Thermodynamic consideration of the positronium decay

Abstract

Electron-positron annihilation has mainly two decay channels. Firstly into two gamma-photons of equal energy forming a narrow line spectrum, and secondly into three gamma-photons forming a continuous energy spectrum. The ratio of decay events N 3 /N 2 is experimentally found with about 1:379 and depends only on the fine-structure constant a like N 3 /N 2 = 4(π 2 - 9)a/37r to the first QED expansion order. The given consideration tries to understand this ratio of decay events in a thermodynamic way and allows the computation of a theoretical ratio of 1:356 on the base of the Boltzmann distribution and the calculated temperatures of the 27-decay with k B T ≅ 1.04737·mc 2 and the 3γ-decay with k B T ≅ 1/8.0125·mc 2 . The radiation entropy produced at the 2γ-decay was calculated with 1.90975 k B and the radiation entropy of the 3γ-continuum with 5.9663 k B . The positronium system could be seen in some kind of conflict: Due to the smallness of a the construction of an additional third gamma-photon is improbable. On the other hand, much more entropy could be generated by three gamma quanta. This antagonism could be transformed into an understanding of the ratio of decay events and thus the actual value of the fine-structure constant. Due to entropy, this seems to be the optimal value for the positronium ecay-or, more general -the optimal value for the building probability of a photon. As entropy is an observable physical quantity, the calculated values should experimentally be measurable, so that the given calculations could experimentally be verified.