A quantum theory of heavy-particle channeling is used to make predictions of channeling effects for a realistic model of a vibrating crystal. The quantum theory requires the total wave function for a screened-Coulomb potential, which is developed using an eikonal method. The shapes of predicted back-scattering dips are shown to depend on two-body effects due to blocking of Fresnel diffraction peaks, and thus to depend sensitively on spatial correlations between the vibrating lattice atoms; corresponding classical calculations contain no analogous effect. Using a Debye model, calculations are compared with data on back scattering of 300 keV protons in silicon, with limited success. Proposals are made for similar experiments in which the effects of correlations should be considerably enhanced.