Lamb shift 251 experiment

Having in mind that the data from the muonic hydrogen Lamb shift experiment will be used for measurement of the rms proton charge radius [2] it is useful to write this correction in the form... 

Beams of slow negative muons have been developed and are for example employed in the muonic hydrogen Lamb shift experiment at PSI. Other developments are under way at the Rutherford Appleton Laboratory (RAL) in Chilton,... 

Figure 20 Experimental apparatus used in the LAMPF muonium Lamb shift experiment.

The future experimental investigations will target in particular the accurate spectroscopy of the excited states in heavy He-like systems. In contrast to the ground-state properties, this topic has almost not been addressed up to now experimentally. In addition, very recently, there has been a considerable progress in developments for the next generation Lamb shift experiments on H-like heavy ions. Here, the first beam-time has already been conducted utilising the high-resolution X-ray spectrometers (in combination with novel position-sensitive solid-state detectors) as well as the X-ray microcalorimeter. 

Soon after the Schrodinger equation was introduced in 1926, several works appeared dealing with the fundamental problem of the nuclear motion in molecules. Very soon after, the relativistic equations were introduced for one-and two-electron systems. The experiments on the Lamb shift stimulated... 

As mentioned, most calculations we have done so far have concerned molecular systems. However, prior to development of the non-BO method for the diatomic systems, we performed some very accurate non-BO calculations of the electron affinities of H, D, and T [43]. The difference in the electron affinities of the three systems is a purely nonadiabatic effect resulting from different reduce masses of the pseudoelectron. The pseudoelectrons are the heaviest in the T/T system and the lightest in the H/H system. The calculated results and their comparison with the experimental results of Lineberger and coworkers [44] are shown in Table 1. The calculated results include the relativistic, relativistic recoil. Lamb shift, and finite nuclear size corrections labeled AEcorr calculated by Drake [45]. The agreement with the experiment for H and D is excellent. The 3.7-cm increase of the electron affinity in going from H to D is very well reproduced by the calculations. No experimental EA value is available for T. 

The mass dependence of the correction of order a Za) beyond the reduced mass factor is properly described by the expression in (3.7) as was proved in [11, 12]. In the same way as for the case of the leading relativistic correction in (3.4), the result in (3.7) is exact in the small mass ratio m/M, since in the framework of the effective Dirac equation all corrections of order Za) are generated by the kernels with one-photon exchange. In some earlier papers the reduced mass factors in (3.7) were expanded up to first order in the small mass ratio m/M. Nowadays it is important to preserve an exact mass dependence in (3.7) because current experiments may be able to detect quadratic mass corrections (about 2 kHz for the IS level in hydrogen) to the leading nonrecoil Lamb shift contribution. 

Prom the theoretical point of view the accuracy of calculations is limited by the magnitude of the yet uncalculated contributions to the Lamb shift. Corrections to the P levels are known now with a higher accuracy than the corrections to the S levels, and do not limit the results of the comparison between theory and experiment. 

Many experiments on the precise measurement of the classic Lamb shift were performed since its experimental discovery in 1947. We have collected modern post 1979 experimental results in Table 12.2. Two entries in this Table are changed compared to the original published experimental results [16, 15]. These alterations reflect recent improvements of the theory used for extraction of the Lamb shift value from the raw experimental data. 

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... 

The theory of high order corrections to the Lamb shift described above for H and D may also be applied to other light hydrogenlike ions. The simplest such ion is He+. Originally the classic Lamb shift in 17e+ was measured in [50] by the quenching-anisotropy method with the result L 2Si — 2Pi,17e+) = 14 042.52 (16) MHz. Later the authors of [50] discovered a previously unsuspected source of systematic error in their experiment. Their new measurement of the classic Lamb shift in 17e+ by the anisotropy method resulted in the value L 2Si — 2Pi,He ) = 14 041.13 (17) MHz [51]. Besides the experimental data this result depends also on the theoretical value of the hne structure interval. In [51] the value AE 2Pz —2Pi) = 175 593.50 (2) MHz was used. We recalculated this interval using tire latest theoretical results discussed above and obtained AE 2P3 — 2Pi) = 175 593.33 (1) MHz. Then the value of the... 

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]. 

What can be tested As mentioned before, CPT invariance guarantees the equality of masses, charges and lifetimes of particles and antiparticles. This means that the experimental investigations of masses, charges, etc. of particle - antiparticle pairs are tests of CPT symmetry. Such experiments are not easy to do with the charged particles themselves (because of their interactions with stray fields). Comparison of neutral atom - antiatom pairs is much more convenient. In particular, the fine structure, hyperfine structure and Lamb shifts of atoms and antiatoms should be identical - and can be tested in laboratory. 

Before the individual parts of this function are discussed, the energy eigenvalue will be considered. The ground state energy g of the helium atom is just the energy value for double-ionization which can be determined accurately by several different kinds of experiments. Before the experimental value can be compared with the calculated one, some small corrections (for the reduced mass effect, mass polarization, relativistic effects, Lamb shift) are necessary which, for simplicity, are... 

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. 

In initial experiments at Garching we have combined the IS1 — 2S spectrometer with another atomic beam apparatus for the excitation of the 25 — 45/4.0 transition in atomic hydrogen similar to the experiments in Paris [17,18,19], aiming at an improved measurement of the hydrogen ground state Lamb shift L(15) [20]. 

The discovery of the 25 — 2P Lamb shift has led to the development of the theory of quantum electrodynamics. Today, radio frequency measurements of this splitting have reached the uncertainty limits imposed by the 100 MHz natural linewidth of the 2P state. The considerably sharper optical two-photon resonances used in optical experiments leave significant room for future improvements. 

The experimental set-up on the 2S—nS/D transitions has also been used in Paris to deduce the Lamb shift of the IS1 level via a comparison of the frequencies of the IS1 — 3S and 2S — 6S/D transitions [57]. The principle of this experiment is similar to the ones made at Garching and at Yale, where the IS1 — 2S frequency was compared to the 2S — 4S, 2S — 4P or 2S — 4D frequencies [23,58], In the Bohr model, these frequencies lie exactly in a ratio 4 1, and the deviation from this factor is mainly due to the Lamb shifts which vary as 1/n3. 

As already mentioned in the second part of this review, we made an average of these different determinations of R00 by performing a least squares adjustment [72] which takes into account all the precise experiments the measurements of the 251/2 Lamb shift, the optical frequency measurements of the 15— 25 and 25 — nD transitions in hydrogen and deuterium, and also the measurements of... 

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