frequency. The laser frequency stability, at 1 s timescale, has been improved of, at least, two orders of magnitude, and even better for longer time scales. Simultaneous 3He —4 He spectroscopy, as well as absolute frequency measurements of 1083 nm helium transitions can be allowed by using the Li-locked laser as frequency standard. We discuss the implication of these measurements for a new determination of the isotope and 23 5 Lamb shifts. 

An important feature of the study of the g factor of a bound electron at Z = 20 — 30 is also the possibility to learn about higher-order two-loop corrections, which are one of the crucial problems of bound state QED theory. Below we discuss in detail the present status of theory and experiment. We consider a new opportunity to precisely test bound state QED and to accurately determine two fundamental constants the electron-to-proton mass ratio and the fine structure constant. 

A study of the electron mass is now of interest also because of determination of the fine structure constant a from the photon-recoil-spectroscopy [22,23], A measurement of the recoil frequency shift... 

Concluding our consideration we would like to underline, that the study of the g factor of a bound electron [1] offers a new opportunity for us to precisely test bound state QED theory and to determine two important fundamental constants the fine structure constant a and the electron-to-proton mass ratio m/mp. The experiment can be performed at any Z with about the same accuracy [1] and one can expect new data at medium Z which will allow to verify the present ability to estimate unknown higher-order corrections (i. e. theoretical uncertainty) in both low-Z and high-Z calculations. 

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. 

K. von Klitzing, G. Dorda, and M. Pepper, M. (1980). New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45 494 97 (1980). 

With respect to [the fine structure constant] we are in the rather humOiating position of people who have to wrap a piece of string around a cylinder to determine pi. 

X 10- ) follows from the g — 2 results. To resolve this unsatisfactory situation it is most desirable to determine a value for the fine structure constant that is comparable in accuracy with the value from the g — 2 experiment but does not depend heavily on QED calculations. A promising way is to use the accurately known Rydberg constant 7 oo according to ... 

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