= Photon mean free path in an ionized universe
{title2=$\ell_\gamma=(n_e\sigma_T)^{-1},\quad t_{\mathrm{sc}}=\ell_\gamma/c$}
For a dilute ionized plasma with nonrelativistic <electrons> and photon energies well below $m_ec^2$, independent <Thomson scattering> events give photon survival probability $\exp(-n_e\sigma_Ts)$ over proper distance $s$. Its mean gives the displayed <mean free path>. The scattering rate is $\Gamma_\gamma=n_e\sigma_Tc$. Photons are tightly coupled when this rate greatly exceeds the <Hubble parameter>; <photon decoupling> becomes possible as the free-electron fraction falls. Frequent elastic scattering does not by itself imply chemical equilibration of the photon number.
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