Anomalous transmission-time moments in the ballistic limit of isotropic scattering

The ballistic limit of isotropic elastic scattering in an infinite slab of thickness L is studied using rigorous lower bounds for the transmission-time distribution. In this model particles with velocity v enter the slab normal to its face. They then scatter isotropically with mean free path λ. In the ballistic limit, where λ/L→∞, the transmission-time distribution moments 〈${\mathit{t}}^{\mathit{n}}$〉 might be expected to converge to those of the input distribution, properly translated in time. It is shown, however, that all moments with n>2 diverge as ${\mathit{c}}_{\mathit{n}}$ ${\mathit{L}}^2$ ${\mathit{v}}^{\mathrm{-}\mathit{n}}$ ${\lambda }^{\mathit{n}\mathrm{-}2}$. Comparison between Monte Carlo simulations and rigorous, analytic lower bounds for the moments show excellent agreement in the ballistic limit. It is conjectured that the anomalous asymptotic behavior of the moments is completely due to trajectories involving at most two scattering events.