Effect of cascade gamma-radiation summation processes on the precision of calculating the probability of three-photon annihilation of positronium

The processes of cascade gamma-quanta summation, disregarded when measuring the energy spectrum of 22Na in samples by a one-detector spectrometer, are studied, along with the effect of these processes on the change in the area bounded by the 511-keV annihilation line in the calculation of the probability P3γ of three-photon annihilation of positronium. An increase in the number of annihilation quanta in “positronium-forming” samples and their redistribution to the low-energy spectral region are responsible for the difference between the areas of the photopeak of the accompanying nuclear quantum, with respect to which the spectra are normalized, and of the corresponding peak in the aluminum standard. The departure of the real value of P3γ from its value, determined without taking into account the summation processes on a highly effective scintillation NaI(T1) detector and a semiconducting Ge detector, amounts to 56 and 25%, respectively, for a distance of 3 cm between the positronium source and the detector surface.