Positronium fine structure

Egan, P.O., Hughes, V.W. and Yam, M.H. (1977). Precision determination of the fine-structure interval in the ground state of positronium. IV. Measurement of positronium fine-structure density shifts in noble gases. Phys. Rev. A 15 251-260. 

In principle, positronium can be observed through the emission of its characteristic spectral lines, which should be similar to hydrogen s except that the wavelengths of all corresponding lines are doubled. Positronium is also the ideal system in which the calculations of quantum electrodynamics can be compared with experimental results. Measurement of the fine-structure splitting of the positronium ground state has served as an important confirmation of the theory of quantum electrodynamics. 

In Chapter 1, the first order contributions to the annihilation rates from the dominant modes of decay of the S-states of both ortho- and para-positronium (for arbitrary principal quantum number nPs) were given as equations (1.5) and (1.6). These contributions are included in the following equations for the rates for the two ground states, which also contain terms of higher order in the fine structure constant, a ... 

Deutsch. M. and Dulit, E. (1951). Short range interaction of electrons and fine structure of positronium. Phys. Rev. 84 601-602. 

Hatamian, S., Conti, R.S. and Rich, A. (1987). Measurements of the 23Si-23Pj (J = 0,1,2) fine-structure splittings in positronium. Phys. Rev. Lett. 58 1833-1836. 

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 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. 

Figure 6 Positron target chamber and microwave cavity for measuring fine structure interval in the n=2 state of positronium. G, grid T, copper target M, mirror W, window K, CsTe photocathode of the uv photon detector A, antennae Nal(TI), annihilation y -ray detector.

Spectroscopy of Positronium and Muonium Table Ilb. Experimental values of Lamb shift and fine structure. 

A further term, which has no analogue in hydrogen, arises in the fine structure of positronium. This comes from the possibility of virtual annihilation and re-creation of the electron-positron pair. A virtual process is one in which energy is not conserved. Real annihilation limits the lifetimes of the bound states and broadens the energy levels (section 12.6). Virtual annihilation and re-creation shift the levels. It is essentially a quantum-electrodynamic interaction. The energy operator for the double process of annihilation and re-creation is different from zero only if the particles coincide, and have their spins parallel. There exists, therefore, in the triplet states, a term proportional to y 2(0). It is important only in 3S1 states, and is of the same order of magnitude as the Fermi spin-spin interaction. Humbach [65] has given an interpretation of this annihi-... 

The range of nuclei of interest in the types of studies mentioned above is extensive. Correspondingly, the range of spectroscopy is also rather broad. One has at the long wavelength end to deal with fine structure and hyperfine structure in, e.g., positronium and muonium. Also optical spectroscopy is possible for positronium, especially the recently demonstrated Doppler-free two photon absorption Is -> 2s [32], These spectral regions have been already mentioned above along with their problems in scale normalization. 

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