A conduction electron in a metal is scattered by phonons through small-angle events

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Electronic transport in solids · Electronic transport in solids

Solid State Physics, Ch The Boltzmann equation and electrical transport

Problem

A conduction electron in a metal is scattered by phonons through small-angle events, each turning its wavevector through 3∘3^\circ. Estimate the ratio τtr/τc\tau_{\rm tr}/\tau_c between the transport time and the collision time for this scattering, where τc\tau_c is the mean time between any collision and τtr\tau_{\rm tr} is the time that enters the conductivity through 1/τtr=∑k′Wkk′(1−cos⁡θ)1/\tau_{\rm tr}=\sum_{\mathbf{k}'}W_{\mathbf{k}\mathbf{k}'}(1-\cos\theta).

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