Determination the Rydberg constant

When one considers the myriad of measurements that are made in the conduct of science, the measurements of spectral wavelengths stand apart in that they can be measured with great precision. Thus, from the measurement of the wavelength of the Ha line, physicists over the years have determined the Rydberg constant. A few of the early results are given in Table 19.1. 

Mention should be made here of a new experiment using millimetre radiation (about 256 GHz) to determine the Rydberg constant from the energy spacings of neighbouring circular Rydberg states of atomic hydrogen [43] in a way essentially free of QED and the Lamb shift. 

The absolute wavelength, together with the fine structure formula, can be used to determine the Rydberg constant. The... 

The intervals of gross structure are mainly determined by the Rydberg constant, and the same transition frequencies should be used both for measurement of the Rydberg constant and for measurement of the IS Lamb shift. 

Determination of the most precise value of the Rydberg constant requires a comprehensive analysis of results of the same experiments used for determination of the 15 Lamb shift [26, 31, 32, 33, 34, 35, 36]. This analysis was performed in [1], and resulted in the value in (12.1) which has relative uncertainty 6 = 6.6 X 10. This uncertainty is limited by the experimental... 

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])-... 

Figure 14 compares the recent determinations of the Rydberg constant and shows the different steps of this improvement since 1986 (references in chronological order [67,68,69,70,21,22,10,24,45,46,47,49,61,28]). 

The spectrum of hydrogen is composed of a major structure, determined by the Rydberg constant, QED corrections like the Lamb shift and finally nuclear shape... 

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. 

Table 3. Summary of measured transition frequencies v considered in the 1998 constants adjustment for the determination of the Rydberg constant Roc (H is hydrogen and D is deuterium)...

Using the theoretical work of Erickson /12/ for the 2P-nD interval and either the experimental value of the 2S Lamb-shift in hydrogen /13/ or the theoretical value of the 2S Lamb-shift in deuterium (= 1059.229 MHz) /14/, we can deduce six independent determinations of the Rydberg constant. These values are in excellent agreement each with other. Our final result is ... 

As has already been pointed out, two different methods of calibration have been used in the work so far reported. One can measure in terms of H/3, and in this way determine the ground state Lamb shift. If instead one uses a frequency standard, one can determine the IS Lamb shift by allowing for the other contributions to the measured IS - 2S interval this requires a value of the Rydberg constant from another source. Alternatively, if one assumes the IS Lamb shift known from theory at the level of accuracy of the experiment, one can regard the measurement as a determination of the Rydberg constant. All the most recent work has been in terms of the external standards provided by the tellurium transitions, but these introduce an uncertainty which in the case of the cw experiments dominates the final error. This situation must be... 

A measurement of the 1S-2S frequency alone can therefore give only a modest further improvement of the Rydberg constant before its interpretation is limited by other uncertainties. At one time it has been suggested to determine the proton-electron mass ratio from the 1S-2S isotope shift. However, after the most recent measurements by VAN DYCK et al. [37], the uncertainty of the isotope shift is now dominated by nuclear size effects. 

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 Rydberg constant is one of the most important constants of atomic physics because of its connection with the fundamental atomic constants (e, h, m c) and because of the high accuracy with which it can be determined. 

Table 19.1 Values of the Rydberg constant determined by optical...

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