Quantum elasticity in Debye solids

The rigid behaviour of a crystal lattice submitted to sudden and localized events (such as emission, absorption and scattering of quanta and/or light particles) is currently treated in terms of the well known Debye-Waller expression. Starting from first principles, and referring to solids described according to the Debye model, we present here a rigorous and general expression of the fraction of recoilless events, of which the Debye-Waller form is shown to represent only a first approximation, holding in the case of very low temperature solids.