= Saha baryon-abundance normalization
{c}
{title2=$\eta_\gamma=(s/n_\gamma)\eta_s$}
For a hydrogen-only gas with $g_e=g_p=2$, $g_H=4$ and $m_H\simeq m_p$, the <Saha equation> is $(1-X_e)/X_e^2=n_B[2\pi/(m_eT)]^{3/2}e^{I/T}$. Defining $\eta_\gamma=n_B/n_\gamma$ and using $n_\gamma=2\zeta(3)T^3/\pi^2$ gives coefficient $2\zeta(3)\eta_\gamma/\pi^2$ multiplying $(2\pi T/m_e)^{3/2}e^{I/T}$. If instead $\eta_s=n_B/s$, with <entropy density> $s=(2\pi^2/45)g_{*s}T^3$, that coefficient is $(2\pi^2/45)g_{*s}\eta_s$. The two expressions agree because $s/n_\gamma=\pi^4g_{*s}/[45\zeta(3)]$. The reference entropy sector must be specified, especially after particles have decoupled.
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