Relaxation of Positron Momentum Distribution in Metals

Abstract

The time-dependent momentum distribution is calculated for positrons, initially of high energy, in contact with a low-temperature electron gas. A Boltzmann-equation approach is used; the positrons are taken to have an effective mass different from the electron mass, as is observed experimentally, and to interact with the electrons via the screened Coulomb interaction. High-momentum components of the distribution decay very quickly; therefore, the Boltzmann equation is solved numerically only for momenta in the thermal range. The distribution function is found to decay with time toward the Maxwell-Boltzmann distribution, while depleting through annihilation. Effective distribution functions, describing the average properties of the positrons throughout the relaxation-annihilation process, are computed for various ratios of lifetime to thermalization time. A prediction is made of the minimum positron energy observable in annihilation experiments.