We present the analysis of three-body correlations in the fluid and solid phases of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The results are from exact (Green’s-function Monte Carlo) and variational calculations of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ described by the Lennard-Jones two-body potential. A set of angular order parameters derived from the three-body distribution function are defined and we find that certain of these parameters change significantly at the onset of freezing to a quantum solid. We then trace the evolution of the parameters from the quantum solid regime, near melting, to an approximately harmonic solid at high density. We have also computed the angular order parameters for two different kinds of variational functions: the traditional Jastrow function and a function which includes triplet correlations. The parameters computed from the Jastrow function show clear differences from the exact results. The variational function with triplet correlations, however, closely resembles the exact results in both the fluid and solid phases. In this respect it is clearly superior to the Jastrow function.

• Received 3 December 1986

DOI:https://doi.org/10.1103/PhysRevB.35.4719