  We consider the binding energy of a two-body system with a repulsive Coulomb
interaction in a finite periodic volume. We define the finite-volume Coulomb
potential as the usual Coulomb potential, except that the distance is defined
as the shortest separation between the two bodies in the periodic volume. We
investigate this problem in one and three-dimensional periodic boxes and derive
the asymptotic behavior of the volume dependence for bound states with zero
angular momentum in terms of Whittaker functions. We benchmark our results
against numerical calculations and show how the method can be used to extract
asymptotic normalization coefficients for charged-particle bound states. The
results we derive here have immediate applications for calculations of atomic
nuclei in finite periodic volumes for the case where the leading finite-volume
correction is associated with two charged clusters.
