Helium Lamb shift

Theoretical calculation of the fLe+ Lamb shift is straightforward with all the formulae given above. It is only necessary to recall that all contributions scale with the power of Z, and the terms with high power of Z are enhanced in comparison with the hydrogen case. Theoretical uncertainty is estimated by scaling with Z the uncertainty of the hydrogen formulae. After calculation we obtain Lth(2S — 2P,He ) = 14 041.46 (3) MHz. We see that the theoretical and experimental results for the classic Lamb shift in helium differ by about two standard deviations of the experimental result. Clearly, further reduction of the experimental error is desirable, and the reason for this mild discrepancy should be clarified. 

Schwartz, C. (1961a). Lamb shift in the helium atom. Phys. Rev. 123 1700-1705. 

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... 

A number of data are available for Is and 2s hfs intervals in hydrogen, deuterium and the helium-3 ion. The potential of this difference for the hfs intervals in the helium-3 ion [21] with respect to testing bound state QED is compatible with the ground state hfs in muonium both values are sensitive to fourth-order perturbative contributions. The difference of the Lamb shift plays an important role in the evaluation of optical data on the hydrogen and deuterium spectrum [22]-... 

The latter presents the largest sources of uncertainty in the theory of the muo-nium hfs interval, positronium energy spectrum and the specific nuclear-structure-independent difference for the hfs in the helium ion. The former are crucially important for the theory of the Lamb shift in hydrogen and medium-Z ions, for the difference in Eq. (2) applied to the Lamb shift and hyperfine structure in hydrogen and helium ion, and for the bound electron (/-factor. In the case of high-Z, the Lamb shift, (/-factor and hyperfine structure require an exact treatment of the two-loop correction. 

Abstract. We report progress towards making a precise measurement of the 2S Lamb shift in singly-ionised helium by spectroscopy of the 2S-3S transition. The motivation for the experiment is discussed with reference to recent developments in the theory of quantum electrodynamics (QED) and a description of the apparatus and techniques used is given. 

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. 

Our target is to develop a theory for the Lamb shift and the fine structure in these two atomic systems. Eventually we need to determine the 2s — 2pi/2 splitting in the helium ion (for comparison with the experiment [6]), difference of the Lamb shifts ER(2s) — ER(3s) in 4He+ (for the project [7]) and the 2p3/2 — 2s interval in hydrogen-like nitrogen. The difference mentioned is necessary [12,1] if one needs to compare the results of the Lamb shift (n = 2) measurement [6] and the 2s — 3s experiment. 

Table 5. Different contributions to the Lamb shift in hydrogen-like helium 4He ( MHz)...

The uncertainty of theoretical calculations including the estimation of missing or uncalculated terms has been receiving increasing scrutiny as techniques have advanced. One of the most recent two-electron Lamb shift calculations by Persson et al. [9] estimates missing correlation effects in QED contributions at 0.1 eV for all elements or 20 ppm of transition energies in medium Z ions. In earlier work, Drake [4] claimed uncertainty for Z = 23 was < 0.005 eV or 1 ppm of helium-like resonance lines due to uncalculated higher order terms. Some of the latest theoretical calculations for the w transition in medium Z ions are summarized in Table 3. 

Laser Spectroscopy of Hydrogen-Like and Helium-Like Ions Table 1. Lamb shift in mid- hydrogen-like ions... 

QED can be considered to be one of the most precisely tested theories in physics at present. It provides an extremely accurate description of systems such as hydrogen and helium atoms, as well as for bound-leptonic systems, for example, positronium and muonium. Remarkable agreement between theory and experiment has been achieved with respect to the determination of the hyperfine structure and the Lamb shift. The same holds true for the electronic and muonic g-factors. The free-electron g-factor is determined at present as... 

Still the agreement was not satisfactory. We also noted that some QED corrections could be of the same order of magnitude as the relativistic corrections. Lamb shift for one electron in a helium-like atom with a nuclear charge Z can be expressed as ... 

The history of the spectrum of atomic hydrogen—with which we include that of ionized helium and other one-electron atoms—is therefore closely linked wdth the history of the quantum theory. The study of the spectrum at the present time rests upon half a century of detailed experimental and theoretical work which illustrates in a remarkable way the interdependence of theory and experiment in physics. Interest in the contemporary work is enhanced when it is seen in its historical context. The following chapters will give an outline of the successive theories, the experimental findings which they could interpret, and the points of detail at which they proved deficient. The work on the Lamb shift itself, and related topics, will be described in considerably greater detail. 

Fig. 8. Fine structure of the He+ line 4686 A, showing calculated Lamb shifts. Beneath is a photometer tracing of the structure resolved by Series [122]. The line marked (L) is a band line duo to molecular helium. Lines marked ( ) are false Hues which arise with the use of double interferometers, and which may readily be moved, to different places within the pattern.

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