Virial expansion of the positron and positronium decay rate in a dilute gas: The linear contribution

A systematic theory of the lifetimes of positrons or positronium atoms in a low-density gas is lacking. This paper describes our recent efforts to fill this void. In analogy with the virial expansion for the pressure of a gas, we develop a quantum virial expansion for the properties of a low-mass particle thermalized in a dilute gas. The discrete Feynman path integral is employed to numerically evaluate the quantum traces that comprise the coefficients of each power of the density. By considering two applications of the linear contribution, positron and ortho-positronium decay in xenon, we show how the temperature dependence of the decay rate depends on the interaction between the light particle and an atom. We also explain the observed lack of temperature dependence in experimental measurements of the orthopositronium pick-off decay rate observed in most gases.