Effect of an Electric Field on Positronium Formation in Gases: Theoretical

Abstract

A theory is developed to explain the influence of an electric field on positronium formation in gases. The Boltzmann equation is used to describe the behavior of the positrons under the combined influence of the electric field and molecular collisions. A diffusion equation in velocity space is deduced wherein the annihilation of free positrons and the disappearance of positrons by positronium formation are absorption terms. From this equation the functional dependence of the increase in positronium formation on the experimental parameters is calculated. The result describes correctly the experimental observations and yields information on the pertinent atomic processes. In particular, the cross sections for the elastic scattering of positrons by helium, neon, and argon are found to be $0.023\pi {a_0}^2$, $0.12\pi {a_0}^2$, and $1.5\pi {a_0}^2$, respectively, to about ±25%. These values are considerably smaller than the corresponding quantities for electrons, and are in agreement with simple theoretical estimates.