The role of positronium decoherence in positron annihilation in matter

A small difference between the energies of the para-positronium (p-Ps) and ortho-positronium (o-Ps) states suggests the possibility of the superposition of p-Ps and o-Ps during the formation of positronium (Ps) from pre-Ps, terminating its migration in the matter in a void. It is shown that such a superposition decoheres in the basis of p-Ps and o-Ps. The decoherence time scale estimated here motivates a correction in the precise analysis of the positron annihilation lifetime spectra. More generally, the superposited Ps state should contribute to the theory of the evolution of positronium in matter.