Virial expansion of a quantum particle in a classical gas: Application to the orthopositronium decay rate

Experiments measuring the decay of positrons and orthopositronium in gases show a complicated dependence of the annihilation rate on the gas density. Theoretical and experimental studies indicate that the nonlinear dependence of the decay rate on gas density is the result of local alterations in the gas density surrounding the decaying particle. In this paper the virial expansion of the decay rate of both free positrons and positronium atoms in powers of the gas density is developed. The temperature-dependent coefficients in the density expansion of the decay rate are expressed in terms of modified cluster integrals that are determined by the interaction of the free positron or positronium atom with the host gas. Explicit expressions are given for the decay rate through terms of order [Formula Presented] in the gas density. The term linear in the gas density is investigated analytically for the specific case of a hard-sphere interaction and its relevance to the decay of orthopositronium is demonstrated. Both the low- and high-temperature limits of the decay rate are determined analytically and the lack of temperature dependence observed in most experimental measurements of the decay rate at low density is explained. Finally, the results of path-integral Monte Carlo calculations for the decay rate over a wide temperature range are presented.