 Thomson limit

ID: past-exam-of-the-optics-and-electrodynamics-course-of-the-university-of-cambridge/2019/section-b/b5/thomson-limit

q

and mass

m

, the weak incident field gives peak acceleration

∣ q ∣ E_{0} / m

⟨ P ⟩ = \frac{q ^{4} ∣ E _{0} ∣ ^{2}}{12 π ϵ _{0} m ^{2} c ^{3}} .

There is no binding force to introduce a characteristic frequency. Dividing by the same incident light intensity gives the Thomson cross-section:

σ_{T} = \frac{q ^{4}}{6 π ϵ _{0}^{2} m ^{2} c ^{4}} = \frac{8 π}{3} (\frac{q ^{2}}{4 π ϵ _{0} m c ^{2}})^{2} .

For an Electron, the length inside parentheses is the classical electron radius. The cross section has units

m^{2}

and is independent of wavelength in this classical limit. The driven velocity must remain small compared with

c

, and

ℏ ω ≪ m c^{2}

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