  We incorporate the effect of lattice thermal vibrations into the Glauber
theory description of particle- and nucleus-crystal Coulomb interactions at
high-energy. The allowance for the lattice thermal vibrations is shown to
produce strong absorption effect: the phase shift function of the
multiple-diffraction scattering on a chain of $N$ identical atoms acquires
large imaginary part and the radius of the absorption region in the impact
parameter plane grows logarithmically with $N$. Consequences of this
observation for the elastic and quasi-elastic Coulomb scattering are discussed.
Practically interesting example of the coherent Coulomb excitation of
ultra-relativistic particles and nuclei passing through the crystal is
considered in detail.
