  This note concerns the problem of minimizing a certain family of non-local
energy functionals over measures on $\mathbb{R}^n$, subject to a mass
constraint, in a strong attraction limit. In these problems, the total energy
is an integral over pair interactions of attractive-repulsive type. The
interaction kernel is a sum of competing power law potentials with attractive
powers $\alpha \in (0, \infty)$ and repulsive powers associated with Riesz
potentials. The strong attraction limit $\alpha \to \infty$ is addressed via
Gamma-convergence, and minimizers of the limit are characterized in terms of an
isodiametric capacity problem. We also provide evidence for symmetry-breaking
in high dimensions.
