Four-Particle Exchange in SolidHe3

We report calculations which suggest that there is a physically important four-atom exchange process in bcc ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and thus an important four-spin term in the exchange Hamiltonian. A simple, mean-field analysis of this Hamiltonian appears to account for a number of the perplexing properties of bcc ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. An understanding of other properties may require treatment of the exact four-spin term. It is our hope to stimulate such effort by this Letter.