Solution
= Solution
For <elastic scattering>, \b[$E_f=E_i$] and \b[$\mathbf k_f-\mathbf k_i=\mathbf G$], where $\mathbf G$ is a <reciprocal lattice vector>. In the ideal static crystal, coherent scattering obeys this lattice selection rule; the crystal as a whole can take the mechanical recoil with negligible <energy>. <crystal momentum> is defined modulo $\hbar\mathbf G$, not as unconstrained free-particle <momentum>.