Correlation functions for simple hopping in a face-centered-cubic lattice

The correlation functions for a single specific particle and for a pair of specific particles are calculated for an ensemble of particles making nearest-neighbor simple jumps in a fcc lattice. The correlation functions are used to obtain diffusion coefficients and NMR relaxation times due to $I-S$ (unlike spin) and $I-I$ (like spin) dipolar interactions for various concentrations of particles. Our results are compared to previous theories and to experimental results on $\mathrm{Pd}{\mathrm{H}}_x$.