Theory of SolidHe3

Abstract

A theoretical analysis is given of the properties of solid ${\mathrm{He}}^3$ on the basis of: (1) a gas-phase Lennard-Jones "12-6" potential modified at small interatomic distances; (2) a Heitler-London type variational-trial wave function for all the atoms in the solid constructed from a properly antisymmetrized product of individual atom orbitals localized on the various lattice points; (3) a Dirac vector model to describe the symmetry energy with an exchange integral deduced from (1) and (2); (4) a spin-wave approximation at "low" temperatures and a Kramers-Opechowski approximation at "high" temperatures for calculation of the free energy of the nuclear spins; and (5) a Debye phonon model for the description of the vibrationally excited states of the solid. On this basis, calculated values at low pressures and temperatures ($p\approx 30$ atm; $T\lesssim 1°$K) are presented for: (a) the cohesive energy per atom; (b) the root mean square deviation of an atom from its lattice site: ≅0.36×nearest neighbor distance; (c) the nuclear magnetic susceptibility which corresponds to an antiferromagnetic behavior with a "paramagnetic" Curie temperature $T_C\cong 0.1°$K; (d) the variation (decrease) of $T_C$ with increasing pressure corresponding to a possible nuclear antiferromagnetic to nuclear ferromagnetic transition for $p\approx 150$ atm; (e) the specific heat which exhibits an anomaly at $T\approx 0.1°$K associated with the alignment of the nuclear spins; (f) the thermal expansion coefficient which becomes negative below about 0.6 °K; (g) the melting curve which is characterized by a minimum at $T\cong 0.37°$K and a maximum at $T\cong 0.08°$K. Comparison of the theory is made with available experimental data.