Solution
= Solution
The eight body-centred cubic neighbour vectors are $(a/\sqrt3)(\pm1,\pm1,\pm1)$ with independent signs. Their diagonal sums are $8a^2/3$ and the sign-paired off-diagonal sums cancel. Hence
$$
\boxed{\boldsymbol\sigma_{\rm bcc}=\frac83Ka^2 I=\frac43\frac{nQ^2Fa^2}{k_BT}I}.
$$
The conventional cubic cell edge is $2a/\sqrt3$ in this comparison; using that edge as the hopping distance would spoil the stipulated equal-distance comparison.