Hyperfeine Positronium-Linien am Hamburger DESY - kann es so kleine Photonen geben ?

09/03/2013 - 17:17 von D Orbital | Report spam
Die Ordnung ist Alpha hoch 7.

Wer von euch weiß noch, was Alpha ist ?

Positronium, which is an electromagnetic bound state of the electron e− and the
positron e+, is the lightest known atom. Thanks to the smallness of the electron mass
me, strong- and weak-interaction effects are negligible, and its properties can be calculated
perturbatively in quantum electrodynamics (QED), as an expansion in Sommerfeld’s finestructure
constant α, with very high precision, only limited by the complexity of the
calculations. Positronium is thus a unique laboratory for testing the QED theory of weakly
bound systems. However, the theoretical analysis is complicated due to annihilation and
recoil effects.
The positronium hyperfine splitting (HFS) ν = E (13S1)−E (11S0), where E (11S0)
and E (13S1) are the energy levels of para- and orthopositronium, respectively, is the most
precisely measured quantity in positronium spectroscopy as far as the absolute precision
is concerned.

The nonlogarithmic O(α6) term includes the contribution due to the radiative correction
to the Breit potential [7], the three-, two- and one-photon annihilation contributions [8],
the non-annihilation radiative recoil contribution [9], and the pure recoil correction computed
numerically in Ref. [10] and analytically in Ref. [11]. In O(α7), only the leading
double-logarithmic α7 ln2(1/α) term is available [12].
Including all the terms known so far, we have
νth = 203.392 01GHz, (4)
which exceeds Eqs. (1) and (2) by approximately 2.8 and 3.9 experimental standard
deviations, respectively. In contrast to the well known orthopositronium lifetime puzzle,1
the experimental situation for the HFS is unambiguous. In fact, the experimental error
1For the most recent developments of this problem, see, for example, Ref. [13] and the references cited
is compatible with a naive estimate of the theoretical uncertainty due to as-yet unknown
higher-order corrections. Should this discrepancy persist after the dominant terms of the
latter have been calculated, this would provide a signal for new physics. This makes the
HFS to be one of the most interesting topics in positronium spectroscopy, both from the
experimental and theoretical points of view.
Thus, it is an urgent matter to improve the prediction of the HFS as much as possible,
and one is faced with the task of analyzing the third-order correction, which is extremely
difficult. However, there is a special subclass of the O(α7) contributions which can be
analyzed separately, namely those which are enhanced by powers of ln(1/α)  5. They
may reasonably be expected to provide an essential part of the full O(α7) contributions.
This may be substantiated by considering Eq. (3) in O(α6), where the logarithmic term
is approximately 2.6 times larger than the nonlogarithmic one. While the leading doublelogarithmic
O(α7) contribution to Eq. (3) is known [12], the subleading single-logarithmic
one is yet to be found. In fact, from the positronium lifetime calculation [13,14,15] we
know that the subleading terms can be as important as the leading ones. The purpose of
this Letter is complete our knowledge of the logarithmically

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#1 Volker Meyer
09/03/2013 - 23:25 | Warnen spam
D Orbital wrote:


So what? Hyperfeine Strukturen ergeben grosse und nicht kleine Photonen. Frequenzmàssig scharfe Photonen sind ortsmàssig sehr ausgedehnt. Siehe auch: Unschàrferelation.

Grüsse, Volker Meyer

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