The three photon yield from e+ annihilation in biological liquids

Positrons annihilate either by the emission of 2-511 keV photons or 3-photons (from the decay of positronium in the triplet state.) The fraction of the 3-photon decay depends on the chemical environment and notably on the concentration of O$_{2}$. Consequently, 3-photon event detection has been proposed as a mean to measure hypoxia, a condition prevailing in cancer.~ The (delayed) three-photon yield in various fluids, at both high and low O$_{2}$ levels, has been extracted by fitting the time dependence of the two-photon yield to a set of coupled differential equations. The differential equations, in a simple and satisfactory fashion account for the e+ capture to form positronium and the decay and interconversion of the two forms. The total fraction of three photon events (both direct and delayed), which could be used for event-by-event position localization in PET-like imaging, is estimated to be $\sim $ 0.5 {\%} with the measured (from our work) delayed component of no more than 0.25{\%} in water (or blood-like) samples. There is no (or an exceedingly small) dependence on the dissolved oxygen content in aqueous solutions.