The interaction Hamiltonian describing coherent neutron capture and neutron removal from nuclei in a lattice is presented. The explicit development of the interaction Hamiltonian leads to a new nonlinear phonon operator that enforces the physical constraint that the center-of-mass coordinates for the initial- and final-state nuclei must coincide to within fermis in order for a transfer to occur. An immediate application of the model to the Mossbauer limit of neutron capture shows increased phonon coupling relative to predictions from Lamb's theory.