= Thomson limit
<Thomson scattering> describes the low-recoil scattering of <electromagnetic radiation> by a free charge. For charge $q$ and <mass> $m$, the weak incident field gives peak <acceleration> $|q|E_0/m$. The mean <Larmor formula> <power> is therefore
$$
\langle P\rangle=\frac{q^4|E_0|^2}{12\pi\epsilon_0m^2c^3}.
$$
There is no binding force to introduce a characteristic <frequency>. Dividing by the same incident <light intensity> gives the <Thomson cross-section>:
$$
\boxed{\sigma_T=\frac{q^4}{6\pi\epsilon_0^2m^2c^4}
=\frac{8\pi}{3}\left(\frac{q^2}{4\pi\epsilon_0mc^2}\right)^2.}
$$
For an <Electron>, the length inside parentheses is the <classical electron radius>. The <cross section> has units $\mathrm m^2$ and is independent of <wavelength> in this classical limit. The driven <velocity> must remain small compared with $c$, and $\hbar\omega\ll mc^2$ must make <Compton recoil kinematics> negligible.
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