Long transmission times for transport through a weakly scattering slab

We consider the theoretical problem of transmission of a pulse of particles through a transversely infinite slab of thickness L, in which they travel at speed v and are isotropically and elastically scattered with mean-free path length λ. In the case λ/L=∞ there is no scattering, the pulse is transmitted intact, and the transmission-time moments are simply 〈${\mathit{t}}_{\mathrm{trans}}^{\mathit{n}}$〉=(L/v${)}^{\mathit{n}}$. However, we find that in the weak-scattering limit λ/L→∞, the transmission-time probability density develops a long tail resulting in anomalous scaling of the moments. The relevance of these results to recent experiments is discussed.