= Blackbody-peak photon pair-production estimate
{title2=$E_{2,\rm th}=(m_ec^2)^2/E_1$}
Two head-on <photons> can create an electron-positron pair at the limiting product $E_1E_2=(m_ec^2)^2$. A target at the peak of the frequency-density <blackbody spectrum> has $E_1=2.82144k_BT$, whereas the wavelength-density peak corresponds to $E_1=4.96511k_BT$. At $T=3\,\mathrm K$ these conventions give incident thresholds approximately $3.58\times10^{14}\,\mathrm{eV}$ and $2.03\times10^{14}\,\mathrm{eV}$ respectively. A real blackbody has a continuum of target energies and angles, so an absorption calculation integrates the spectrum and cross section rather than imposing a sharp peak-photon opacity boundary.
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