Ground State of SolidHe3

Abstract

A ground-state wave function for solid ${\mathrm{He}}^3$ in the body-centered cubic phase is calculated in the form of a product of single-particle orbitals and pair correlations. The correlation part is an eigenfunction of the Pluvinage Hamiltonian with each pair in a state of zero energy in a frame in which their center of mass is at rest. Assuming that exchange effects are small, we obtain an approximate single-particle probability function from this wave function. The many-body energy is obtained from this single-particle probability function from basic principles by a plausibility argument, and leads to a pressure-volume relation that is in good agreement with observation. Exchange effects arise from the original wave function, when suitably antisymmetrized. This predicts an exchange energy of about 0.005°K near the melting curve, in agreement with a recent experiment of Adams, Meyer, and Fairbank; this exchange energy favors antiferromagnetic alignment.