Blackbody-peak photon pair-production estimate ($E_{2,\mathrm{th}}=(m_e{c}^2{)}^2/E_1$)

Two head-on photons can create an electron-positron pair at the limiting product $E_1{E}_2=(m_e{c}^2{)}^2$. A target at the peak of the frequency-density blackbody spectrum has $E_1=2.82144k_{B}T$, whereas the wavelength-density peak corresponds to $E_1=4.96511k_{B}T$. At $T=3\mathrm{K}$ these conventions give incident thresholds approximately $3.58\times 10^{14}\mathrm{eV}$ and $2.03\times 10^{14}\mathrm{eV}$ 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.