Helium fine structure

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. 

Although the proper point of departure for relativistic atomic structure calculations is quantum electrodynamics (QED), very few atomic structure calculations have been carried out entirely within the QED framework. Indeed, almost all relativistic calculations of the structure of many-electron atoms are based on some variant of the Hamiltonian introduced a half century ago by Brown and Ravenhall [1] to understand the helium fine structure. By decoupling the electron and radiation fields in QED to order a (the fine-structure constant) using a contact transformation. Brown and Ravenhall obtained a relativistic momentum-space Hamiltonian in which the electron-electron Coulomb interaction was surrounded by positive-energy projection operators. Owing to the fact that contributions from virtual electron-positron pairs are automatically projected out of... 

The need for testing QED is illustrated by the inconsistencies currently observed in the atomic helium fine structure between experiments and theories. Obtaining predictions that match experiments is also useful for helium fine structure measurements to contribute to the determination of the fine structure constant a (recent work in this domain is presented in Ref. [8]). Many experiments have recently been performed on the helium fine structure by Gabrielse in Harvard [9], ... 

T. Zelevinsky, D. Farkas, G. Gabrielse, Precision measurement of the three 2 Pj helium fine structure intervals, Phys. Rev Lett. 95 (20) (2005) 203001. 

G. Drake, Progress in helium fine-structure calculations and the fine-structure constant. Can. J. Phys. 80 (11) (2002) 1195-1212. 

K. Pachucki, J. Sapirstein, Higher-order recoil corrections to helium fine structure, /. Phys. B At. Mol. Opt. Phys. 36 (2003) 803-809. 

Turner and coworkers [7] applied the photoelectric effect to gases. By using the sharp UV line from a helium resonance they could even resolve vibrational fine structure of the electron levels. The subject is outside the scope of the present book we refer to excellent books on the subject [7, 8]. 

Fine structure. Evidently the set of term values is exactly the same as on the usual theory but the quantum numbers are different, making new transitions possible and changing the intensities of the fine structure. The hydrogen fine structiure is so obscured by the natural breadth of the lines that no information can be obtained from it, and we must turn to the spectrum of ionized helium. For Paschen s data the reader is referred to Sommerfeld, figures 89-92. The only measurements of value for the... 

The splitting of triplet terms of helium is unusual in two respects. First, multiplets may be inverted and, second, the splittings of the multiplet components do not obey the splitting rule of Equation (7.20). For this reason we shall discuss fine structure due to spin orbit coupling in the context of the alkaline earth atomic spectra where multiplets are usually normal and... 

The fine structure of a 3P — S transition of an alkaline earth metal is illustrated in Figure 7.10(a). The A J selection rule (Equation 7.22) results in a simple triplet. (The very small separation of 23P1 and 23P2 in helium accounts for the early description of the low-resolution spectrum of triplet helium as consisting of doublets .)... 

A comparison between theory and experiment for the fine structure intervals in helium holds the promise of providing a measurement of the fine structure constant a that would provide a significant test of other methods such as the ac Josephson effect the and quantum Hall effect. The latter two differ by 15 parts in 108 and are not in good agreement with each other [59]. 

Table 9. Comparison of theory and experiment for the fine structure splittings of helium 2 3Pj. Units are MHz...

The results for the fine structure measurements in N5+, F7+ and Mg10+ are summarized in table 4. In fig. 11 they are compared with theory and other precision measurements Z < 12. The scaling factor Z(Z — l)5a7mec2 is the order of the spin-dependent part of the one-electron self-energy [88]. As the figure shows, the sensitivity of the recent measurements to QED corrections of this order, matches or exceeds that of the high precision measurements in helium. 

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. 

At present, five experimental measurements for the 23P splittings are available all but the first [6] are from groups still active and working at helium FS measurements [4,7,8,9,10,11]. Although these experiments use different approaches to measure the fine structure, ranging from microwave spectroscopy in the 23P levels [6,9,10] to frequency difference of the 23,S —> 23P optical transitions [4,7,8,11], helium spectroscopy at 1083 nm is always present (see Fig. 1). A detailed description of all related experiments is out of the scope of this paper, and we will confine the discussion to our measurement [4], and briefly, to other measurements to compare with it. 

P. Cancio et al. Fine structure constant a and precision laser spectroscopy of Helium . In Recent advances in Metrology and Fundamental constants, Proceedings of the International School of Physics Enrico Fermi , ed. By S. Leschiutta, T.J. Quinn (SIF, Bologna) in press... 

Numerical results (in kHz) for hydrogen and deuterium atoms and the helium-3 ion are collected in Table 2. One can see that the new corrections essentially shift the theoretical predictions. A comparison of the QED predictions (in kHz) against the experiments is summarized in Table 1. We take the values of the fundamental constants (like e. g. the fine structure constant a) from the recent adjustment (see Ref. [25]). 

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