= Small baryon abundance delays hydrogen recombination
{title2=$B/T\simeq\log[\eta^{-1}(m_e/T)^{3/2}]$}
For <hydrogen ionization fraction> $X_e$ of order one, the <hydrogen-only Saha equation> gives $1\sim n_b(2\pi/(m_eT))^{3/2}e^{B/T}$. The <baryon-to-photon ratio> and <photon number density> imply $n_b\sim\eta T^3$. Therefore $1\sim\eta(T/m_e)^{3/2}e^{B/T}$ and the displayed logarithmic balance follows. A small $\eta$ supplies many ionizing <photons> per <baryon>, so neutral <hydrogen> forms at a <temperature> much smaller than its <Hydrogen binding energy>. The numerical temperature depends on the ionization-fraction convention and on whether equilibrium remains valid.
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