The overlap of the positron component of the wave function of positronium (Ps) in dense molecular substances with the lattice wave function determines the $2\gamma$ annihilation rate of positrons bound in orthopositronium via electron pickup from the lattice (${\tau }_2$ decay), and in part the $2\gamma$ 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 ${\tau }_2$ decay on lattice parameters is derived. This dependence was tested experimentally by ${\tau }_2$ 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.

An anomalous behavior is found for the ice-water transition, where ${\tau }_2$ increases significantly despite the contraction of water between the melting point and 4°C.

• Received 16 March 1960

DOI:https://doi.org/10.1103/PhysRev.120.1289