Ground state of solid He(3)

Commander, Civil Engineer Corps, U.S.N., participant in the Advanced Science Curriculum, sponsored by the Bureau of Naval Personnel, Office of Naval Research, and U.S. Naval Postgraduate SchoolA ground-state wave function for solid 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.Supported in part by the United States Air Force through the Air Force Office of Scientific Researc