Positronium precision

In some applications (e.g. precision laser spectroscopy, see section 7.1) it is the speed distribution of the positronium which deserves consideration. Owing to its small mass, the temperature usually required for... 

Note that, as can be seen from the discussion in subsection 1.2.1, the contributions from the higher order annihilation modes are negligible at the present levels of precision. Thus, the rate for the annihilation of ortho-positronium into five gamma-rays is only 10-6 of that for three gamma-rays, with a similar value for the ratio of the rates for para-positronium annihilation into four and two gamma-rays. 

Fig. 7.1. Schematic illustration of the positronium formation chamber and detector arrangement used by Westbrook et al. (1987, 1989). Reprinted from Physical Review A40, Westbrook et al., Precision measurement of the ortho-positronium vacuum decay rate using the gas technique, 5489-5499, copyright 1989 by the American Physical Society.

Fig. 7.4. Extrapolations of the measured ortho-positronium decay rates in A /V and S/V (see text). Reprinted from Physical Review Letters 65, Nico el at, Precision measurement of the ortho-positronium decay rate using the vacuum technique, 1344-1347, copyright 1990 by the American Physical Society.

Fig. 7.5. Plot of the measured A(p), as defined by equation (7.7), in N2-isobutane mixtures. Data were taken at magnetic fields of 0.375 T (x) and 0.425 T (o). Reprinted from Physical Review Letters 72, Al-Ramadhan and Gidley, New precision measurement of the decay rate of singlet positronium, 1632-1635, copyright 1994 by the American Physical Society.

Al-Ramadhan, A.H. and Gidley, D.W. (1994). New precision measurement of the decay rate of singlet positronium. Phys. Rev. Lett. 72 1632-1635. 

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. 

Hughes, V.W. (1998). High precision spectroscopy of positronium and muonium. Adv. Quant. Chem. 30 99-123. 

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]. 

We will review here experimental tests of quantum electrodynamics (QED) and relativistic bound-state formalism in the positron-electron (e+,e ) system, positronium (Ps). Ps is an attractive atom for such tests because it is purely leptonic (i.e. without the complicating effects of nuclear structure as in normal atoms), and because the e and e+ are antiparticles, and thus the unique effects of annihilation (decay into photons) on the real and imaginary (related to decay) energy levels of Ps can be tested to high precision. In addition, positronium constitutes an equal-mass, two-body system in which recoil effects are very important. 

The ubiquitous problem encountered in all positronium decay rate measurements to date is isolating the positronium from the formation medium in order to determine the vacuum decay rate. In both gas and powder experiments the interactions (Ps quenching and Ps polarization) with these media need to be accounted for. This can involve extrapolations of A to zero density in the formation medium, as in the Michigan experiment, and/or spectroscopic corrections for 2q decays as in the Tokyo experiment. At Michigan we decided a decade ago to abandon powder media in future precision experiments because we could... 

Systematic improvements in the measurement of the 23S i — l3Laser cooled Ps would permit a measurement of the 1S — 2S transition to reach a precision significantly better than the 1.3 MHz natural linewidth . 

Spectroscopy of positronium provides a sensitive test of the bound state theory in Quantum Electrodynamics (QED). Because of the small value of the electron mass, the effects of strong interactions are negligible compared to the accuracy achieved in present experiments. For this reason positronium represents a unique system which can, in principle, be described with very high accuracy by means of QED only. Tests of QED predictions are made possible thanks to a high precision of positronium spectroscopic measurements. 

There are several quantities in positronium physics where higher order radiative corrections have to be taken into account for the theoretical prediction to match the experimental precision. For the hyperfine splitting of the ground state, Av = E(13Si) — Eil1 So), the two best experimental values are [5,6]... 

A different type of precisely measured quantities are the decay properties of the positronium atoms, e.g. total decay widths of both ortho (S = 1) and para (S = 0) positronium ground states into three and two photons, respectively. The orthopositronium decay width is a controversial issue because the theoretical prediction differs significantly from the most precise experimental result [8]. The... 

Here we intend to summarize several calculations on precision positronium physics which we have recently completed. We will describe the calculation of recoil corrections to positronium nS energy levels and the hyperfine splitting at 0(ma6), (D(ma7 In2 a) corrections to positronium energy levels and second order corrections to parapositronium lifetime. Additional details of those projects can be found in the original papers [1,2,3,4]. For the summary of the experimental situation, we refer to Ref. [11]. 

The electron and positron in positronium move with a typical velocity a and have a momentum mot and energy mo . If we are interested in a precision level where relativistic effects become important, the usual quantum mechanical treatment of the bound state has to be merged with the complete field theory description. Then, no matter how weak the coupling is, we deal with the problem of bound states in the field theory, which is rather complicated. One of the possible computational approaches (not always the most convenient) is the Bethe-Salpeter equation. 

The purely leptonic hydrogen atom, muonium, consists of a positive muon and an electron. It is the ideal atom, free of the nuclear structure effects of H, D and T and also of the difficult, reduced mass corrections of positronium. An American-Japanese group has observed the 1S-2S transition in muonium to a precision somewhat better than a part in 107. [10] Because there were very few atoms available, the statistical errors precluded an accurate measurement. The "ultimate" value of this system is very great, being limited by the natural width of the 1S-2S line of 72 kHz, set by the 2.2 nsec lifetime of the muon. 

This article will outline the experimental techniques we have used in the laser spectroscopy of these atoms and briefly indicate current plans for the refinement of these measurements. As Fig. 1 shows, the laser spectroscopy of positronium and muonium is not competitive with comparable measurements in hydrogen, largely due to the low density sources of these atoms. In the case of positronium, the first measurements were done at peak densities of a few atoms/cm3 during a laser pulse. The muonium work was limited by atom densities 10 2 atom/cm3 per laser pulse. As feeble as these sources might seem to spectroscopisis of less exotic atoms, one must remember that these instantaneous densities represent many orders of magnitude improvement of above pre-existing sources of thermal positronium and muonium. Clearly, improved sources will lead to more precise measurements. 

The rate of positronium formation has been increased by 2-3 orders of magnitude using recently developed accelerator based slow positron sources. This opens the possibility of improvements of precision experiments on the Ps atom as well as new experiments on excited states First evidence for enhanced metastable Ps formation is presented and future possibilities are discussed. 

Thirty-six years after the first production of positronium by Deutsch it seems somewhat surprising that our experimental knowledge of this system is restricted to the states of principal quantum numbers n=l and n=2. Table I summarizes the present most precise data. 

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