Ground-State Energy of SolidHe3

The ground-state energy of solid ${\mathrm{He}}^3$ is computed using a cluster expansion terminated in third order. A 6-9 potential is used that gives a better fit to virial data than the 6-12 Lennard-Jones potential does. A substantial improvement in energy for a particle localization corresponding to the crystal is obtained, although the crystal is not stable against further particle delocalization. Thus, for this potential, the interaction is too weak to give a stable crystal structure. Some simplifying features of the cluster expansion are also demonstrated.