 Monovalent BCC direct optical threshold

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 $G=2\sqrt{2}\pi /a$. The free folded-branch difference ${\hslash }^2(G^2-2Gk)/(2m_e)$ 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.