Resumen
We study a model of supersolids or quantum crystals introduced in (Josserand et al 2007 Phys. Rev. Lett. 98 195301, Josserand et al 2007 Eur. Phys. J. S. T. 146 47–61), following recent experiments in helium 4. This model is based on a Gross–Pitaevskii energy with a nonlocal interaction term. We give a description of the ground state in the limit of strong interaction, and relate it to a sphere packing problem. We also study the effect of rotation. In dimension one, we prove that the ground state has a periodic structure.