Multiterm solution of a generalized Boltzmann kinetic equation for electron and positron transport in structured and soft condensed matter

Abstract

In this paper, we generalize the semiclassical Boltzmann kinetic equation for dilute gases to consider highly nonequilibrium electrons and positrons in soft condensed matter, accounting rigorously for all types of interactions, including positronium formation, and allowing for both coherent and incoherent scattering processes. The limitations inherent in the seminal paper of Cohen and Lekner [ M. H. Cohen and J. Lekner Phys. Rev. 158 305 (1967); Y. Sakai J. Phys. D 40 R441 (2007)] are avoided by solving the kinetic equation using a "multiterm" spherical harmonic representation of the velocity distribution function, as well as formulating a necessarily nonperturbative treatment of nonconservative collisional processes such as positronium formation. Numerical calculations of transport properties are carried out for a Percus-Yevick model of a hard-sphere system, and for positrons in liquid argon. New phenomena are predicted, including structure-induced negative conductivity and anisotropic diffusion.