Positron–Electron Annihilation in Hydrogen–Antihydrogen Collisions

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The rate of direct positron–electron annihilation in cold hydrogen–antihydrogen collisions has been calculated and compared to the rate of proton–antiproton annihilation. We show that the lepton annihilation rate in H̄H collisions depends on the relative orientation of spins of the electron and positron. In the low-energy limit of hydrogen–antihydrogen scattering, the presence of leptonic annihilation introduces an absorptive, imaginary component to the hydrogen–antihydrogen scattering length; this component is β+=1.4×10−4a0 for the singlet state of the leptonic spins, and β=1.2×10−7a0 for the triplet state. Leptonic annihilation turns out to be about three orders of magnitude slower than proton–antiproton annihilation.

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