Coulomb Interactions in an Atomic Dielectric

The Coulomb interaction between two impurity charges is evaluated for an atomic dielectric. The point-dipole model is used to describe the model dielectric. The interaction potential between the two impurity charges may be expressed as an asympotic series in $\frac{1}{R}$, where $R$ is the separation of the two charges. We derive a method for systematically evaluating the coefficients of this series, and explicitly calculate all terms up to and including those for $\frac{1}{R^3}$ for the monatomic cubic lattices. The leading term is $\frac{1}{\epsilon R}$.