  We determine the pair correlations of countable sets $T \subset \mathbb{R}^n$
satisfying natural equidistribution conditions. The pair correlations are
computed as the volume of a certain region in $\mathbb{R}^{2n}$, which can be
expressed in terms of the incomplete Beta function. For $n=2$ and $n=3$ we give
closed form expressions, and we obtain an expression in the $n \rightarrow
\infty$ limit. We also verify that sets of lattice points and primitive lattice
points satisfy the required distribution criteria.
