Diffusion blocking in a frozen rigid-sphere fluid

The diffusion and localization of a classical particle of diameter ${\sigma }_0$ in an environment of fixed spherical scatterers of diameter ${\sigma }_1$ in arbitrary dimensionality is considered by extending the self-consistent current relaxation theory for the Lorentz gas of a point particle and overlapping spheres. The variation of the diffusion coefficient with scatterer density $n$ and diameter ratio $\delta =\frac{{\sigma }_0}{{\sigma }_1}$ is calculated analytically. Different factorization schemes are examined and compared. The overlapping $\delta =\infty$ and nonoverlapping $\delta =0\mathrm{}$ Lorentz gas are discussed briefly as special cases. The critical density $n_c\left(\delta \right)$ in the ($n$,$\delta$) phase diagram separating diffusive from localized behavior is established and good agreement with Monte Carlo results for the percolation density of hard-core disks is obtained.