Positronium Decay in Molecular Substances

The overlap of the positron component of the wave function of positronium (Ps) in dense molecular substances with the lattice wave function determines the $2\ensuremath{\gamma}$ annihilation rate of positrons bound in orthopositronium via electron pickup from the lattice (${\ensuremath{\tau}}_{2}$ decay), and in part the $2\ensuremath{\gamma}$ angular correlation. Ps acts as a probe for the dependence of one-particle wave functions in lattices on structural lattice parameters, and of radical-molecule interactions on atomic lattice parameters. To explore the sensitivity of this probe Ps wave functions are calculated for different lattice structures in the Wigner-Seitz approximation, and the dependence of ${\ensuremath{\tau}}_{2}$ decay on lattice parameters is derived. This dependence was tested experimentally by ${\ensuremath{\tau}}_{2}$ measurements on carefully characterized molecular substances in different physical states. It is confirmed that the temperature and state dependence is primarily a "free volume" effect in the sense that the overlap between the Ps and lattice wave functions decreases with increasing lattice spacing. The effects of a spherical confinement on the self-annihilation rates and stability of Ps are shown to be small for radii relevant to molecular lattices.