Positronium reduced mass

Positronium, reduced mass, 109 Postulates, quantum mechanics, 51-52 Propanol, infrared spectroscopy, 222-223... 

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. 

Positronium (e+e ) is a purely leptonic system, free of nuclear structure effects, but suffers from reduced corrections in the worst possible case of equal masses. This makes the system difficult to treat, since quantum electrodynamical calculations start from an infinite nuclear mass and treat reduced mass effects as a perturbation. 

Positronium still presents rather formidable theoretical challenges [39], since it is a relativistic two-body system which cannot be approximated by the motion of a particle of reduced mass in a fixed Coulomb potential. In addition, QED calculations must include annihilation terms. First laser measurements of the 1S-2S two-photon transition frequency in positronium [40] give a result about five standard deviation lower than the theoretical predictions, after taking a recalibration of the tellurium reference line into account [41]. On the other hand, as yet uncalculated higher order terms could well account for this discrepancy. 

Another interesting example involves the reduced mass of positronium, a shortlived combination of an electron and a positron—the electron s antiparticle. The electron and positron mutually annihilate with a half-life of approximately 10 sec, and positronium most frequently decays into two gamma rays (see Fig. 7.12). The reduced mass of positronium is... 

The Schrodinger equation gives only the stationary states (the ground state and the excited ones), which live forever. It cannot describe, therefore, the annihilation process, but it is able to describe the positronium before the annihilation takes place. This equation for the positronium is identical to that for the hydrogen atom, except that the reduced mass changes from /i 1 a.u. to /T = 2 a.u. ( = Y + Y = 2). As a result (see the definition of oq on p. 202), one may say that the size of the orbitals of the positronium doubles when compared to that of the... 

The muonium system resembles more closely the structure of hydrogen than does positronium the reduced mass is not substantially changed... 

Reducing the degrees of freedom of the only nucleus is fruitful in the case of a heavy nucleus. In the positronium atom the nucleus has the same mass as the electron and it is useful to treat both particles symmetrically. It is well known that the a4m terms originate not only from relativistic effects, but also from annihilation contributions and the Fermi interaction. Due to that, the most useful approximation is a non-relativistic one and the final single-body equation is an effective Schrodinger equation with Coulomb interaction. This approach, based on an effective equation, was also developed for the few-body problem in nucleus physics. 

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