Three-body correlations in liquidHe4

Abstract

We report results of variational calculations of liquid $^{4}\mathrm{He}$ with wave functions containing optimized two-body and three-body correlations. The hypernetted-chain (HNC) summation method is used, and the elementary and Abe diagrams are calculated with the scaling approximation. Comparisons with the existing Monte Carlo calculations suggest that this HNC-scaling method is almost exact. The logarithm of the three-body correlation of ${f}_{\mathrm{ijk}}$ contains terms having ${P}_{l}({\stackrel{^}{r}}_{\mathrm{ij}}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{^}{r}}_{\mathrm{ik}})$, $l=0, 1, \mathrm{and} 2$. As expected on theoretical grounds, the $l=1$ term of $\mathrm{ln}{f}_{\mathrm{ijk}}$ dominates, while the $l=0 \mathrm{and} 2$ terms give rather small changes in the binding energy. The ${f}_{\mathrm{ijk}}$ makes up \ensuremath{\sim}85% of the difference between the Jastrow and presumably exact Green's-function Monte Carlo (GFMC) energies. The best variational energies obtained with the HFDHE2 potential of Aziz et al. are within (2 \ifmmode\pm\else\textpm\fi{} 1)% of the GFMC and experimental results. The liquid structure function $S(k)$ is also well explained by the variational wave function.