Decay of the positronium molecule into a positronium atom and photons

Decays of the positronium molecule Ps₂ into para- or orthopositronium Ps in the ground state and photons are investigated. The differential probabilities of the decays are determined. The total probabilitiesw _2γ ^(Ps2) andw _3γ ^(Ps2) of Ps₂ annihilation with the production of two and three photons and positronium are calculated to be $$w_{2gamma }^{(P_{S_2 } )} = 1.6 cdot 10^{10} sec ^{ - 1} ,w_{3gamma }^{(P_{S_2 } )} = 0.43 cdot 10^8 sec ^{ - 1} $$ . The curve of the angular correlation of the γ rays on the decay of Ps₂ into two photons and parapositronium is studied. The width of this curve is Δ¦P¦=0.128 a.u. (¦P¦ is the total photon momentum), which corresponds to a deviation of the emission angle of the γ rays from π: θ ? 0.934 mrad. The maximum in the distribution of the photons with respect to the momenta ¦P¦ in the center of mass of the annihilating pair is attained at ¦P¦=0.175 a.u. The calculations were made on an M-222 computer, and their accuracy is determined by the choice of the wave function of the positronium molecule and the accuracy in the computer calculation of the integrals.