A theory is presented of the diffractive scattering of a light atom by a semi-infinite crystal in which the atoms are executing thermal vibrations about their equilibrium positions. The intensities of the diffracted beams can be expressed in terms of the average of the scattered wave function over the canonical ensemble defined by the vibrational Hamiltonian of the crystal (this is not true for the inelastic component of the scattered intensity). With the aid of projection operators we obtain the integral equation satisfied by the averaged atomic wave function. The effective potential entering this equation is nonlocal in space and time, complex, and temperature dependent. The change in intensity of each diffracted beam due to scattering out of the beam by the thermal vibrations of the atoms constituting the crystal is related to this effective potential.

• Received 14 May 1984

DOI:https://doi.org/10.1103/PhysRevB.31.825