Momentum transfer to atoms bound in a crystal

A complete self-contained calculation is given for the relation between the momentum and energy transferred to the lattice in processes involving the recoil of a single atom (e.g. emission, absorption, or scattering of photons or neutrons). The calculation, using Ott's theorems, is exact and leads to Lamb's original results for a harmonic crystal in thermal equilibrium. Detailed proofs of Ott's relevant theorems are given. The height of the Mössbauer peak is calculated, showing small deviations from the Debye-Waller factor usually used.