Vol 2 - Landau, Lifshitz - The classical theory of fields (4th, 1994) (1) · Problem 9.10

Radiation of Electromagnetic Waves

Physics — Landau & Lifshitz · radiation-scattering

Problem

When electromagnetic radiation falls on a free electron (Thompson scattering), the electron is accelerated by the electric field of the wave and re-radiates. (a) Show that the time-averaged power scattered is ⟨P⟩=μ02q4E0212πm2c.\langle P \rangle = \frac{\mu_0^2 q^4 E_0^2}{12 \pi m^2 c}. (b) The scattering cross-section is defined as σ≡⟨P⟩/⟨S⟩incident\sigma \equiv \langle P \rangle / \langle S \rangle_{\text{incident}}. Show that σ=μ02q46πm2c2=8π3re2,\sigma = \frac{\mu_0^2 q^4}{6\pi m^2 c^2} = \frac{8\pi}{3} r_e^2, where re≡μ0q2/(4πmc2)r_e \equiv \mu_0 q^2 / (4\pi m c^2) is the classical electron radius.

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