= Monovalent BCC direct optical threshold
{title2=$E_0/E_F=(G/k_F)^2-2G/k_F\simeq0.63763$}
For two electrons per conventional monovalent BCC cell, $k_F=(6\pi^2)^{1/3}/a$ lies inside the first zone. The shortest reciprocal vector is $G=2\sqrt2\pi/a$. The free folded-branch difference $\hbar^2(G^2-2Gk)/(2m_e)$ is smallest on the occupied Fermi-sphere point toward G, giving the displayed ratio. The destination has magnitude $G-k_F>k_F$ and is empty. A weak periodic potential supplies band mixing and optical matrix elements; its finite corrections and absorption peak shape are not fixed by this leading threshold.
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