Positronium hyperfine interval

Mills Jr., A.P. (1983c). Line-shape effects in the measurement of the positronium hyperfine interval. Phys. Rev. A 27 262-267. 

Fig. 7.7. Schematic of the Yale experiment to measure the hyperfine interval of ground state positronium. On the left there is an overall view of the apparatus, whilst the right-hand figure shows the microwave cavity and gas cell in which the positronium is formed. 

In the case of the positronium spectrum the accuracy is on the MHz-level for most of the studied transitions (Is hyperfine splitting, Is — 2s interval, fine structure) [13] and the theory is slightly better than the experiment. The decay of positronium occurs as a result of the annihilation of the electron and the positron and its rate strongly depends on the properties of positronium as an atomic system and it also provides us with precise tests of bound state QED. Since the nuclear mass (of positronium) is the positron mass and me+ = me-, such tests with the positronium spectrum and decay rates allow one to check a specific sector of bound state QED which is not available with any other atomic systems. A few years ago the theoretical uncertainties were high with respect to the experimental ones, but after attempts of several groups [17,18,19,20] the theory became more accurate than the experiment. It seems that the challenge has been undertaken on the experimental side [13]. 

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. 

The energy level diagram of the n=l and n=2 states of positronium is shown in Fig. 1. By now the hyperfine structure interval (really of order fine structure) in the ground n=l state (or the S, to So interval), the fine structure intervals in the n=2 state, and the 1S-2S interval have been measured with high precision. 

Studies of the positronium atom have been previously limited to measurements of the ground state decay rates[8], and microwave studies of the n=l "hyperfine"[9,10] I Sq - interval, and a... 

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