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

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.

Figure 1

The variation of the static structure factor with momentum exchange $Q$ for the modified Percus-Yevick model at various volume fractions.

Figure 2

The energy variation of the structure-modified momentum transfer cross section for the modified Percus-Yevick model for various volume fractions.

Figure 3

The energy variation of low-order, structure-modified, partial cross-section combinations for the modified Percus-Yevick model with a volume fraction $\Phi =0.4$.

Figure 4

Variation of the mean energy with reduced electric field for various volume fractions $\Phi$ for a dense gas of hard spheres.

Figure 5

Variation of the drift velocity with reduced electric field for various volume fractions $\Phi$ for a dense gas of hard spheres.

Figure 6

Variation of the charged-particle diffusion coefficients with reduced electric field for various volume fractions $\Phi$ for a dense gas of hard spheres (solid line is $n_0{D}_T$; dashed line is $n_0{D}_L$).

Figure 7

Variation of the charged-particle gradient energy parameter $\gamma$ with reduced electric field for various volume fractions $\Phi$ for a dense gas of hard spheres.

Figure 8

Accuracy of the two-term approximation for the various charged-particle transport properties for a dense gas of hard spheres with volume fraction $\Phi =0.4$.

Figure 9

The flux diffusion coefficients of positrons in liquid and dilute gaseous Ar at 85 K as a function of $E/n_0$.

Figure 10

The positronium formation rate and gradient energy parameter for positrons in liquid and dilute gaseous Ar at 85 K as a function of $E/n_0$.