Quantum electrodynamics Rydberg constant

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. 

A dimensionless frequency ratio, such as f(lS-2S)/f(2S-nS), on the other hand, is independent of the Rydberg constant. Its measurement can serve as a sensitive test of quantum electrodynamic level shifts and as a means to determine the size of the proton or deuteron, provided QED is correct. 

The possibilities of Doppler-free two-photon spectroscopy for metrology and fundamental physics has been impressively demonstrated by precision measurements of the IS-2S transition in atomic hydrogen [7.53-55]. Precise measurements of this one-photon forbidden transition with a very narrow natural linewidth of 1.3 Hz yields accurate values of fundamental constants and can provide stringent tests of quantum electrodynamic theory (Sect. 1.4.7). A comparison of the 1S-2S transition frequency with the 2S-3P frequency allows the precise determination of the Lamb shift of the IS ground state [7.54] whereas the 2S Lamb-shift was already measured long ago by the famous Lamb-Rutherford experiments where the RF transition between 2Si/2 and 2Pj/2 were observed. Because of the isotope shift the 1S-2S transitions of and = D differ by about 336 GHz (Fig. 7.34). The Rydberg constant has been determined within a relative uncertainty of 10 [7.55,56]. 

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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